The page declares the new functionalities of the 3.1 version of the TFEL project.

The TFEL project is a collaborative development of CEA and EDF dedicated to material knowledge manangement with special focus on mechanical behaviours. It provides a set of libraries (including TFEL/Math and TFEL/Material) and several executables, in particular MFront and MTest.

TFEL is available on a wide variety of operating systems and compilers.

# 1 Highlights

The MFront gallery is meant to present well-written implementation of behaviours that will be updated to follow MFront latest evolutions. In each case, the integration algorithm is fully described.

The MFrontGallery project is a cmake project which builds material libraries for all the codes and/or languages supported by MFront based on the implementation described in the gallery. The purpose of this project is twofold:

• it delivers ready-to-use shared libraries for a wide variety of phenomena.
• it provides an example of how to build a compilation project for MFront files, including lots of useful cmake macros, recipes to build shared libraries and add tests.

The MFrontGallery project is available as a github repository: https://github.com/thelfer/MFrontGallery

### 1.1.1 Hyperelastic behaviours

The implementation of various hyperelastic behaviours can be found here:

### 1.1.2 Hyperviscoelastic behaviours

The following page describes how to implement standard hyperviscoelastic behaviours based on the development in Prony series:

http://tfel.sourceforge.net/hyperviscoelasticity.html

### 1.1.4 Viscoplasticity

This following article shows how to implement an isotropic viscoplastic behaviour combining isotropic hardening and multiple kinematic hardenings following an Armstrong-Frederic evolution of the back stress:

http://tfel.sourceforge.net/isotropicplasticityamstrongfrederickinematichardening.html

## 1.2 Support for additional yield criteria

The TFEL/Material provides functions to handle advanced yield criteria, such as:

• the Hosford yield criterion (see Hosford (1972)). The associated functions are described in Paragraph  2.4.1.
• the Barlat yield criterion (see Barlat et al. (2005)). The associated functions are described in Paragraph  2.4.2.

Following Scherzinger (see Scherzinger (2017) for details), special care has been taken to avoid overflow in the evaluation of the yield stress.

Those two yield criteria are based on the eigenvalues and of the stress. The computation of the second derivative, required to build the jacobian of the implicit system, is thus quite involved.

## 1.3 Enhanced numerical reproducibility and stability

This release has seen lot of work in the overall numerical reproducibility and stability of TFEL algorithms and lead to duplicate most of tests, who are now run using different rounding modes.

Tests based on mtest are run $$5$$ times, one for each of the four rounding modes defined in the IEEE754 norm, plus one time using a specific mode which randomly switches between those modes at various stages of the computations.

Although very crude with respect to advanced approaches such as the CADNA library (see (Lamotte, Chesneaux, and Jézéquel 2010,Université Pierre et Marie Curie (2017))) or the verrou software, developped by EDF on top of valgrind (see Févotte and Lathuilière (2016)), those checks, combined with demanding convergence criteria, have proven to be helpful and led to several developments: see for example the section  2.3.1.2 which compares various algorithms to find the eigen vectors of symmetric tensors.

Note

Old versions of the libm library (such as the one package with Debian Wheezy and those found on some exotic systems, such as Haiku), do not support working in other rounding mode than the default one (rounding to the nearest) and can crash (segfaults !).

Disabling changing the rounding mode on those systems can be specified by passing -DTFEL_BROKEN_LIB_MATH=ON to cmake.

### 1.3.1 Enabling the -ffast-math with GCC an clang

One side effect of the work on the enhanced numerical stability is that the -ffast-math flag of GCC and clang can now be enabled more safely. This significantly improve the performances of the generated code by allowing optimizations that do not preserve strict IEEE compliance. For instance, the overall tests delivered with TFEL runs almost $$10\,\%$$ faster with this option enabled.

Most of those optimizations are used by default by the Intel compiler.

There are two potential issues with this flags:

• due to the lack of the strict IEEE compliance, the resulting code can be less portable. This can also lead to less accurate and more unstable code. In TFEL/MFront, it has been seen that the algorithm used to compute the eigenvalues and the eigenvectors of symmetric tensors can be affected. New algorithms, more stable but less efficient, have been introduce, as discussed below.
• under GCC, various mathematical functions of the standard library behaves in an unexpected manner and can not be trusted. For example, the isnan function returns true, even if its argument is NaN. This issue has been overcome by implementing proper versions of the fpclassify, isnan, isfinite functions, as described below in paragraph  2.3.3.

To build TFEL with the -ffast-math, just pass the -Denable-fast-math=ON option to cmake.

Note

Even if TFEL is not built with the -ffast-math, this option can be used to compile MFront files, by specifying the --obuild=level2 option to MFront, as follows:

mfront --obuild=level2 --interface=.... ## 1.4 Single crystal behaviours in MFront Support for writting single crystal behaviours have been greatly improved thanks to the TFELNUMODIS library, which borrows code for the NUMODIS project. The following new keywords are now available in MFront: • @CrystalStructure. The following crystal structures are supported: • Cubic: cubic structure. • BCC: body centered cubic structure. • FCC: face centered cubic structure. • HCP: hexagonal closed-packed structures. • A single slip systems family can be defined by one of the following synonymous keywords: @SlidingSystem, @GlidingSystem or @SlipSystem. Several slip systems families ca be defined by @SlidingSystems, @GlidingSystems or @SlipSystems. • Two kinds of interaction matrix are supported: • The first interaction is defined through the @InteractionMatrix keyword and is meant to describe the effect of dislocations on hardening. • The second interaction is defined through the @DislocationsMeanFreePathInteractionMatrix keyword and is meant to evaluate the effect of all the dislocations on the mean free path of dislocations of a specific system. Those keywords are fully documented on this page. As most of the information relative to the slip system and the interaction matrix are automatically generated, the use of the mfront-query tool is strongly advised. ## 1.5 The DDIF2 brick DDIF2 is the name of a description of damage which formulation is inspired by softening plasticity. This description is the basis of most mechanical behaviour used in CEA’ fuel performance. The DDIF2 brick can be used in place of the StandardElasticity brick. Internally, the DDIF2 brick is derived from the StandardElasticity brick, so the definition of the elastic properties follows the same rules. ### 1.5.1 Local coordinate This description is currently limited to initially isotropic behaviours, but the damage is described in three orthogonal directions. Those directions are currently fixed with respect to the global system. For $$2D$$ and $$3D$$ modelling hypotheses, those directions are determined by a material property, which external name is AngularCoordinate, giving the angular coordinate in a cylindrical system. ### 1.5.2 Material properties associated with damage The description of damage is based on the following material properties: • the fracture stresses in each direction. Two options can be used to described them: • if the fracture_stress option is used, the fracture stresses are equal in each directions. • otherwise, the fracture_stresses keyword can be used to describe the fracture stresses in each of the three directions. • the softening slopes stresses in each direction. Two options can be used to described them: • if the softening_slope option is used, the softening slopes are equal in each directions. • otherwise, the softening_slopes keyword can be used to describe the softening slopes in each of the three directions. In each case, a material property must be given as a value or as an external MFront file. #### 1.5.2.1 Fracture energies Following Hillerborg approach (see Hillerborg, Modéer, and Perterson (1976)), softening slopes can be related to fracture energies by the mesh size. Thus, rather than the softening slopes, the user can provide the fracture energies through one the fracture_energy or fracture_energies options. In this case, an array of three material properties, which external name is ElementSize, is automatically declared. ### 1.5.3 External pressure effect The effect of external pressure on the crack surface can be taken into account using the option handle_pressure_on_crack_surface. If this option is true, an external state variable called pr, which external name is PressureOnCrackSurface, is automatically declared. ### 1.5.4 Example Here is an example of a behaviour based on the DDIF2 brick: @DSL Implicit; @Author Thomas Helfer; @Date 25/10/2017; @Behaviour DDIF2_4; @Brick DDIF2 { fracture_stresses : {150e6,150e6,1e11}, softening_slope : -75e9, handle_pressure_on_crack_surface : true }; Here, the fracture stresses are different in each direction. The softening slope is the same in each direction. When a crack is open, the external pressure is applied on the crack surface. ## 1.6 The @StrainMeasure keyword In previous versions of TFEL, the user would write strain based behaviour. The definition of the strain, and by energetic duality the definition of the stress, were not part of the behaviour. This is very important for a generic behaviour, which describe a physical phenomenon with no reference to a particular material, but it is not appropriate for a specific behaviour, identified for a specific material, because the definition of the strain is intrinsically part of the behaviour. Three strain measure are currently supported: • the Hencky strain (see Miehe, Apel, and Lambrecht (2002)). • the Green-Lagrange strain. • the linearised strain. The two first strain measures are suitable for use in finite strain analyses (including finite rotation), whereas the latter is limited to infinitesimal strain analyses (no rotation, small strain). For the two first strain measures, the definition of the strain is done at a pre-processing stage, before calling the behaviour integration. The interpretation of the dual stress and its conversion to the stress measure expected by the solver is done after the behaviour integration, at a post-processing stage. During this post-processing stage, the consistent tangent operator is also converted to the one expected by the solver. Those pre- and post-processing stages can be performed: • by the calling solver (Code_Aster, ZeBuLoN). In this case, the consistent use of the behaviour was the responsability of the user. • by the MFront interface (Cast3M, Europlexus, CalculiX, etc.). In this case, one has to use one following keywords: • @CastemFiniteStrainStrategy or @CastemFiniteStrainStrategies for the Cast3M interface. For backward compatibility, those keywords are synonymous of @UmatFiniteStrainStrategy or @UmatFiniteStrainStrategies. • @EuroplexusFiniteStrainStrategy (or @EPXFiniteStrainStrategy) for the Europlexus interface. • @AbaqusFiniteStrainStrategy for the Abaqus/Standard and Abaqus/Explicit interfaces. • etc. For a given behaviour, one may had to use several of those keywords for every interface supported. This was cumbersome. Each case was quite error-prone and could lead to an improper usage of the behaviour. To circumvent this issue, the @StrainMeasure keyword was introduced. This keyword has two distinct effect, depending on the interface: • if the pre- and post-processing stages are performed by the solver (Code_Aster), appropriate symbols are defined in the shared library, so that the calling solver can deduce the appropriate strain measure to be used. • otherwise, the the pre- and post-processing stages are handled by the interface. ## 1.7 Improved installation options ### 1.7.1 Appending the version number The TFEL_APPEND_VERSION option will append the version number to the names of: • The executables. • The libraries. • The python modules. Note that, to comply with python restriction on module’ names, the characters . and - are replace by _ and that only the first level modules are affected. • The directories in the share folder. This allows multiple executables to be installed in the same directory. This option is available since TFEL version $$3.0.2$$ ### 1.7.2 Specifying a version flavour The TFEL_VERSION_FLAVOUR let the user define a string that will be used to modify the names of executables, libraries and so on (see the previous paragraph for details). For example, using -DTFEL_VERSION_FLAVOUR=dbg at the cmake invocation, will generate an executable called mfront-dbg. This option can be combined with the TFEL_APPEND_VERSION option. ## 1.8 Better support of the Windows operating system There are various ways of getting TFEL and MFront working on the the Windows operating system: • One may use the Visual Studio IDE and compilers suite. This is the de facto standard on the Windows OS. This is also the compiler used by the Salome platform. An installation guide for Visual Studio is available here. • One may use the MINGW, which is a native Windows port of the GNU Compiler Collection (GCC). This port can be used in the MSYS) environment. The Windows port of the Cast3M finite element solver is built on the MINGW. An installation guide for TFEL/MFront with Cast3M 2017 is available [here][http://tfel.sourceforge.net/install-windows-Cast3M2017.html). In the MSYS environment, the compilation and installation steps are similar to those in Linux. More details can be found here. • One may compile TFEL/MFront under Cygwin, which provides a large collection of GNU and Open Source tools which provide functionality similar to a Linux distribution on Windows and a substantial POSIX API functionality. Various ports of the CalculiX finite element solver is built upon Cygwin • One may compile TFEL/MFront using one of the Linux distribution available with the Windows Subsystem for LinuX. This is not officially supported yet, but has been successfully tested by various contributors. ### 1.8.1Visual Studio support Support of the Visual Studio has been greatly improved. TFEL versions 3.0.x could be compiled and tested with Visual Studio 2015 and later, but the resulting executables were not really usable by an end user. Indeed, those versions of mfront could not generate a build system compatible with Visual Studio. For this reason, the cmake generator, described below in section 3.1, has been introduced. ## 1.9 New interfaces Two new interfaces were introduced in MFront: • a native interface for the CalculiX solver. Here native is used to distinguish this interface from the Abaqus/Standard interface which can also be used within CalculiX. This interface can be used with CalculiX 2.13. • an interface for the ANSYS APDL solver. The latter is still experimental. ## 1.10Travis CI and Appveyor continous integration services As an open-source project available on (github](https://github.com/thelfer/tfel), one have free access to the Travis CI and Appveyor continous integration services: • Travis CI allows us to build TFEL/MFront on various combinations compilers (gcc and clang) and operating systems (Ubuntu and Mac Os). • Appveyor allows us to build TFEL/MFront with Visual Studio 2017. Since builds are limited a one hour, one can only test a subset of the TFEL/MFront functionalities. # 2 Updates in TFEL libraries The TFEL project provides several libraries. This paragraph is about updates made in those libraries. ## 2.1 TFEL/Utilities ### 2.1.1 String algorithms #### 2.1.1.1 The starts_with string algorithm The starts_with string algorithm is an helper function used to determine if a given string starts with another. #### 2.1.1.2 The ends_with string algorithm The ends_with string algorithm is an helper function used to determine if a given string ends with another. ## 2.2 TFEL/System #### 2.2.0.1 The LibraryInformation class This release introduces the LibraryInformation class that allow querying a library about exported symbols. Note This class has been adapted from the boost/dll library version 1.63 and has been originally written by Antony Polukhin, Renato Tegon Forti and Antony Polukhin. #### 2.2.0.2 Improvements to the ExternalLibraryManager class ##### 2.2.0.2.1 Completion of libraries names If a library is not found, the ExternalLibraryManager class will try the following combinaisons: • Append lib in front of the library name (except for Microsoft Windows platforms). • Append lib in front of the library name and the standard library suffix at the end (except for Microsoft Windows platforms). • Append the standard library suffix at the end of the library name. The standard library suffix is: • .dll for Microsoft Windows platforms. • .dylib for Apple MacOs plateforms. • .so on all other supported systems. ##### 2.2.0.2.2 Retrieving the path of a library The getLibraryPath method returns the path to a shared library: • The method calls the GetModuleFileNameA function on Windows which is reliable. • On Unix, no portable way exists, so the method simply looks if the library can be loaded. If so, the method looks if the file exists locally or in a directory listed in the LD_LIBRARY_PATH variable. ##### 2.2.0.2.3 Better handling of behaviour parameters The ExternalLibraryManager class has several new methods for better handling of behaviours’ parameters: • The getUMATParametersNames returns the list of parameters. • The getUMATParametersTypes returns a list of integers which gives the type of the associated paramater: The integer values returned have the following meaning: • 0: floatting point value • 1: integer value • 2: unsigned short value • The getRealParameterDefaultValue, getIntegerParameterDefaultValue, and getUnsignedShortParameterDefaultValue methods allow retrieving the default value of a parameter. #### 2.2.0.3 Retrieving bounds values The ExternalLibraryManager class has several new methods for better handling of a behaviour’ variable bounds: • The hasBounds,hasLowerBound and hasUpperBound allow querying about the existence of bounds for a given variable. • The getLowerBound method returns the lower bound a variable, if defined. • The getUpperBound method returns the upper bound a variable, if defined. #### 2.2.0.4 Retrieving physical bounds values The ExternalLibraryManager class has several new methods for better handling of a behaviour’ variable bounds: • The hasPhysicalBounds,hasLowerPhysicalBound and hasUpperPhysicalBound allow querying about the existence of bounds for a given variable. • The getLowerPhysicalBound method returns the physical lower bound a variable, if defined. • The getUpperPhysicalBound method returns the physical upper bound a variable, if defined. ##### 2.2.0.4.1 Retrieving all mfront generated entry points and associated information The getEntryPoints method returns a list containing all mfront generated entry points. Those can be functions or classes depending on the interface’s needs. The getMaterialKnowledgeType allows retrieving the material knowledge type associated with and entry point. The returned value has the following meaning: • 0: Material property. • 1: Behaviour. • 2: Model. The getInterface method allows retrieving the interface of used to generate an entry point. The value returned is defined by MFront following Table 1. Table 1: MFront interface name associated to finite element solvers Finite element solver MFront interface name Cast3M Castem Code_Aster Aster Cyrano Cyrano Europlexus Europlexus Abaqus/Standard Abaqus Abaqus/Explicit AbaqusExplicit Ansys APDL Ansys CalculiX CalculiX The following code retrieves all the behaviours generated with the aster interface in the libAsterBehaviour.so library: auto ab = std::vector<std::string>{}; const auto l = "AsterBehaviour"; auto& elm = ExternalLibraryManager::getExternalLibraryManager(); for(const auto& e : elm.getEntryPoints(l)){ if((elm.getMaterialKnowledgeType(l,e)==1u)&&(elm.getInterface(l,e)=="Aster")){ ab.push_back(e); } } Note that we did not mention the prefix and the suffix of the library. The library path is searched through the getLibraryPath method. The equivalent python code is the following: ab = [] l = 'AsterBehaviour'; elm = ExternalLibraryManager.getExternalLibraryManager(); for e in elm.getEntryPoints(l): if ((elm.getMaterialKnowledgeType(l,e)==1) and (elm.getInterface(l,e)=='Aster')): ab.append(e) The getMaterial method allows retrieving the material to which an entry point is associated. If no material is defined, this method returns an empty string. ### 2.2.1 Improvements the ThreadPool class The ThreadPool class is used to handle a pool of threads that are given tasks. This class now has a wait method which blocks the main thread up to tasks completion. std::atomic<int> res(0); auto task = [&res](const int i){ // update the res variable return [&res,i]{ res+=i; }; }; // create a pool of two threads tfel::system::ThreadPool p(2); // Create two tasks that can be executed // using one or two threads. p.addTask(task(-1)); p.addTask(task(2)); // Waiting for the tasks to end p.wait(); // At this point, res is equal to 1. // The 2 threads in the pool are *not* joined // and are waiting for new tasks. ## 2.3 TFEL/Math ### 2.3.1 Symmetric tensor eigen values and eigen vectors The computation of the eigen values and eigen vectors of a symmetric tensor has been improved in various ways: • Various overloaded versions of the computeEigenValues, computeEigenVectors and computeEigenTensors methods have been introduced for more readable usage and compatibility with structured bindings construct introduced in C++17: the results of the computations are returned by value. There is also a new optional parameter allowing to sort the eigen values. • New eigen solvers have been introduced. #### 2.3.1.1 New overloaded versions of the computeEigenValues, computeEigenVectors and computeEigenTensors methods ##### 2.3.1.1.1 Return by value Various overloaded versions of the computeEigenValues, computeEigenVectors and computeEigenTensors methods have been introduced for more readable usage and compatibility with structured bindings construct introduced in C++17: the results of the computations are returned by value. For example: tmatrix<3u,3u,real> m2; tvector<3u,real> vp2; std::tie(vp,m)=s.computeEigenVectors(); Thanks to C++17 structured bindings construct, the previous code will be equivalent to this much shorter and more readable code: auto [vp,m] = s.computeEigenVectors(); Even better, we could write: const auto [vp,m] = s.computeEigenVectors(); ##### 2.3.1.1.2 Eigen values sorting The computeEigenValues and computeEigenVectors methods now have an optional argument which specify if we want the eigen values to be sorted. Three options are available: • ASCENDING: the eigen values are sorted from the lowest to the greatest. • DESCENDING: the eigen values are sorted from the greatest to the lowest. • UNSORTED: the eigen values are not sorted. Here is how to use it: tmatrix<3u,3u,real> m2; tvector<3u,real> vp2; std::tie(vp,m)=s.computeEigenVectors(Stensor::ASCENDING); #### 2.3.1.2 New eigen solvers The default eigen solver for symmetric tensors used in TFEL is based on analitical computations of the eigen values and eigen vectors. Such computations are more efficient but less accurate than the iterative Jacobi algorithm (see (Kopp 2008, 2017)). With the courtesy of Joachim Kopp, we have created a C++11 compliant version of his routines that we gathered in header-only library called FSES (Fast Symmetric Eigen Solver). This library is included with TFEL and provides the following algorithms: • Jacobi • QL with implicit shifts • Cuppen • Analytical • Hybrid • Householder reduction We have also introduced the Jacobi implementation of the Geometric Tools library (see (Eberly 2016, 2017)). Those algorithms are available in 3D. For 2D symmetric tensors, we fall back to some default algorithm as described below. Table 2: List of available eigen solvers. Name Algorithm in 3D Algorithm in 2D TFELEIGENSOLVER Analytical (TFEL) Analytical (TFEL) FSESJACOBIEIGENSOLVER Jacobi Analytical (FSES) FSESQLEIGENSOLVER QL with implicit shifts Analytical (FSES) FSESCUPPENEIGENSOLVER Cuppen’s Divide & Conquer Analytical (FSES) FSESANALYTICALEIGENSOLVER Analytical Analytical (FSES) FSESHYBRIDEIGENSOLVER Hybrid Analytical (FSES) GTESYMMETRICQREIGENSOLVER Symmetric QR Analytical (TFEL) The various eigen solvers available are enumerated in Table 2. The eigen solver is passed as a template argument of the computeEigenValues or the computeEigenVectors methods as illustrated in the code below: tmatrix<3u,3u,real> m2; tvector<3u,real> vp2; std::tie(vp,m)=s.computeEigenVectors<stensor::GTESYMMETRICQREIGENSOLVER>(); Table 3: Test on $$10^{6}$$ random symmetric tensors in single precision (float). Algorithm Failure ratio $$\Delta_{\infty}$$ Times (ns) Time ratio TFELEIGENSOLVER 0.000642 3.29e-05 250174564 1 GTESYMMETRICQREIGENSOLVER 0 1.10e-06 359854550 1.44 FSESJACOBIEIGENSOLVER 0 5.62e-07 473263841 1.89 FSESQLEIGENSOLVER 0.000397 1.69e-06 259080052 1.04 FSESCUPPENEIGENSOLVER 0.019469 3.49e-06 274547371 1.10 FSESHYBRIDEIGENSOLVER 0.076451 5.56e-03 126689850 0.51 FSESANALYTICALEIGENSOLVER 0.108877 1.58e-01 127236908 0.51 Table 4: Test on $$10^{6}$$ random symmetric tensors in double precision (double). Algorithm Failure ratio $$\Delta_{\infty}$$ Times (ns) Time ratio TFELEIGENSOLVER 0.000632 7.75e-14 252663338 1 GTESYMMETRICQREIGENSOLVER 0 2.06e-15 525845499 2.08 FSESJACOBIEIGENSOLVER 0 1.05e-15 489507133 1.94 FSESQLEIGENSOLVER 0.000422 3.30e-15 367599140 1.45 FSESCUPPENEIGENSOLVER 0.020174 5.79e-15 374190684 1.48 FSESHYBRIDEIGENSOLVER 0.090065 3.53e-10 154911762 0.61 FSESANALYTICALEIGENSOLVER 0.110399 1.09e-09 157613994 0.62 Table 5: Test on $$10^{6}$$ random symmetric tensors in extended precision (long double). Algorithm Failure ratio $$\Delta_{\infty}$$ Times (ns) Time ratio TFELEIGENSOLVER 0.000575 2.06e-17 428333721 1 GTESYMMETRICQREIGENSOLVER 0 1.00e-18 814990447 1.90 FSESJACOBIEIGENSOLVER 0 5.11e-19 748476926 1.75 FSESQLEIGENSOLVER 0.00045 1.83e-18 548604588 1.28 FSESCUPPENEIGENSOLVER 0.009134 3.23e-18 734707748 1.71 FSESHYBRIDEIGENSOLVER 0.99959 4.01e-10 272701749 0.64 FSESANALYTICALEIGENSOLVER 0.999669 1.36e-11 315243286 0.74 #### 2.3.1.3 Some benchmarks We have compared the available algorithm on $$10^{6}$$ random symmetric tensors whose components are in $$[-1:1]$$. For a given symmetric tensor, we consider that the computation of the eigenvalues and eigenvectors failed if: $\Delta_{\infty}=\max_{i\in[1,2,3]}\left\|\underline{s}\,\cdot\,\vec{v}_{i}-\lambda_{i}\,\vec{v}_{i}\right\|>10\,\varepsilon$ where $$\varepsilon$$ is the accuracy of the floatting point considered. The results of those tests are reported on Tables 3, 4 and 5: • The standard eigen solver available in previous versions of TFEL offers a very interesting compromise between accuracy and numerical efficiency. • If very accurate results are required, the FSESJACOBIEIGENSOLVER eigen solver is a good choice. ### 2.3.2 Isotropic functions and Isotropic function derivatives of symmetric tensors Given a scalar valuated function $$f$$, one can define an associated isotropic function for symmetric tensors as: $f\left(\underline{s}\right)=\sum_{i=1}^{3}f\left(\lambda_{i}\right)\underline{n}_{i}$ where $$\left.\lambda_{i}\right|_{i\in[1,2,3]}$$ are the eigen values of the symmetric tensor $$\underline{s}$$ and $$\left.\underline{n}_{i}\right|_{i\in[1,2,3]}$$ the associated eigen tensors. If $$f$$ is $$\mathcal{C}^{1}$$, then $$f$$ is a differentiable function of $$\underline{s}$$. $$f$$ can be computed with the computeIsotropicFunction method of the stensor class. $$\displaystyle\frac{\displaystyle \partial f}{\displaystyle \partial \underline{s}}$$ can be computed with computeIsotropicFunctionDerivative. One can also compute $$f$$ and $$\displaystyle\frac{\displaystyle \partial f}{\displaystyle \partial \underline{s}}$$ all at once by the computeIsotropicFunctionAndDerivative method. All those methods are templated by the name of the eigen solver (if no template parameter is given, the TFELEIGENSOLVER is used). Various new overloaded versions of those methods have been introduced in TFEL-3.1. Those overloaded methods are meant to: • allow the user to explicitly give the values of $$f$$ or $$df$$, rather than the functions to compute them. This allows to reduce the computational cost of the evaluation of the isotropic function when the values of the derivatives can directly be computed from the values of $$f$$. See the example $$\exp$$ example below. • return the results by value. This allow a much more readable code if the structured bindings feature of the C++17 standard is available. To illustrate this new features, assuming that the structured bindings feature of the C++17 standard is available, one can now efficiently evaluate the exponential of a symmetric tensor and its derivative as follows: const auto [vp,m] = s.computeEigenVectors(); const auto evp = map([](const auto x){return exp(x)},vp); const auto [f,df] = Stensor::computeIsotropicFunctionAndDerivative(evp,evp,vp,m,1.e-12); ### 2.3.3 Portable implementation of the fpclassify, isnan, isfinite functions The C99 standard defines the fpclassify, isnan, isfinite functions to query some information about double precision floatting-point numbers (double): • Following the IEEE754 standard, the fpclassify categorizes a floating point number into one of the following categories: zero, subnormal, normal, infinite, NaN (Not a Number). The return value returned for each category is respectively FP_ZERO, FP_SUBNORMAL, FP_NORMAL, FP_INFINITE and FP_NaN. • The isnan function returns a boolean stating if its argument has a not-a-number (NaN) value. • The isfinite function returns true if its argument falls into one of the following categories: zero, subnormal or normal. The C++11 provides a set of overload for single precision (float) and extended precision (long double) floatting-point numbers. Those functions are very handy to check the validity of a computation. However, those functions are not compatible with the use of the -ffast-math option of the GNU compiler which also implies the -ffinite-math-only option. This latter option allows optimizations for floating-point arithmetic that assume that arguments and results are finite numbers. As a consequence, when this option is enabled, the previous functions does not behave as expected. For example, isnan always returns false, whatever the value of its argument. To overcome this issue, we have introduced in TFEL/Math the implementation of these functions provided by the musl library (see Musl development community (2017)). Those implementations are compatible with the -ffast-math option of the GNU compiler. Those implementations are defined in the TFEL/Math/General/IEEE754.hxx header file in the tfel::math::ieee754 namespace. ## 2.4TFEL/Material ### 2.4.1 Hosford equivalent stress The header TFEL/Material/Hosford.hxx introduces three functions which are meant to compute the Hosford equivalent stress and its first and second derivatives. This header is automatically included by MFront The Hosford equivalent stress is defined by: $\sigma_{\mathrm{eq}}^{H}=\sqrt[a]{\displaystyle\frac{\displaystyle 1}{\displaystyle 2}\left({\left|\sigma_{1}-\sigma_{2}\right|}^{a}+{\left|\sigma_{1}-\sigma_{3}\right|}^{a}+{\left|\sigma_{2}-\sigma_{3}\right|}^{a}\right)}$ where $$s_{1}$$, $$s_{2}$$ and $$s_{3}$$ are the eigenvalues of the stress. Therefore, when $$a$$ goes to infinity, the Hosford stress reduces to the Tresca stress. When $$n = 2$$ the Hosford stress reduces to the von Mises stress. The following functions has been implemented: • computeHosfordStress: return the Hosford equivalent stress • computeHosfordStressNormal: return a tuple containing the Hosford equivalent stress and its first derivative (the normal) • computeHosfordStressSecondDerivative: return a tuple containing the Hosford equivalent stress, its first derivative (the normal) and the second derivative. #### 2.4.1.1 Example The following example computes the Hosford equivalent stress, its normal and second derivative: stress seq; Stensor n; Stensor4 dn; std::tie(seq,n,dn) = computeHosfordStressSecondDerivative(s,a,seps); In this example, s is the stress tensor, a is the Hosford exponent, seps is a numerical parameter used to detect when two eigenvalues are equal. If C++-17 is available, the previous code can be made much more readable: const auto [seq,n,dn] = computeHosfordStressSecondDerivative(s,a,seps); ### 2.4.2 Barlat equivalent stress The header TFEL/Material/Barlat.hxx introduces various functions which are meant to compute the Barlat equivalent stress and its first and second derivatives. This header is automatically included by MFront for orthotropic behaviours. The Barlat equivalent stress is defined as follows (see Barlat et al. (2005)): $\sigma_{\mathrm{eq}}^{B}= \sqrt[a]{ \frac{1}{4}\left( \sum_{i=0}^{3} \sum_{j=0}^{3} {\left|s'_{i}-s''_{j}\right|}^{a} \right) }$ where $$s'_{i}$$ and $$s''_{i}$$ are the eigenvalues of two transformed stresses $$\underline{s}'$$ and $$\underline{s}''$$ by two linear transformation $$\underline{\underline{\mathbf{L}}}'$$ and $$\underline{\underline{\mathbf{L}}}''$$: \left\{ \begin{aligned} \underline{s}' &= \underline{\underline{\mathbf{L'}}} \,\colon\,\underline{\sigma}\\ \underline{s}'' &= \underline{\underline{\mathbf{L''}}}\,\colon\,\underline{\sigma}\\ \end{aligned} \right. The linear transformations $$\underline{\underline{\mathbf{L}}}'$$ and $$\underline{\underline{\mathbf{L}}}''$$ are defined by $$9$$ coefficients (each) which describe the material orthotropy. There are defined through auxiliary linear transformations $$\underline{\underline{\mathbf{C}}}'$$ and $$\underline{\underline{\mathbf{C}}}''$$ as follows: \begin{aligned} \underline{\underline{\mathbf{L}}}' &=\underline{\underline{\mathbf{C}}}'\,\colon\,\underline{\underline{\mathbf{M}}} \\ \underline{\underline{\mathbf{L}}}''&=\underline{\underline{\mathbf{C}}}''\,\colon\,\underline{\underline{\mathbf{M}}} \end{aligned} where $$\underline{\underline{\mathbf{M}}}$$ is the transformation of the stress to its deviator: $\underline{\underline{\mathbf{M}}}=\underline{\underline{\mathbf{I}}}-\displaystyle\frac{\displaystyle 1}{\displaystyle 3}\underline{I}\,\otimes\,\underline{I}$ The linear transformations $$\underline{\underline{\mathbf{C}}}'$$ and $$\underline{\underline{\mathbf{C}}}''$$ of the deviator stress are defined as follows: $\underline{\underline{\mathbf{C}}}'= \displaystyle\frac{\displaystyle 1}{\displaystyle 3}\, \begin{pmatrix} 0 & -c'_{12} & -c'_{13} & 0 & 0 & 0 \\ -c'_{21} & 0 & -c'_{23} & 0 & 0 & 0 \\ -c'_{31} & -c'_{32} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & c'_{44} & 0 & 0 \\ 0 & 0 & 0 & 0 & c'_{55} & 0 \\ 0 & 0 & 0 & 0 & 0 & c'_{66} \\ \end{pmatrix} \quad \text{and} \quad \underline{\underline{\mathbf{C}}}''= \begin{pmatrix} 0 & -c''_{12} & -c''_{13} & 0 & 0 & 0 \\ -c''_{21} & 0 & -c''_{23} & 0 & 0 & 0 \\ -c''_{31} & -c''_{32} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & c''_{44} & 0 & 0 \\ 0 & 0 & 0 & 0 & c''_{55} & 0 \\ 0 & 0 & 0 & 0 & 0 & c''_{66} \\ \end{pmatrix}$ The following functions have been implemented: • computeBarlatStress: return the Barlat equivalent stress • computeBarlatStressNormal: return a tuple containing the Barlat equivalent stress and its first derivative (the normal) • computeBarlatStressSecondDerivative: return a tuple containing the Barlat equivalent stress, its first derivative (the normal) and the second derivative. #### 2.4.2.1 Linear transformations To define the linear transformations, the makeBarlatLinearTransformation function has been introduced. This function takes two template parameter: • the space dimension ($$1$$, $$2$$, and $$3$$) • the numeric type used (automatically deduced) This functions takes the $$9$$ coefficients as arguments, as follows: const auto l1 = makeBarlatLinearTransformation<3>(c_12,c_21,c_13,c_31, c_23,c_32,c_44,c_55,c_66); Note In his paper, Barlat and coworkers uses the following convention for storing symmetric tensors: $\begin{pmatrix} xx & yy & zz & yz & zx & xy \end{pmatrix}$ which is not consistent with the TFEL/Cast3M/Abaqus/Ansys conventions: $\begin{pmatrix} xx & yy & zz & xy & xz & yz \end{pmatrix}$ Therefore, if one wants to uses coeficients $$c^{B}$$ given by Barlat, one shall call this function as follows: const auto l1 = makeBarlatLinearTransformation<3>(cB_12,cB_21,cB_13,cB_31, cB_23,cB_32,cB_66,cBB_55,cBB_44); The TFEL/Material library also provide an overload of the makeBarlatLinearTransformation which template parameters are the modelling hypothesis and the orthotropic axis conventions. The purpose of this overload is to swap appriopriate coefficients to get a consistent definition of the linear transforamtions for all the modelling hypotheses. ### 2.4.3 The SlipSystemsDescription class # 3 New functionalities of the MFront code generator ## 3.1cmake Generator For Visual Studio users, who do not have access to the GNU make utility, a cmake generator was introduced. This generator is the default with Visual Studio. In other development environment, the default generator is the Makefile generator. One can switch from a generator to another using the --generator (-G) option of mfront, as follows: mfront -G cmake --obuild --interface=python YoungModulusTest.mfront

In this case, MFront will perform the following operations:

• Generate the sources of the python module.
• Generate a CMakeLists.txt file in the src directory.
• Configure the src directory using cmake.
• Build the python module using cmake.

The output of the previous command is, on LinuX:

Treating target : all
-- The C compiler identification is GNU 4.9.2
-- The CXX compiler identification is GNU 4.9.2
-- Check for working C compiler: /usr/bin/cc
-- Check for working C compiler: /usr/bin/cc -- works
-- Detecting C compiler ABI info
-- Detecting C compiler ABI info - done
-- Check for working CXX compiler: /usr/bin/c++
-- Check for working CXX compiler: /usr/bin/c++ -- works
-- Detecting CXX compiler ABI info
-- Detecting CXX compiler ABI info - done
-- tfel-config         : /home/th202608/codes/tfel/trunk/install/bin/tfel-config
-- tfel oflags         : -fvisibility-inlines-hidden;-fvisibility=hidden;-fno-fast-math;-DNO_RUNTIME_CHECK_BOUNDS;-O2;-DNDEBUG;-ftree-vectorize;-march=native
-- Configuring done
-- Generating done
-- Build files have been written to: /tmp/src
Scanning dependencies of target materiallaw
[ 50%] Building CXX object CMakeFiles/materiallaw.dir/YoungModulusTest-python.o
[100%] Building CXX object CMakeFiles/materiallaw.dir/materiallawwrapper.o
[100%] Built target materiallaw
The following library has been built :
- materiallaw.so :  YoungModulusTest

### 3.1.1 Chaning the build system targeted used by cmake

By default, cmake generates configuration files for a default build system which is determined as follows:

• if TFEL was built using cmake, the same build system is used.
• otherwise, the Unix Makefiles build system is used.

This can be changed by the user using the CMAKE_GENERATOR environment variable. For example, one my select the Ninja build system as follows:

$CMAKE_GENERATOR="Ninja" mfront --obuild --interface=aster -G cmake Norton.mfront Treating target : all -- The C compiler identification is GNU 4.9.2 -- The CXX compiler identification is GNU 4.9.2 -- Check for working C compiler using: Ninja -- Check for working C compiler using: Ninja -- works -- Detecting C compiler ABI info -- Detecting C compiler ABI info - done -- Check for working CXX compiler using: Ninja -- Check for working CXX compiler using: Ninja -- works -- Detecting CXX compiler ABI info -- Detecting CXX compiler ABI info - done -- tfel-config : /home/th202608/codes/tfel/trunk/install-python-3.4/bin/tfel-config -- tfel oflags : -fvisibility-inlines-hidden;-fvisibility=hidden;-fno-fast-math;-DNO_RUNTIME_CHECK_BOUNDS;-O2;-DNDEBUG;-ftree-vectorize;-march=native -- Configuring done -- Generating done -- Build files have been written to: /tmp/src [3/3] Linking CXX shared library libAsterBehaviour.so The following library has been built : - libAsterBehaviour.so : asternorton ### 3.1.2 Environment variables affecting the build system generated by cmake The build system generated by cmake can be affected by various environment variables. For example, with the Ninja and Unix Makefiles build systems, one can select the C++ compiler using the CXX environment variable, as follows:$ CC=clang CXX=clang++ CMAKE_GENERATOR="Ninja" mfront --obuild --interface=aster -G cmake Norton.mfront
Treating target : all
-- The C compiler identification is Clang 3.5.0
-- The CXX compiler identification is Clang 3.5.0
-- Check for working C compiler using: Ninja
-- Check for working C compiler using: Ninja -- works
-- Detecting C compiler ABI info
-- Detecting C compiler ABI info - done
-- Check for working CXX compiler using: Ninja
-- Check for working CXX compiler using: Ninja -- works
-- Detecting CXX compiler ABI info
-- Detecting CXX compiler ABI info - done
-- tfel-config         : /home/th202608/codes/tfel/trunk/install-python-3.4/bin/tfel-config
-- tfel oflags         : -fvisibility-inlines-hidden;-fvisibility=hidden;-fno-fast-math;-DNO_RUNTIME_CHECK_BOUNDS;-O2;-DNDEBUG;-ftree-vectorize;-march=native
-- Configuring done
-- Generating done
-- Build files have been written to: /tmp/src
[3/3] Linking CXX shared library libAsterBehaviour.so
The following library has been built :
- libAsterBehaviour.so :  asternorton

## 3.2Implicit DSL

### 3.2.1@NumericallyComputedJacobianBlocks

Computing the jacobian of the implicit system is the most difficult part of implementing a behaviour. Computing the jacobian by finite difference is interesting but significantly decreases the performances of the behaviour and can be (very) sensitive to the choice of the numerical perturbation.

The @NumericallyComputedJacobianBlocks keyword is used select a list of jacobian blocks that have to be computed numerically. This is more efficient than computing the whole jacobian numerically. Combined with the ability to compare the jacobian to a numerical approximation, the user now has the ability to build the jacobian incrementally, block by block and checks at each steps that their analytical expressions are correct.

This keyword can optionnaly be followed by a list of modelling hypotheses. The list of jacobian blocks is given as an array.

#### 3.2.1.1 Notes

• This keyword can be used multiple times. The newly declared jacobian blocks are added to the existing ones.

#### 3.2.1.2 Example

@NumericallyComputedJacobianBlocks {dfp_ddeel,dfeel_ddeel};

## 3.3 Behaviours interfaces

### 3.3.1 Native CalculiX interface

A native interface for the CalculiX solver has been added.

Calling external libraries from CalculiX for the native interface requires a patch in version 2.12 that can be downloaded here.

### 3.3.2 The Cast3M interface

#### 3.3.2.1 The MieheApelLambrechtLogarithmic finite strain strategy

The pre- and post-computations performed by the MieheApelLambrechtLogarithmic finite strain strategy , which require the computation of the eigen values and eigen vectors of the right Cauchy strecth tensor, are now based the Jacobi algorithm from the FSES library for improved accuracy.

### 3.3.3 The Code_Aster interface

#### 3.3.3.1 Support for the GROT_GDEP finite strain formulation

GROT_GDEP is the name in Code_Aster of a finite strain formulation based on the principle of virtual work in the reference configuration expressed in term of the Green-Lagrange strain and the second Piola-Kirchhoff stress. Such a formulation is also called Total Lagrangian in the litterature (see Belytschko (2000)) and in other finite element solvers.

Prior to this version, MFront behaviours were meant to be used with the SIMO_MIEHE finite strain formulation and could not be used with the GROT_GDEP finite strain formulation.

From the behaviour point of view, using SIMO_MIEHE or GROT_GDEP differs from the choice of the output stress and the definition of the consistent tangent operator.

#### 3.3.3.2 The @AsterFiniteStrainFormulation keyword

The @AsterFiniteStrainFormulation keyword can now be used to choose one of these finite strain formulation.

This keyword must be followed by one of the following choice:

• SIMO_MIEHE
• GROT_GDEP or TotalLagrangian

The choice SIMO_MIEHE remains the default for backward compatibility.

### 3.3.4 The Europlexus interface

#### 3.3.4.1 The MieheApelLambrechtLogarithmic finite strain strategy

The pre- and post-computations performed by the MieheApelLambrechtLogarithmic finite strain strategy, which require the computation of the eigen values and eigen vectors of the right Cauchy strecth tensor, are now based the Jacobi algorithm from the FSES library for improved accuracy.

### 3.3.5 The Abaqus-Explicit interface

#### 3.3.5.1 The MieheApelLambrechtLogarithmic finite strain strategy

The pre- and post-computations performed by the MieheApelLambrechtLogarithmic finite strain strategy, which require the computation of the eigen values and eigen vectors of the right Cauchy strecth tensor, are now based the Jacobi algorithm from the FSES library for improved accuracy.

# 4 New functionalities of MTest solver

## 4.1 Choice of the rounding mode from the command line

$$4$$ rounding mode are defined in the IEEE754 standard. Changing the rounding mode is a gross way to check the numerical stability of the computations performed with MTest and MFront.

The rounding mode can be set using the --rounding-direction-mode option. Valid values for this option are:

• DownWard: Round downward.
• ToNearest: Round to nearest (the default).
• TowardZero: Round toward zero.
• UpWard: Round upward.
• Random: rounding mode is changed randomly a various stage of the computation to one of the four previous rounding modes.

Most unit-tests based on MTest are now executed five times, one for each available choice of the rounding mode.

## 4.2 Abritrary non linear constraints

Abritrary non linear constraints on driving variables and thermodynamic forces can now be added using the @NonLinearConstraint keyword.

Note

This keyword can also be used to define linear constraints, although the numerical treatment of such a constraint will be sub-optimal. A special treatment of such a constraint is planned.

Note

This development of this functionality highlighted the issue reported in Ticket #39. For more details, see: https://sourceforge.net/p/tfel/tickets/39/

### 4.2.1 Normalisation policy

This keyword must be followed by an option giving the normalisation policy. The normalisation policy can have one of the following values:

• DrivingVariable, Strain, DeformationGradient, OpeningDisplacement stating that the constraint is of the order of magnitude of the driving variable.
• ThermodynamicForce, Stress, CohesiveForce stating that the constraint is of the order of magnitude of the thermodynamic force.

### 4.2.2 Examples

@NonLinearConstraint<Strain> 'FRR*FTT*FZZ-1';
// impose the first piola kirchoff stress
// in an uniaxial compression test
@Real 'Pi0' -40e6
@NonLinearConstraint<Stress> 'SXX*FYY*FZZ-Pi0';

## 4.3 The @Print and @Message keywords

The @Print keyword, or its alias named @Message, is used to display some informative message on the standard output.

This keyword is followed by floatting point values and/or strings.

Strings are first interpreted as formula. If the interpretation is successfull, the result is printed. Otherwise, the string is display witout interpretation.

All the following tokens are appended to the message up to a final semi-colon.

### 4.3.1 Example:

@Print "Complex computation result: " "12*5";

In this example, the first string can’t be interpreted as a formula, so its contents is printed. The second part can be interpreted, so its result ($$60$$) is displayed. The message printed is thus:

Complex computation result: 60

## 4.4 The @Import keyword

Depending of the option used (given between ‘<’ and ‘>’), the @Import keyword is meant to have various meanings.

In this version, the only option available is the castem option.

### 4.4.1 The castem option

The castem (or Castem or Cast3M) option let you import a function generated by MFront with the castem interface. This function can be used in every formula.

The keyword is followed by the library an function names.

#### 4.4.1.1 Example

@Import<castem> 'CastemW' 'W_ThermalExpansion';
// height at 20°C
@Real 'h0' 16e-3;
// height at 1500°C
@Real 'h' 'h0*(1+W_ThermalExpansion(1723.15)*(1723.25-293.15))';

## 4.5python bindings

### 4.5.1 The Behaviour class

The Behaviour class has been introduced in the mtest modules. This class can be used to determine at runtime time the material properties, internal state variables, parameters and external state variables required by a specific implementation.

Contrary the tfel.system.ExternalBehaviourDescription class, the information given by the Behaviour class takes into account the variables that are implicitly declared by the interface to match its specific (internal) requirements. For example:

• The castem interface usually adds additional material properties describing the thermo-elastic properties. Such properties are may be unused by the behaviour.
• The abaqus interface may declare additional state variables to describe the orthotropic axes (this is mandatory for finite strain ortotropic behaviours).
• etc…

### 4.5.2 The MTest class

In the python bindings, the setNonLinearConstraint method has been added to the MTest class.

This method takes two named arguments:

• constraint, the equation to be satified
• normalisation_policy. The normalisation policy can have one of the following values:
• DrivingVariable, Strain, DeformationGradient, OpeningDisplacement stating that the constraint is of the order of magnitude of the driving variable
• ThermodynamicForce, Stress, CohesiveForce stating that the constraint is of the order of magnitude of the thermodynamic force

# 5 New functionalities of the mfront-query tool

## 5.1 New behaviours queries

• --static-variables: show the list of the behaviour static variables.
• --parameter-default-value: display a parameter default value.
• --static-variable-value: display the value of a static variable.
• --has-bounds: return true if a variable has bounds, false otherwise.
• --bounds-type: return the bounds type associated to a variable. The returned value has the follwing meaning:
• None
• Lower
• Upper
• LowerAndUpper
• --bounds-value: show the bounds value associated as a range.
• --has-physical-bounds: return true if a variable has physical bounds, false otherwise.
• --physical-bounds-type: return the physical bounds type associated to a variable. The returned value has the follwing meaning:
• None
• Lower
• Upper
• LowerAndUpper
• --physical-bounds-value: show the bounds value associated as a range.

### 5.1.1 Queries associated with the strain measure

• --is-strain-measure-defined: return true if a strain measure has been defined, false otherwise.
• -strain-measure: return the strain measure on which the behaviour is built. The following values are valid: Linearised, GreenLagrange and Hencky.

### 5.1.2 Queries associated with the crystal structure

• --has-crystal-structure: return true if a crystal structure has been defined.
• --crystal-structure: return the crystal structure.
• --slip-systems: list all the slip systems, sorted by family.
• --slip-systems-by-index: list all the slip systems, sorted by index.
• --orientation-tensors: list all the orientation tensors, sorted by family“.
• --orientation-tensors-by-index: list all the orientation tensors.
• --orientation-tensors-by-slip-system: list all the orientation tensors.
• --interaction-matrix: display the interaction matrix where the sliding systems’ interaction are represented by their ranks.
• --interaction-matrix-structure: return the number of independent coefficients and the sliding systems sorted by rank.

# 6 New functionalities of the tfel-config tool

tfel-config provides new options for better integration with build systems, such as cmake:

• --major-version: returns the major version of TFEL
• --minor-version: returns the minor version of TFEL
• --revision-version: returns the revision version of TFEL
• --ldflags: returns appropriate flags for the linker to link against specified libraries (see --math, --system the options and others). This option is equivalent to the --libs options but better reflects the intent of the option.
• --include-path: returns the path the TFEL headers.
• --library-path: returns the path the TFEL libraries.
• --library-dependency: returns the list of dependencies of a TFEL library. The given library is included in the list.
• --python-version: returns the python version used to build the python bindings.
$tfel-config --library-dependency --material TFELMaterial TFELMath TFELUtilities TFELException TFELNUMODIS # 7 Introduction of the mfm tool mfm is a tool that allow querying a library about the entry points defined by MFront. Depending on the interface, an entry point can be a class name, a function, a name of an entity that will be registered in an abstract factory when the library is loaded, etc…$ mfront --obuild --interface=aster ImplicitNorton.mfront
Treating target : all
The following library has been built :
- libAsterBehaviour.so :  asterimplicitnorton
th202608@pleiades098:/tmp$mfm src/libAsterBehaviour.so - asterimplicitnorton The entry points can be filtered. The following filters are available: • --filter-by-interface. • --filter-by-material • --filter-by-name. • --filter-by-type. This option can be followed by material-property, behaviour or model Filters are based on case-insensitive regular expressions. Apart from filters, mfm also have the following options: • --verbose: set the verbosity level. The following values are accepted: quiet, level0, level1, level2, debug, full. If no value is given, level1 is selected. • --show-libs: show library name in front of entry points. For example:$ mfm --filter-by-material='M5' --filter-by-type=material_property --filter-by-name='.*YoungModulus.*' --filter-by-interface=castem --show-libs  \$(find . -type f)
- ./lib/libM5MaterialProperties-castem.so: M5_YoungModulus
- ./lib/libM5MaterialProperties-castem.so: M5_YoungModulus_Crocodile2015
- ./lib/libM5MaterialProperties-castem.so: M5_YoungModulus_MATPRO2001

# 8 Tickets fixed

This release also takes into account the tickets fixed for tfel-3.0.1, tfel-3.0.2, tfel-3.0.3. For a detailed list, see:

## 8.1 Ticket #37: Add the ability to compute part of the jacobian numerically

The @NumericallyComputedJacobianBlocks keyword can be used for that purpose.

For more details, see: https://sourceforge.net/p/tfel/tickets/37/

## 8.2 Ticket #40: ImplicitDSL: Detect non finite values during resolution

During the resolution of the implicit system, invalid results may occur. In previous versions, no check were made leading to a propagation of those values and finally the failure of integration.

A test to check that the residual of the implicit system is finite have been added. If this test is not satisfied after the first iteration, the last increment of the unknowns is divided by two and the resolution is restarted with this guess. If this test is not satisfied at the first iteration, the behaviour integration can not be performed.

## 8.3 Ticket #41: MTest: check if the residual is finite and not NaN

In previous versions, if the behaviour integration returned a not-a-number value (NaN ), this value propagated throughout the computation.

This situation can be detected by checking that the convergence criteria are finite as defined by the IEEE754 standard.

For more details, see: https://sourceforge.net/p/tfel/tickets/41/

## 8.4 Ticket #42: Check for infinite and NaN values in material properties

In the previous versions of MFront, generated sources for material properties checked that the errno value to determine is something had gone wrong, but this check does not appear to portable nor reliable with the INTEL compiler or when the -ffast-math option of the GNU compiler is activated.

The current version now check that the return value is finite.

For more details, see: https://sourceforge.net/p/tfel/tickets/42/

## 8.5 Ticket #43: Add the list of parameters’ names and types to generated library for the UMAT++ interface

In previous versions of MFront, the list of parameters’ names and types were not exported to the generated library for the UMAT++ interface, i.e. the additional symbols defined in the generated shared libraries that can be read through the ExternalLibraryManager class.

For more details, see: https://sourceforge.net/p/tfel/tickets/43/

## 8.6 Ticket #45: Support for bounds on parameters

For more details, see: https://sourceforge.net/p/tfel/tickets/45/

## 8.7 Ticket #46: Improvements to the mfrontpython module

The following improvements to the mfront python module have been made:

• Add missing metods in the BehaviourDescription class to retrieve information about the material symmetry
• Add missing methods to retrieve information about standard and physical variables’ bounds.

For more details, see: https://sourceforge.net/p/tfel/tickets/46/

## 8.8 Ticket #47: Add python bindings for the mtest::Behaviour class

The mtest module now contains bindings for the mtest::Behaviour class. This class allow querying information about how to use a behaviour in a specific context (interface and modelling hypothesis): for example, if a behaviour has the requireStiffnessTensor attribute, the list of material properties is updated appropriately if required by the interface for the considered modelling hypothesis. The Behaviour class has the following useful methods:

• getBehaviourType: Return the behaviour type.
• getBehaviourKinematic: Return the behaviour kinematic.
• getDrivingVariablesSize: Return the size of a vector able to contain all the components of the driving variables.
• getThermodynamicForcesSize: Return the size of a vector able to contain all the components of the thermodynamic forces.
• getStensorComponentsSuffixes: Return the components suffixes of a symmetric tensor.
• getVectorComponentsSuffixes: Return the components suffixes of a vector.
• getTensorComponentsSuffixes: Return the components suffixes of a tensor.
• getDrivingVariablesComponents: Return the components of the driving variables.
• getThermodynamicForcesComponents: Return the components of the thermodynamic forces.
• getDrivingVariableComponentPosition: Return the position of the component of a driving variable.
• getThermodynamicForceComponentPosition: Return the position of the component of a thermodynamic force.
• getSymmetryType: Return the symmetry of the behaviour: – 0 means that the behaviour is isotropic. – 1 means that the behaviour is orthotropic.
• getMaterialPropertiesNames: return the names of the material properties.
• getInternalStateVariablesNames: Return the names of the internal state variables.
• expandInternalStateVariablesNames: Return the names of the internal state variables, taking into account the suffixes for vectors, symmetric tensors and tensors.
• getInternalStateVariablesSize: Return the the size of the array of internal variables.
• getInternalStateVariablesDescriptions: Return the descriptions the internal variables.
• getInternalStateVariableType: Return the type of an internal variable:
• 0 means that the internal state variable is a scalar.
• 1 means that the internal state variable is a symmetric tensor.
• 3 means that the internal state variable is a tensor.
• getInternalStateVariablePosition: Return the internal state variable position.
• getExternalStateVariablesNames: Return the names of the external state variables.
• getParametersNames: Return the names of the floating point parameters.
• getIntegerParametersNames: Return the names of the integer parameters.
• getUnsignedShortParametersNames: Return the names of the unsigned short parameters.
• The getRealParameterDefaultValue, getIntegerParameterDefaultValue and getUnsignedShortParameterDefaultValue methods can be used to retrieve the default value of a parameter.
• The hasBounds method returns true if the given variable has bounds.
• The hasLowerBound method returns true if the given variable has a lower bound.
• The hasUpperBound method hasUpperBound returns true if the given variable has an upper bound.
• The getLowerBound method returns the lower bound of the given variable.
• The getUpperBound method returns the uppert bound of the given variable.
• The hasPhysicalBounds methodreturns true if the given variable has physical bounds.
• The hasLowerPhysicalBound method returns true if the given variable has a physical lower bound.
• The hasUpperPhysicalBound method returns true if the given variable has a physical upper bound.
• The getLowerPhysicalBound method returns the lower bound of the given variable.
• The getUpperPhysicalBound method returns the upper bound of the given variable.

For more details, see: https://sourceforge.net/p/tfel/tickets/47/

Here is an example of the usage of the Behaviour class in python:

import mtest
b= mtest.Behaviour('AsterBehaviour','asternorton','Tridimensional');
for p in b.getParametersNames():
print('- '+p+': '+str(b.getRealParameterDefaultValue(p)))
for p in b.getIntegerParametersNames():
print('- '+p+': '+str(b.getIntegerParameterDefaultValue(p)))
for p in b.getUnsignedShortParametersNames():
print('- '+p+': '+str(b.getUnsignedShortParameterDefaultValue(p)))

## 8.9 Ticket #46: Improved python bindings for the mfront::BehaviourDescription class

The python bindings of the mfront::BehaviourDescription now gives access to the parameters default values, and information about a variable standard or physical bounds (type, range).

Here is an example of its usage:

from tfel.material import ModellingHypothesis
import mfront

def printBounds(n,b):
print('Bounds of variable \''+n+'\':')
if((b.boundsType==mfront.VariableBoundsTypes.LOWER) or
(b.boundsType==mfront.VariableBoundsTypes.LOWERANDUPPER)):
print('- lower bound: '+str(b.lowerBound))
if((b.boundsType==mfront.VariableBoundsTypes.UPPER) or
(b.boundsType==mfront.VariableBoundsTypes.LOWERANDUPPER)):
print('- upper bound: '+str(b.upperBound))
print('')

dsl = mfront.getDSL('Norton.mfront')
dsl.analyseFile('Norton.mfront',[])

# behaviour description
bd = dsl.getBehaviourDescription()

if(bd.getSymmetryType()==mfront.BehaviourSymmetryType.ISOTROPIC):
print 'Isotropic behaviour\n'
else:
print 'Orthropic behaviour\n'

if(bd.getElasticSymmetryType()==mfront.BehaviourSymmetryType.ISOTROPIC):
print 'Isotropic elasticity\n'
else:
print 'Orthropic elasticity\n'

# a deeper look at the 3D case
d = bd.getBehaviourData(ModellingHypothesis.TRIDIMENSIONAL)
for p in d.getParameters():
if(p.arraySize==1):
if(p.hasBounds()):
printBounds(p.name,p.getBounds())
else:
for i in range(p.arraySize):
if(p.hasBounds(i)):
printBounds(p.name+'['+str(i)+']',p.getBounds(i))

## 8.10 Ticket #48: Add the ability to retrieve bounds for material properties and parameters from the mtest::Behaviour class

The following methods were added to the mtest.Behaviour class: - The hasBounds method returns true if the given variable has bounds. - The hasLowerBound method returns true if the given variable has a lower bound. - The hasUpperBound method hasUpperBound returns true if the given variable has an upper bound. - The getLowerBound method returns the lower bound of the given variable. - The getUpperBound method returns the uppert bound of the given variable. - The hasPhysicalBounds methodreturns true if the given variable has physical bounds. - The hasLowerPhysicalBound method returns true if the given variable has a physical lower bound. - The hasUpperPhysicalBound method returns true if the given variable has a physical upper bound. - The getLowerPhysicalBound method returns the lower bound of the given variable. - The getUpperPhysicalBound method returns the upper bound of the given variable.

Here is an example:

from mtest import Behaviour

b = Behaviour('AsterBehaviour','asternorton','Tridimensional')

for p in b.getParametersNames():
if b.hasLowerBound(p):
print(p+" lower bound: "+str(b.getLowerBound(p)))
if b.hasUpperBound(p):
print(p+" lower bound: "+str(b.getUpperBound(p)))

For more details, see: https://sourceforge.net/p/tfel/tickets/48/

## 8.11 Ticket #49: Add the ability to retrieve the symmetry of the behaviour and the symmetry of the elastic behaviour from mfront-query

The following queries are now available:

• --elastic-symmetry: return the symmetry of the elastic part of the behaviour. If the returned value is 0, this part of the behaviour is isotropic. If the returned value is 1, this part of the behaviour is orthotropic.the behaviour is orthotropic.
• --symmetry: return the behaviour symmetry. If the returned value is 0, the behaviour is isotropic. If the returned value is 1, the behaviour is orthotropic.

For more details, see: https://sourceforge.net/p/tfel/tickets/49/

## 8.12 Ticket #50: Add the ability to retrieve bounds values from mfront-query

The following queries are now available:

• --has-bounds: return true if a variable has bounds, false otherwise.
• --bounds-type: return the bounds type associated to a variable.
• --bounds-value: show the bounds value associated as a range.
• --has-physical-bounds: return true if a variable has physical bounds, false otherwise.
• --physical-bounds-type: return the physical bounds type associated to a variable.
• --physical-bounds-value: show the bounds value associated as a range.

For more details, see: https://sourceforge.net/p/tfel/tickets/50/

## 8.13 Ticket #55: New functionnalities for multi-yield-surfaces plasticity

The @AdditionalConvergenceChecks keyword is meant to introduce a code block returning stating if convergence has been reached. More precisely, this code block is meant to modify a boolean variable called converged. This boolean is true if the standard convergence criterion has been reached, false otherwise.

One possible usage of this code block is multi-surfaces’ plasticity treated by activating or desactivating statuses.

### 8.13.1 Example

Consider a two surfaces plastic behaviour. To handle it, we will need two arrays of boolean:

• the first one tells if the ith surface is activable during the time step.
• the second one gives the current status of the ith surface: if the corresponding status is set to true, this surface is active.
@Brick StandardElasticity; // to have computeElasticPrediction

@LocalVariable bool status[2];

@Prediction{
// initial status based of the elastic prediction
auto sigel = computeElasticPrediction();
for(unsigned short i=0;i!=2;++i){
status[i] = ...
}
} // end of @Prediction

@Integrator{
for(unsigned short i=0;i!=2;++i){
if(status[i]){
...
}
}
} // end of @Integrator

// initial status based of the elastic prediction
for(unsigned short i=0;i!=2;++i){
// change the status if needed. If a status a changed,
//set converged to false
...
}
}

## 8.14 Ticket #60: Compute the consistent tangent operator for the MieheApelLambrechtLogarithmicStrain finite strain strategy

The LogarithmicStrainHandler class has been introduced to gather the implementations of MieheApelLambrechtLogarithmicStrain finite strain strategy in all interfaces. The computation of the consistent tangent operator has been implemented in this class.

This feature is available in the Cast3M, Abaqus/Standard and CalculiX interfaces.

## 8.15 Ticket #61: Introduce a general @FiniteStrainStrategy keyword. Deprecate definition of the finite strain strategies in the interfaces.

The StrainMeasure keyword has been introduced. This keyword is followed by the name of a strain measure:

• Linearised (small strain behaviour)
• Green-Lagrange
• Hencky

The stress tensor computed by the behaviour is interpreted as the dual of the strain measure chosen.

The definition of the finite strain strategies in interfaces has not been deprecated, as this allows to define general purpose behaviours available in various “flavours”.

The StrainMeasure keyword has been introduced. This keyword is followed by the name of a strain measure:

• Linearised (small strain behaviour)
• Green-Lagrange
• Hencky

The stress tensor computed by the behaviour is interpreted as the dual of the strain measure chosen.

The definition of the finite strain strategies in interfaces has not been deprecated, as this allows to define general purpose behaviours available in various “flavours”.

For more details, see: https://sourceforge.net/p/tfel/tickets/61/

## 8.16 Ticket #65: @ElasticMaterialProperties does not work for DSL describing isotropics behaviours

The @ElasticMaterialProperties is now available for domain specific languages (DSL) describing isotropics behaviours.

@DSL IsotropicStrainHardeningMisesCreep;
@Behaviour StrainHardeningCreep2;
@Author    Helfer Thomas;
@Date      23/11/06;

@ElasticMaterialProperties {"Inconel600_YoungModulus.mfront",0.3};

@MaterialProperty real A;
@MaterialProperty real Ns;
@MaterialProperty real Np;

@FlowRule{
const real p0  = 1.e-6;
const real tmp = A*pow(seq,Ns-1.)*pow(p+p0,-Np-1);
f       = tmp*seq*(p+p0);
df_dseq =  Ns*tmp*(p+p0);
df_dp   = -Np*tmp*seq;
}

For more details, see: https://sourceforge.net/p/tfel/tickets/65/

## 8.17 Ticket 74: mfront-query: handle static variables

mfront-query now has the following options:

• --static-variables: list all the static variables
• --static-variable-value: return the value of a given static variable

For more details, see: https://sourceforge.net/p/tfel/tickets/74/

## 8.18 Ticket 76: Add python bindings for the SearchPathsHandler class in the mfront module

The SearchPathsHandler class is used in MFront to search additional files. Bindings for this class has been added to the mfront module. The following methods are available:

• addSearchPaths: Add new search paths. Multiple paths are separated by commas under unices systems and by semicolons under Windows systems.
• search: search a file and return the path to it if found.
• getSearchPaths: return all the registred search paths.

For more details, see: https://sourceforge.net/p/tfel/tickets/76/

# 9 Know regressions

## 9.1 Stricter rules on variable declarations

All variables, to the very exception of local variables, must be declared before the first user defined code block to allow appropriate analysis of those code blocks.

Some variables are automatically declared by keywords. For instance, the @Epsilon keyword defines implicitly a parameter named epsilon.

In previous versions of MFront, those rules were only partially enforced: it may happen that some keywords or variable declaration shall now be moved before the first user defined code block.

# 10 Portability

Portability is a convincing sign of software quality and maintainability:

• usage of functionalities specific to operating systems are well identified.
• it demonstrates that the code is not dependant of the system libraries, such as the C or C++ libraries.

TFEL has been tested successfully on a various flavours of LinuX and BSD systems (including FreeBSD and OpenBSD). The first ones are mostly built on gcc, libstdc++ and the glibc. The second ones are built on clang and libc++.

TFEL can be built on Windows in a wide variety of configurations and compilers:

• native ports can be built using the Visual Studio (2015 and 2017) or MingGW compilers.
• TFEL can be built in the Cygwin environment.

TFEL have reported to build successfully in the Windows Subsystem for LinuX (WSL) environment.

Although not officially supported, more exotic systems, such as OpenSolaris and Haiku, have also been tested successfully. The Minix operating systems provides a pre-release of clang 3.4 that fails to compile TFEL.

## 10.1 Supported compilers

Version 3.1 has been tested using the following compilers:

• gcc on various POSIX systems: versions 4.7, 4.8, 4.9, 5.1, 5.2, 6.1, 6.2, 7.1, 7.2
• clang on various POSIX systems: versions 3.5, 3.6, 3.7, 3.8, 3.9, 4.0, 5.0
• intel. The only tested version is the 2018 version on LinuX. Intel compilers 15 and 16 are known not to work due to a bug in the EDG front-end that can’t parse a syntax mandatory for the expression template engine. The same bug affects the Blitz++ library (see http://dsec.pku.edu.cn/~mendl/blitz/manual/blitz11.html). Version 2017 shall work but were not tested.
• Visual Studio The only supported versions are the 2015 and 2017 versions. Previous versions do not provide a suitable C++11 support.
• PGI compiler (NVIDIA): version 17.10 on LinuX
• MinGW has been tested successfully in a wide variety of configurations/versions, including the version delivered with Cast3M 2017.

## 10.2 Benchmarcks

A comparison of various compilers and specific options
Compiler and options Success ratio Test time
gcc 4.9.2 100% tests passed 681.19 sec
gcc 4.9.2+fast-math 100% tests passed 572.48 sec
clang 3.5 100% tests passed 662.50 sec
clang 3.5+libstcxx 99% tests passed 572.18 sec
clang 5.0 100% tests passed 662.50 sec
icpc 2018 100% tests passed 511.08 sec
PGI 17.10 99% tests passed 662.61 sec

Concerning the PGI compilers, performances may be affected by the fact that this compiler generates huge shared libraries (three to ten times larger than other compilers).

# 11 References

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Belytschko, Ted. 2000. Nonlinear Finite Elements for Continua and Structures. Chichester ; New York: Wiley-Blackwell.

Eberly, David. 2016. “A Robust Eigensolver for 3 × 3 Symmetric Matrices.” https://www.geometrictools.com/Documentation/RobustEigenSymmetric3x3.pdf.

———. 2017. “Geometric Tools.” 2017. http://www.geometrictools.com/.

Févotte, François, and Bruno Lathuilière. 2016. “VERROU: Assessing Floating-Point Accuracy Without Recompiling.” https://hal.archives-ouvertes.fr/hal-01383417/.

Hillerborg, A., M. Modéer, and P.-E. Perterson. 1976. “Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements.” Cement and Concrete Research 6:779–82.

Hosford, W. F. 1972. “A Generalized Isotropic Yield Criterion.” Journal of Applied Mechanics 39 (2):607–9.

Kopp, Joachim. 2008. “Efficient Numerical Diagonalization of Hermitian 3x3 Matrices.” International Journal of Modern Physics C 19 (3):523–48. https://doi.org/10.1142/S0129183108012303.

———. 2017. “Numerical Diagonalization of 3x3 Matrices.” 2017. https://www.mpi-hd.mpg.de/personalhomes/globes/3x3/.

Lamotte, J.-L., J.-M. Chesneaux, and F. Jézéquel. 2010. “CADNA_C: A Version of CADNA for Use with c or C++ Programs.” Computer Physics Communications 181 (11):1925–6.

Miehe, C., N. Apel, and M. Lambrecht. 2002. “Anisotropic Additive Plasticity in the Logarithmic Strain Space: Modular Kinematic Formulation and Implementation Based on Incremental Minimization Principles for Standard Materials.” Computer Methods in Applied Mechanics and Engineering 191 (47–48):5383–5425. https://doi.org/10.1016/S0045-7825(02)00438-3.

Musl development community. 2017. “Musl Libc.” 2017. https://www.musl-libc.org/.

Scherzinger, W. M. 2017. “A Return Mapping Algorithm for Isotropic and Anisotropic Plasticity Models Using a Line Search Method.” Computer Methods in Applied Mechanics and Engineering 317 (April):526–53. https://doi.org/10.1016/j.cma.2016.11.026.

Université Pierre et Marie Curie, France, Paris. 2017. “CADNA: Control of Accuracy and Debugging for Numerical Applications.” http://www.lip6.fr/cadna.