set(AKANTU_COPYRIGHT "2010-2021, EPFL (Ecole Polytechnique Fédérale de Lausanne) Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)")
set(AKANTU_MAINTAINER "Nicolas Richart")
set(AKANTU_HOMEPAGE_URL "https://akantu.ch")
if(CMAKE_VERSION VERSION_GREATER 3.12)
project(Akantu
HOMEPAGE_URL "https://akantu.ch")
else()
project(Akantu)
endif()
enable_language(CXX)
set(ENV{RUNNING_IN_CMAKE} True) # Used by sphinx but could be used by any script
If compilation does not work change the path of the failing libraries to brew downloads in `/opt/homebrew/`.
## Using the python interface
You can install ``Akantu`` using pip, this will install a pre-compiled version, this works only on Linux machines for now:
``` sh
> pip install akantu
```
You can then import the package in a python script as:
``` python
import akantu
```
The python API is similar to the C++ one. If you
encounter any problem with the python interface, you are welcome to do a merge
request or post an issue on [GitLab](https://gitlab.com/akantu/akantu/-/issues).
# Contributing
## Contributing new features, bug fixes
Any contribution is welcome, we are trying to follow a [gitflow](https://nvie.com/posts/a-successful-git-branching-model/) workflow, so the project `developers` can create branches named `features/<name of my feature>` or `bugfixes/<name of the fix>` directly in the main `akantu` repository.
External fellows can [Fork](https://gitlab.com/akantu/akantu/-/forks/new) the project.
In both cases the modifications have to be submitted in the form of a [Merge Request](https://gitlab.com/akantu/akantu/-/merge_requests/new).
## Asking for help, reporting issues
If you want to ask for help concerning Akantu's compilation, usage or problem with the code do not hesitate to open an [Issue](https://gitlab.com/akantu/akantu/-/issues/new) on gitlab. If you want to contribute and don't know where to start, you are also invited to open an issue.
# Tutorials with the python interface
To help getting started, multiple tutorials using the python interface are
available as notebooks with pre-installed version of `Akantu` on Renku. The tutorials can be tested here:
-Any contribution is welcome, we are trying to follow a `gitflow <https://nvie.com/posts/a-successful-git-branching-model/>`_ workflow, so the project `developers` can create branches named `features/<name of my feature>` or `bugfixes/<name of the fix>` directly in the main `akantu` repository.
-External fellows can `Fork <https://gitlab.com/akantu/akantu/-/forks/new>`_ the project.
-In both cases the modifications have to be submitted in the form of a `Merge Request <https://gitlab.com/akantu/akantu/-/merge_requests/new>`_.
-
-Asking for help, reporting issues
-`````````````````````````````````
-
-If you want to ask for help concerning Akantu's compilation, usage or problem with the code do not hesitate to open an `Issue <https://gitlab.com/akantu/akantu/-/issues/new>`_ on gitlab. If you want to contribute and don't know where to start, you are also invited to open an issue.
-
-
-Building ``Akantu``
---------------------
-
-Dependencies
-````````````
-
-In order to compile ``Akantu`` any compiler supporting fully C++14 should work.
-In addition some libraries are required:
-
- - CMake (>= 3.5.1)
- - Boost (pre-processor and Spirit)
- - zlib
- - Eigen3 (if not present the build system will try to download it)
-
-For the python interface:
-
- - Python (>=3 is recommended)
- - pybind11 (if not present the build system will try to download it)
-
-To run parallel simulations:
-
- - MPI
- - Scotch
-
-To use the static or implicit dynamic solvers at least one of the following libraries is needed:
-
- - MUMPS (since this is usually compiled in static you also need MUMPS dependencies)
- - PETSc
-
-To compile the tests and examples:
-
- - Gmsh
- - google-test (if not present the build system will try to download it)
-If compilation does not work change the path of the failing libraries to brew downloads in `/opt/homebrew/`.
-
-Using the python interface
---------------------------
-
-You can install ``Akantu`` using pip, this will install a pre-compiled version, this works only on Linux machines for now::
-
- > pip install akantu
-
-You can then import the package in a python script as::
-
- import akantu
-
-The python API is similar to the C++ one, see :ref:`reference` . If you encouter any problem with the python interface, you are welcome to do a merge request or post an issue on `GitLab <https://gitlab.com/akantu/akantu/-/issues>`_ .
-
-Tutorials with the python interface
-```````````````````````````````````
-
-To help getting started, several tutorials using the python interface
-are available as notebooks with pre-installed version of ``Akantu`` on Renku.
\Delta {\boldsymbol{\varepsilon}}^p = \Delta p \frac {\partial{f}}{\partial{\boldsymbol{\sigma}}}=\frac{3}{2} \Delta p \frac{{\boldsymbol{\sigma}}^{{\mathrm{tr}}}}{\sigma_{{\mathrm{eff}}}}
In these expressions, the direction of the plastic strain increment (or
With :math:`\kappa_0` the damage threshold, :math:`A_t` and :math:`B_t`
the damage parameter in traction, :math:`A_c` and :math:`B_c` the damage
parameter in compression, :math:`\beta` is the shear parameter.
:math:`\alpha_t` is the coupling parameter between traction and
compression, the :math:`\varepsilon_i` are the eigenstrain and the
:math:`\varepsilon_{{\mathrm{nd}}\;i}` are the eigenvalues of the strain
if the material were undamaged.
The coefficients :math:`A` and :math:`B` are the post-peak asymptotic
value and the decay shape parameters.
.. _sect:smm:CLNL:
Non-Local Constitutive Laws
-```````````````````````````
+'''''''''''''''''''''''''''
Continuum damage modeling of quasi-brittle materials undergo significant
softening after the onset of damage. This fast growth of damage causes a loss of
ellipticity of partial differential equations of equilibrium. Therefore, the
numerical simulation results won't be objective anymore, because the dissipated
energy will depend on mesh size used in the simulation. One way to avoid this
effect is the use of non-local damage formulations. In this approach a local
quantity such as the strain is replaced by its non-local average, where the size
of the domain, over which the quantitiy is averaged, depends on the underlying
material microstructure. ``Akantu`` provides non-local versions of many
constitutive laws for damage. Examples are for instance the material
:ref:`sect-smm-cl-damage-mazars` and the material
:ref:`sect-smm-cl-damage-marigo`, that can be used in a non-local context. In
order to use the corresponding non-local formulation the user has to define the
non-local material he wishes to use in the text input file:
.. code-block:: none
material constitutive_law_non_local [
name = material_name
rho = $value$
...
]
where ``constitutive_law_non_local`` is the name of the non-local constitutive law, *e.g.* `marigo_non_local`.
In addition to the material the non-local neighborhood, that should be used for the averaging process needs to be defined in the material file as well:
for the non-local averaging, *e.g.* ``base_wf``, followed by the properties of the non-local neighborhood, such as the radius, and the weight function parameters. It is important to notice that the non-local neighborhood must have the same name as the material to which the neighborhood belongs!
The following two sections list the non-local constitutive laws and different type of weight functions available in ``Akantu``.
\subsection{Non-local constitutive laws}
Let us consider a body having a volume :math:`V` and a boundary :math:`\Gamma`. The stress-strain relation for a non-local damage model can be described as follows:
with :math:`\vec{D}` the elastic moduli tensor, :math:`\sigma` the stress tensor, :math:`\epsilon` the strain tensor and :math:`\bar{d}` the non-local damage variable. Note that this stres-strain relationship is similar to the relationship defined in Damage model except :math:`\bar{d}`. The non-local damage model can be extended to the damage constitutive laws: :ref:`sect-smm-cl-damage-marigo` and :ref:`sect-smm-cl-damage-mazars`.
The non-local damage variable :math:`\bar{d}` is defined as follows:
with :math:`W(\vec{x},\vec{y})` the weight function which averages local damage variables to describe the non-local interactions. A list of available weight functions and its functionalities in \akantu are explained in the next section.
Non-local weight functions
-''''''''''''''''''''''''''
+""""""""""""""""""""""""""
The available weight functions in ``Akantu`` are follows:
- ``base_weight_function``: This weight function averages local damage variables by using a bell-shape function on spatial dimensions.
- ``damaged_weight_function``: A linear-shape weight function is applied to average local damage variables. Its slope is determined by damage variables. For example, the damage variables for an element which is highly damaged are averaged over large spatial dimension (linear function including a small slope).
- ``remove_damaged_weight_function``: This weight function averages damage values by using a bell-shape function as ``base_weight_function``, but excludes elements which are fully damaged.
- ``remove_damaged_with_damage_rate_weight_function``: A bell-shape function is applied to average local damage variables for elements having small damage rates.
- ``stress_based_weight_function``: Non local integral takes stress states, and use the states to construct weight function: an ellipsoid shape. Detailed explanations of this weight function are given in Giry et al. :cite:`giry13a`.
with :math:`\vec{Q}^{\text{ext}}` the consistent heat generated.
+The diffusion model is meant as a base to implement different diffusive processes, heat diffusion, chemical diffusion, simple flow problems, etc. Currently only one of this physics is implemented, the heat diffusion, in a model named HeatTransferModel
+
+.. _sect-dm-using:
+
Using the Heat Transfer Model
------------------------------
+`````````````````````````````
A material file name has to be provided during initialization.
Currently, the :cpp:class:`HeatTransferModel <akantu::HeatTransferModel>` object uses dynamic analysis
with an explicit time integration scheme. It can simply be created
like this
.. code-block:: c++
HeatTransferModel model(mesh, spatial_dimension);
while an existing mesh has been used (see \ref{sect:common:mesh}).
Then the model object can be initialized with:
.. code-block:: c++
model.initFull()
This function will load the material properties, and allocate / initialize the nodes and element :cpp:class:`Arrays <akantu::Array>`
More precisely, the heat transfer model contains 4 :cpp:class:`Arrays <akantu::Array>`:
- **temperature** contains the nodal temperature :math:`T` (zero by default after the initialization).
- **temperature_rate** contains the variations of temperature :math:`\dot{T}` (zero by default after the initialization).
- **blocked_dofs** contains a Boolean value for each degree of freedom specifying whether the degree is blocked or not. A Dirichlet boundary condition (:math:`T_d`) can be prescribed by setting the **blocked_dofs** value of a degree of freedom to ``true``. The **temperature** and the **temperature_rate** are computed for all degrees of freedom where the **blocked_dofs** value is set to ``false``. For the remaining degrees of freedom, the imposed values (zero by default after initialization) are kept.
- **external_heat_rate** contains the external heat generations. :math:`\vec{Q^{ext}}` on the nodes.
- **internal_heat_rate** contains the internal heat generations. :math:`\vec{Q^{int}} = -\mat{K} \cdot \vec{T}` on the nodes.
Only a single material can be specified on the domain. A material text file (*e.g.* material.dat) provides the material properties as follows:
.. code-block:: python
model heat_transfer_model [
- capacity = %\emph{XXX}%
- density = %\emph{XXX}%
- conductivity = [%\emph{XXX}% ... %\emph{XXX}%]
+ constitutive_law heat_diffusion [
+ name = %\emph{XXX}%
+ capacity = %\emph{XXX}%
+ density = %\emph{XXX}%
+ conductivity = [%\emph{XXX}% ... %\emph{XXX}%]
+ ]
]
-where the ``capacity`` and ``density`` are scalars, and the ``conductivity`` is specified as a :math:`3\times 3` tensor.
+where the ``capacity`` and ``density`` are scalars, and the ``conductivity`` is
+specified as a :math:`3\times 3` tensor.
Explicit Dynamic
-----------------
+````````````````
-The explicit time integration scheme in ``Akantu`` uses a lumped capacity
-matrix :math:`\mat{C}` (reducing the computational cost, see Chapter :ref:`sect-smm`).
-This matrix is assembled by distributing the capacity of each element onto its nodes. Therefore, the resulting :math:`\mat{C}` is a diagonal matrix stored in the ``capacity`` :cpp:class:`Array <akantu::Array>` of the model.
+The explicit time integration scheme in ``Akantu`` uses a lumped capacity matrix
+:math:`\mat{C}` (reducing the computational cost, see Chapter :ref:`sect-smm`).
+This matrix is assembled by distributing the capacity of each element onto its
+nodes. Therefore, the resulting :math:`\mat{C}` is a diagonal matrix stored in
+the ``capacity`` :cpp:class:`Array <akantu::Array>` of the model.
.. code-block:: c++
model.assembleCapacityLumped();
.. note::
Currently, only the explicit time integration with lumped capacity
matrix is implemented within ``Akantu``.
The explicit integration scheme is *Forward Euler* :cite:`curnier92a`.
- Predictor: :math:`\vec{T}_{n+1} = \vec{T}_{n} + \Delta t \dot{\vec{T}}_{n}`
Any contribution is welcome, we are trying to follow a `gitflow <https://nvie.com/posts/a-successful-git-branching-model/>`_ workflow, so the project `developers` can create branches named `features/<name of my feature>` or `bugfixes/<name of the fix>` directly in the main `akantu` repository.
External fellows can `Fork <https://gitlab.com/akantu/akantu/-/forks/new>`_ the project.
In both cases the modifications have to be submitted in the form of a `Merge Request <https://gitlab.com/akantu/akantu/-/merge_requests/new>`_.
Asking for help, reporting issues
`````````````````````````````````
If you want to ask for help concerning Akantu's compilation, usage or problem with the code do not hesitate to open an `Issue <https://gitlab.com/akantu/akantu/-/issues/new>`_ on gitlab. If you want to contribute and don't know where to start, you are also invited to open an issue.
Building ``Akantu``
--------------------
Dependencies
````````````
In order to compile ``Akantu`` any compiler supporting fully C++14 should work.
In addition some libraries are required:
- CMake (>= 3.5.1)
- Boost (pre-processor and Spirit)
- - zlib
- Eigen3 (if not present the build system will try to download it)
For the python interface:
- Python (>=3 is recommended)
- pybind11 (if not present the build system will try to download it)
To run parallel simulations:
- MPI
- Scotch
To use the static or implicit dynamic solvers at least one of the following libraries is needed:
- MUMPS (since this is usually compiled in static you also need MUMPS dependencies)
- PETSc
To compile the tests and examples:
- Gmsh
- google-test (if not present the build system will try to download it)
If compilation does not work change the path of the failing libraries to brew downloads in `/opt/homebrew/`.
Using the python interface
--------------------------
You can install ``Akantu`` using pip, this will install a pre-compiled version, this works only on Linux machines for now::
> pip install akantu
You can then import the package in a python script as::
import akantu
The python API is similar to the C++ one, see :ref:`reference` . If you encouter any problem with the python interface, you are welcome to do a merge request or post an issue on `GitLab <https://gitlab.com/akantu/akantu/-/issues>`_ .
Tutorials with the python interface
```````````````````````````````````
To help getting started, several tutorials using the python interface
are available as notebooks with pre-installed version of ``Akantu`` on Renku.
This model contains at least the following :cpp:class:`Arrays <akantu::Arrays>`:
- **blocked_dofs** contains a Boolean value for each degree of
freedom specifying whether that degree is blocked or not. A
Dirichlet boundary condition can be prescribed by setting the
**blocked_dofs** value of a degree of freedom to
``true``. The **displacement** is computed for all degrees
of freedom for which the **blocked_dofs** value is set to
``false``. For the remaining degrees of freedom, the imposed
values (zero by default after initialization) are kept.
- **displacement_rotation** contains the generalized displacements (*i.e.* displacements and rotations) of all degrees of freedom. It can be either a computed displacement for free degrees of freedom or an imposed displacement in case of blocked ones (:math:`\vec{u}` in the following).
- **external_force** contains the generalized external forces (forces and moments) applied to the nodes (:math:`\vec{f_{\st{ext}}}` in the following).
- **internal_force** contains the generalized internal forces (forces and moments) applied to the nodes (:math:`\vec{f_{\st{int}}}` in the following).
An example to help understand how to use this model will be presented in the
next section.
.. _sec:structMechMod:setup:
Model Setup
------------
+```````````
Initialization
-``````````````
+''''''''''''''
The easiest way to initialize the structural mechanics model is:
.. code-block:: c++
model.initFull();
The method :cpp:class:`initFull <akantu::StructuralMechanicsModel::initFull>` computes the shape
functions, initializes the internal vectors mentioned above and allocates the
memory for the stiffness matrix, unlike the solid mechanics model, its default
argument is ``_static``.
Material properties are defined using the :cpp:class:`StructuralMaterial
<akantu::StructuralMaterial>` structure described in
:numref:`tab-structmechmod-strucmaterial`. Such a definition could, for
instance, look like
.. code-block:: c++
StructuralMaterial mat1;
mat.E=3e10;
mat.I=0.0025;
mat.A=0.01;
.. _tab-structmechmod-strucmaterial:
.. table:: Material properties for structural elements defined in the class :cpp:class:`StructuralMaterial <akantu::StructuralMaterial>`.
:align: center
====== ======
Field Description
====== ======
``E`` Young's modulus
``A`` Cross section area
``I`` Second cross sectional moment of inertia (for 2D elements)
``Iy`` ``I`` around beam :math:`y`--axis (for 3D elements)
``Iz`` ``I`` around beam :math:`z`--axis (for 3D elements)
``GJ`` Polar moment of inertia of beam cross section (for 3D elements)
====== ======
Materials can be added to the model's ``element_material`` vector using
.. code-block:: c++
model.addMaterial(mat1);
They are successively numbered and then assigned to specific elements.
As explained before, the Dirichlet boundary conditions are applied through the
array **blocked_dofs**. Two options exist to define Neumann conditions.
If a nodal force is applied, it has to be directly set in the array
**force_momentum**. For loads distributed along the beam length, the
method :cpp:class:`computeForcesFromFunction <akantu::computeForcesFromFunction>` integrates them into nodal forces. The
method takes as input a function describing the distribution of loads along the
beam and a functor :cpp:class:`BoundaryFunctionType <akantu::BoundaryFunctionType>` specifing if the function is expressed in the local coordinates (``_bft_traction_local``) or in the
The :cpp:class:`StructuralMechanicsModel <akantu::StructuralMechanicsModel>` class can perform static analyses of structures. In this case, the equation to solve is the same as for the :cpp:class:`SolidMechanicsModel <akantu::SolidMechanicsModel>` used for static analyses
.. math:: \mat{K} \vec{u} = \vec{f_{\st{ext}}}~,
:label: eqn-structmechmod-static
where :math:`\mat{K}` is the global stiffness matrix, :math:`\vec{u}` the
generalized displacement vector and :math:`\vec{f_{\st{ext}}}` the vector of
generalized external forces applied to the system.
is used. First a model has to be created and initialized.
.. code-block:: c++
StructuralMechanicsModel model(mesh);
model.initFull();
- :cpp:func:`model.initFull <akantu::StructuralMechanicsModel::initFull>` initializes all
internal vectors to zero.
Once the model is created and initialized, the boundary conditions can be set as explained in Section :ref:`sect:structMechMod:boundary`. Boundary conditions will prescribe the external forces or moments for the free degrees of freedom :math:`\vec{f_{\st{ext}}}` and displacements or rotations for the others. To completely define the system represented by equation (:eq:`eqn-structmechmod-static`), the global stiffness matrix :math:`\mat{K}` must be assembled.
.. code-block:: c++
model.assembleStiffnessMatrix();
The computation of the static equilibrium is performed using the same
+`contact_explicit_static` and `contact_explicit_dynamic` are solving a 2D Hertz contact patch test using the ``CouplerSolidContact``.
+The two examples follow what is described extensively in section :ref:`sect-cmm-coupling-with-smm`. The only main difference between `contact_explicit_static` and `contact_explicit_dynamic` is the solver used::
+The ``material.dat`` file contain a ``contact_detector`` and a ``contact_resolution penalty_linear`` section as explains in section :ref:`sect-cmm-contact-detection`.
+In ``heat_diffusion_dynamics_2d.cc``, the same example is solved dynamically
+using an explicit time scheme. The time step used is :math:`0.12 \text{s}`. The only main difference with the previous example lies in the model initiation::
+In ``heat_diffusion_dynamics_3d.cc``, a 3D explicit dynamic heat propagation
+problem is solved. It consists of a cube having an initial temperature of
+:math:`100 \text{K}` everywhere but a centered sphere maintained at
+:math:`300 \text{K}`.
+The simulation is set exactly as ``heat_diffusion_dynamics_2d.cc`` except that the mesh is now a 3D mesh and that the heat source has a third coordinate and is placed at the cube center.
+The mesh is initialized with::
+
+ Int spatial_dimension = 3;
+ Mesh mesh(spatial_dimension);
+ mesh.read("cube.msh");
+
+:numref:`fig-ex-diffusion_3d` presents the resulting temperature field evolution.
+`phase_field_notch.cc` shows hot to set a quasi-static fracture simulation with phase-field. The geometry of the solid is a square plate with a notch. The loading is an imposed displacement at the top of the plate (mode I).
+ Notched plate with boundary conditions and imposed displacement.
+
+In addition, this example shows how to extract clusters delimited by the mesh boundaries and elements with damage values beyond a threshold. This can be useful to extract fragments after crack propagation.
+Solid mechanics cohesive model examples are shown in ``solid_mechanics_cohesive_model``. This new model is called in a very similar way as the solid mechanics model::
+
+ SolidMechanicsModelCohesive model(mesh);
+
+Cohesive elements can be inserted intrinsically (when the mesh is generated) or extrinsically (during the simulation).
+During the simulation, stress has to be checked in order to insert cohesive elements where the stress criterion is reached. This check is performed by calling the method ``checkCohesiveStress`` before each step resolution::
+
+ model.checkCohesiveStress();
+ model.solveStep();
+
+For this specific example, a displacement is imposed based on the elements location. The corresponding displacements is shown in :numref:`fig-ex-cohesive-ext`.
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+In ``io/parser``, an example illustrating how to parse an input file with user-defined parameters is shown. As before, the text input file of the simulation is precised using the method ``initialize``. In the input file, additionally to the usual ``material elastic`` section, there is a section ``user parameters`` with extra user-defined parameters.
+Within the main function, those parameters are retrived with::
+In ``io/dumper``, examples of advanced dumping are shown.
+
+``dumper_low_level`` aims at illustrating how to manipulate low-level methods of ``DumperIOHelper``. The goal is to visualize a colorized moving train with Paraview.
+It is shown how to dump only a part of the mesh (here the wheels) using the function ``createElementGroup`` of the mesh object::
+ The wheels and the full train are dumped separately.
+
+``dumpable_interface`` does the same as ``dumper_low_level`` but using ``dumpers::Dumpable`` which is an interface for other classes (Model, Mesh, ...) to dump themselves.
+In ``new_material`` it is shown how to use a user-defined material for the simulation. All the details are described in :ref:`sect-smm-ncl`. The geometry solved is shown in :numref:`fig-ex-new_material`.
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+`phasefield-static.py` shows how to setup a static phase-field fracture simulation. An imposed displacement is imposed on the top of a notched square plate.
+ Notched plate with boundary conditions and imposed displacement.
+
+In static simulations, we use loading steps to apply the displacement incrementally. At each time step, the solvers of the solid mechanics model and the phase-field model are called alternately until convergence is reached.
+`phasefield-dynamic.py` shows how to setup a dynamic phase-field fracture simulation. A notched plate is pre-strained in mode I using Dirichlet BC and a static solve. The simulation is then continued in dynamic using an explicit Neumark scheme.
+In ``custom-material.py`` it is shown how to create a custom material behaviour. In this example, a linear elastic
+material is recreated. It is done by creating a class that inherits from ``aka.Material`` (``LocalElastic(aka.Material)`` in this case) and register it
+This example shows how to create a new functor to set the boundary conditions. This is done by creating a class that inherits from ``aka.FixedValue`` (``MyFixedValue(aka.FixedValue)`` in this case).
+In ``eigen_modes`` it is shown how to compute the eigen modes using the library `scipy.sparse`. The mode can be specify with the ``-m`` argument. Simulation is performed on a bar where a pulse is imposed.
+The ``-p`` argument will plot the following figures :numref:`fig-ex-eigen`:
+In ``plate_hole``, an example of a static solution of a loaded plate with a hole. Because of the symmetries, only a quarter of the problem is modeled. The corresponding domain and boundary conditions is shown in :numref:`fig-ex-plate_hole`.
+common/non_local_toolbox/neighborhoods_criterion_evaluation/neighborhood_max_criterion_inline_impl.hh: auto nb_quadrature_points = this->model.getNbIntegrationPoints(elements);
+solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_intersector.cc: auto segment = this->createSegment(el_connectivity);
+solid_mechanics/solid_mechanics_model_embedded_interface/embedded_interface_intersector.cc: for (auto type : this->mesh.elementTypes(dim, _not_ghost)) {
+solid_mechanics/materials/material_finite_deformation/material_neohookean.cc: for (auto && args : this->getArguments(el_type, ghost_type)) {
+solid_mechanics/materials/material_finite_deformation/material_neohookean.cc: AKANTU_DEBUG_ASSERT(this->plane_stress, "The third component of the strain "
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_inline_impl.hh: if (not this->contact_after_breaking and Math::are_float_equal(damage, 1.)) {
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_inline_impl.hh: if (not this->contact_after_breaking and Math::are_float_equal(damage, 1.)) {
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_inline_impl.hh: Real sigma_c = this->sigma_c;
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_inline_impl.hh: auto && I = Eigen::Matrix<Real, dim, dim>::Identity() * this->beta2_kappa;
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_inline_impl.hh: auto && nn = (n_outer_n * (1. - this->beta2_kappa) + I) * t / delta;
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_inline_impl.hh: auto && mm = opening * this->beta2_kappa2;
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_friction.cc: if (not this->penetration) {
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_friction.cc: Real tau_max = mu * this->penalty * (std::abs(this->normal_opening_norm));
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_friction.cc: if (not this->model->isDefaultSolverExplicit()) {
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_friction.cc: if (not this->penetration) {
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_friction.cc: mu * this->penalty * (std::abs(previous_normal_opening_norm));
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_friction.cc: Real delta_sliding_norm = std::abs(this->tangential_opening_norm -
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_friction.cc: Real tau = std::min(this->friction_penalty * delta_sliding_norm, tau_max);
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_bilinear.cc: if (!Math::are_float_equal(this->volume_s, 0.)) {
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_bilinear.cc: auto nb_quad_per_element = this->fem_cohesive.getNbIntegrationPoints(type);
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_bilinear.cc: auto base_sigma_c = Real(this->sigma_c_eff);
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_bilinear.cc: const auto & mesh_facets = this->model->getMeshFacets();
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_bilinear.cc: const auto & fe_engine = this->model->getFEEngine();
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_bilinear.cc: for (auto && data : zip(this->damage(el_type, ghost_type),
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_fatigue.cc: if (not this->contact_after_breaking and
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_uncoupled.cc: if (not this->contact_after_breaking and
+solid_mechanics/solid_mechanics_model_cohesive/materials/constitutive_laws/material_cohesive_linear_uncoupled.cc: if (not this->contact_after_breaking and
+solid_mechanics/materials/material_viscoelastic/material_standard_linear_solid_deviatoric.cc: stress_dev(this->registerInternal("stress_dev", dim * dim)),
+solid_mechanics/materials/material_viscoelastic/material_standard_linear_solid_deviatoric.cc: history_integral(this->registerInternal("history_integral", dim * dim)),
+solid_mechanics/materials/material_viscoelastic/material_standard_linear_solid_deviatoric.cc: auto & fem = this->getFEEngine();
+solid_mechanics/materials/material_viscoelastic/material_standard_linear_solid_deviatoric.cc: for (auto && type : this->getElementFilter().elementTypes(dim, _not_ghost)) {
+solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.cc: for (const auto & el_type : this->getElementFilter().elementTypes()) {
+solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.cc: Real dt = this->getModel().getTimeStep();
+solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.cc: auto & fem = this->getFEEngine();
+solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.cc: for (auto && type : this->getElementFilter().elementTypes(dim, _not_ghost)) {
+solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.cc: de += fem.integrate(this->dissipated_energy(type, _not_ghost), type,
+solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.cc: auto & fem = this->getFEEngine();
+solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.cc: auto it = make_view(this->mechanical_work(element.type), nb_quadrature_points)
+solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.cc: auto & fem = this->getFEEngine();
+solid_mechanics/materials/material_viscoelastic/material_viscoelastic_maxwell.cc: for (auto && type : this->getElementFilter().elementTypes(dim, _not_ghost)) {
- * Akantu is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
- *
- * Akantu is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.
- *
- * You should have received a copy of the GNU Lesser General Public License along with Akantu. If not, see <http://www.gnu.org/licenses/>.