adtzlr · adtzlr · Nov 3, 2024 · Nov 3, 2024 · Nov 3, 2024 · Nov 3, 2024
diff --git a/CHANGELOG.md b/CHANGELOG.md
@@ -12,7 +12,8 @@ All notable changes to this project will be documented in this file. The format
 - Add `math.inplane(A, vectors)` to return the in-plane components of a symmetric tensor `A`, where the plane is defined by its standard unit vectors.
 - Add `constitution.jax.Hyperelastic` as a feature-equivalent alternative to `Hyperelastic` with `jax` as backend.
 - Add `constitution.jax.Material` as a feature-equivalent alternative to `MaterialAD` with `jax` as backend.
-- Add the MORPH-material formulation for a JAX-based material `felupe.constitution.jax.models.lagrange.morph()`.
+- Add the material models for JAX-based materials `felupe.constitution.jax.models.hyperelastic.mooney_rivlin()`, `felupe.constitution.jax.models.hyperelastic.yeoh()`, `felupe.constitution.jax.models.hyperelastic.third_order_deformation()` and `felupe.constitution.jax.models.lagrange.morph()`.
+- Add `felupe.constitution.jax.total_lagrange()` and `felupe.constitution.jax.updated_lagrange()` function decorators for JAX materials.
 
 ### Changed
 - Change default `np.einsum(..., order="K")` to `np.einsum(..., order="C")` in the methods of `Field`, `FieldAxisymmetric`, `FieldPlaneStrain` and `FieldContainer`.

diff --git a/docs/felupe/constitution/autodiff/jax.rst b/docs/felupe/constitution/autodiff/jax.rst
@@ -13,6 +13,18 @@ This page contains material model formulations with automatic differentiation us
 
    constitution.jax.Hyperelastic
    constitution.jax.Material
+   constitution.jax.total_lagrange
+   constitution.jax.updated_lagrange
+
+**Material Models for** :class:`felupe.constitution.jax.Hyperelastic`
+
+These material model formulations are defined by a strain energy density function.
+
+.. autosummary::
+
+   felupe.constitution.jax.models.hyperelastic.mooney_rivlin
+   felupe.constitution.jax.models.hyperelastic.third_order_deformation
+   felupe.constitution.jax.models.hyperelastic.yeoh
 
 **Material Models for** :class:`felupe.constitution.jax.Material`
 
@@ -38,6 +50,16 @@ This page contains material model formulations with automatic differentiation us
    :undoc-members:
    :inherited-members:
 
+.. autofunction:: felupe.constitution.jax.total_lagrange
+
+.. autofunction:: felupe.constitution.jax.updated_lagrange
+
+.. autofunction:: felupe.constitution.jax.models.hyperelastic.mooney_rivlin
+
+.. autofunction:: felupe.constitution.jax.models.hyperelastic.third_order_deformation
+
+.. autofunction:: felupe.constitution.jax.models.hyperelastic.yeoh
+
 .. autofunction:: felupe.constitution.jax.models.lagrange.morph
 
 .. autofunction:: felupe.constitution.jax.vmap
diff --git a/docs/tutorial/examples/extut01_getting_started.py b/docs/tutorial/examples/extut01_getting_started.py
@@ -24,6 +24,7 @@
 created on the mesh. A vector-valued displacement field is initiated on the region.
 Next, a field container is created on top of the displacement field.
 """
+
 import felupe as fem
 
 mesh = fem.Cube(n=6)

diff --git a/docs/tutorial/examples/extut02_job.py b/docs/tutorial/examples/extut02_job.py
@@ -22,6 +22,7 @@
 argument of the (nearly) incompressible solid body instead of the constitutive
 Neo-Hookean material definition.
 """
+
 import felupe as fem
 
 mesh = fem.Cube(n=6)

diff --git a/docs/tutorial/examples/extut03_building_blocks.py b/docs/tutorial/examples/extut03_building_blocks.py
@@ -23,6 +23,7 @@
 .. image:: examples/extut03_building_blocks_sketch.svg
    :width: 600px
 """
+
 # sphinx_gallery_thumbnail_number = -1
 import felupe as fem
 

diff --git a/examples/ex02_plate-with-hole.py b/examples/ex02_plate-with-hole.py
@@ -21,6 +21,7 @@
 .. image:: ../../examples/ex02_plate-with-hole_sketch.svg
    :width: 400px
 """
+
 # sphinx_gallery_thumbnail_number = -2
 h = 1
 L = 2

diff --git a/examples/ex03_plasticity.py b/examples/ex03_plasticity.py
@@ -22,6 +22,7 @@
 per axis. A three-dimensional vector-valued displacement field is initiated on the
 numeric region.
 """
+
 import numpy as np
 
 import felupe as fem

diff --git a/examples/ex04_balloon.py b/examples/ex04_balloon.py
@@ -39,6 +39,7 @@
        \text{tr}(\boldsymbol{C}) - \ln(\det(\boldsymbol{C})) 
    \right)
 """
+
 # sphinx_gallery_thumbnail_number = -1
 import contique
 import numpy as np

diff --git a/examples/ex05_rubber-metal-bushing.py b/examples/ex05_rubber-metal-bushing.py
@@ -24,6 +24,7 @@
 An elastic bearing is subjected to combined multiaxial radial-torsional-cardanic
 loading. First the meshes for the rubber and the metal sheet rings are created.
 """
+
 # sphinx_gallery_thumbnail_number = -2
 import numpy as np
 import pypardiso

diff --git a/examples/ex06_rubber-metal-spring.py b/examples/ex06_rubber-metal-spring.py
@@ -24,6 +24,7 @@
 Simplified elastic-to-rigid contact definitions simulate the end stops caused by steel
 plates at the bottom and the top in direction :math:`z`.
 """
+
 # sphinx_gallery_thumbnail_number = -3
 import numpy as np
 import pypardiso

diff --git a/examples/ex07_engine-mount.py b/examples/ex07_engine-mount.py
@@ -29,6 +29,7 @@
 * a `mesh for the air <../_static/ex07_engine-mount_mesh-air.vtk>`_ inside the
   engine mount.
 """
+
 # sphinx_gallery_thumbnail_number = -1
 import numpy as np
 

diff --git a/examples/ex08_shear.py b/examples/ex08_shear.py
@@ -37,6 +37,7 @@
 :attr:`Mesh.points_without_cells` and adds them to the list of inactive
 degrees of freedom. Hence, we have to drop our MPC-centerpoint from that list.
 """
+
 # sphinx_gallery_thumbnail_number = -2
 import numpy as np
 

diff --git a/examples/ex11_notch-stress.py b/examples/ex11_notch-stress.py
@@ -26,6 +26,7 @@
 implemented and hence, the quadratic wedges in the mesh are converted to quadratic
 hexahedrons.
 """
+
 # sphinx_gallery_thumbnail_number = -1
 import numpy as np
 import pypardiso

diff --git a/examples/ex13_morph-rubber-wheel.py b/examples/ex13_morph-rubber-wheel.py
@@ -96,6 +96,7 @@
     variables are stored in the solid body.
 
 """
+
 # sphinx_gallery_thumbnail_number = -1
 # sphinx_gallery_start_ignore
 PYVISTA_GALLERY_FORCE_STATIC_IN_DOCUMENT = True

diff --git a/examples/ex14_hyperelasticity.py b/examples/ex14_hyperelasticity.py
@@ -13,6 +13,7 @@
 The :func:`Extended Tube <felupe.extended_tube>` material model formulation [1]_ is
 best-fitted on Treloar's uniaxial and biaxial tension data [2]_.
 """
+
 import numpy as np
 import tensortrax.math as tm
 

diff --git a/examples/ex15_hexmesh-metacone.py b/examples/ex15_hexmesh-metacone.py
@@ -8,6 +8,7 @@
 
    * create a :class:`~felupe.MeshContainer` for meshes associated to two materials
 """
+
 import numpy as np
 
 import felupe as fem

diff --git a/examples/ex16_deeplearning-torch.py b/examples/ex16_deeplearning-torch.py
@@ -22,6 +22,7 @@
 
       pip install torch
 """
+
 # sphinx_gallery_thumbnail_number = -1
 import numpy as np
 

diff --git a/examples/ex20_third-medium-contact.py b/examples/ex20_third-medium-contact.py
@@ -15,6 +15,7 @@
 body. All sub meshes are merged by stacking the meshes of the
 :class:`mesh container <felupe.MeshContainer>` into a :class:`mesh <felupe.Mesh>`.
 """
+
 import numpy as np
 
 import felupe as fem

diff --git a/src/felupe/constitution/jax/__init__.py b/src/felupe/constitution/jax/__init__.py
@@ -2,5 +2,14 @@
 from ._hyperelastic import Hyperelastic
 from ._material import Material
 from ._tools import vmap
+from ._total_lagrange import total_lagrange
+from ._updated_lagrange import updated_lagrange
 
-__all__ = ["Hyperelastic", "Material", "models", "vmap"]
+__all__ = [
+    "Hyperelastic",
+    "Material",
+    "models",
+    "total_lagrange",
+    "updated_lagrange",
+    "vmap",
+]
diff --git a/src/felupe/constitution/jax/_total_lagrange.py b/src/felupe/constitution/jax/_total_lagrange.py
@@ -0,0 +1,78 @@
+# -*- coding: utf-8 -*-
+"""
+This file is part of FElupe.
+
+FElupe is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+FElupe 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 General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with FElupe.  If not, see <http://www.gnu.org/licenses/>.
+"""
+from functools import wraps
+
+
+def total_lagrange(material):
+    r"""Decorate a second Piola-Kirchhoff stress Total-Lagrange material formulation as
+    a first Piola-Kirchoff stress function.
+
+    Notes
+    -----
+    ..  math::
+
+        \delta \psi = \boldsymbol{F} \boldsymbol{S} : \delta \boldsymbol{F}
+
+    Examples
+    --------
+    >>> import felupe as fem
+    >>> import felupe.constitution.jax as mat
+    >>> import jax.numpy as jnp
+    >>>
+    >>> @mat.total_lagrange
+    >>> def neo_hooke_total_lagrange(F, mu=1):
+    >>>     C = F.T @ F
+    >>>     dev = lambda C: C - jnp.trace(C) / 3 * jnp.eye(3)
+    >>>     S = mu * dev(jnp.linalg.det(C)**(-1/3) * C) @ jnp.linalg.inv(C)
+    >>>     return S
+    >>>
+    >>> umat = mat.Material(neo_hooke_total_lagrange, mu=1)
+
+    See Also
+    --------
+    felupe.constitution.jax.Hyperelastic : A hyperelastic material definition with a
+        given function for the strain energy density function per unit undeformed volume
+        with Automatic Differentiation provided by jax.
+    felupe.constitution.jax.Material : A material definition with a given function for
+        the partial derivative of the strain energy function w.r.t. the deformation
+        gradient tensor with Automatic Differentiation provided by jax.
+    """
+    from jax import Array
+
+    @wraps(material)
+    def first_piola_kirchhoff_stress(F, *args, **kwargs):
+        # evaluate the second Piola-Kirchhoff stress
+        res = material(F, *args, **kwargs)
+
+        # check if the material formulation returns state variables and extract
+        # the second Piola-Kirchhoff stress tensor
+        if isinstance(res, Array):
+            S = res
+            statevars_new = None
+        else:
+            S, statevars_new = res
+
+        # first Piola-Kirchhoff stress tensor
+        P = F @ S
+
+        if statevars_new is None:
+            return P
+        else:
+            return P, statevars_new
+
+    return first_piola_kirchhoff_stress
diff --git a/src/felupe/constitution/jax/_updated_lagrange.py b/src/felupe/constitution/jax/_updated_lagrange.py
@@ -0,0 +1,81 @@
+# -*- coding: utf-8 -*-
+"""
+This file is part of FElupe.
+
+FElupe is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+FElupe 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 General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with FElupe.  If not, see <http://www.gnu.org/licenses/>.
+"""
+from functools import wraps
+
+
+def updated_lagrange(material):
+    r"""Decorate a Cauchy-stress Updated-Lagrange material formulation as a first Piola-
+    Kirchoff stress function.
+
+    Notes
+    -----
+    ..  math::
+
+        \delta \psi =  J \boldsymbol{\sigma} \boldsymbol{F}^{-T} : \delta \boldsymbol{F}
+
+    Examples
+    --------
+    >>> import felupe as fem
+    >>> import felupe.constitution.jax as mat
+    >>> import jax.numpy as jnp
+    >>>
+    >>> @fem.updated_lagrange
+    >>> def neo_hooke_updated_lagrange(F, mu=1):
+    >>>     J = jnp.linalg.det(F)
+    >>>     b = F @ F.T
+    >>>     dev = lambda b: b - jnp.trace(b) / 3 * jnp.eye(3)
+    >>>     τ = mu * dev(J**(-2/3) * b)
+    >>>     return τ / J
+    >>>
+    >>> umat = mat.Material(neo_hooke_updated_lagrange, mu=1)
+
+    See Also
+    --------
+    felupe.constitution.jax.Hyperelastic : A hyperelastic material definition with a
+        given function for the strain energy density function per unit undeformed volume
+        with Automatic Differentiation provided by jax.
+    felupe.constitution.jax.Material : A material definition with a given function for
+        the partial derivative of the strain energy function w.r.t. the deformation
+        gradient tensor with Automatic Differentiation provided by jax.
+    """
+    import jax.numpy as jnp
+    from jax import Array
+
+    @wraps(material)
+    def first_piola_kirchhoff_stress(F, *args, **kwargs):
+        # evaluate the Cauchy stress
+        res = material(F, *args, **kwargs)
+
+        # check if the material formulation returns state variables and extract
+        # the Cauchy stress tensor
+        if isinstance(res, Array):
+            σ = res
+            statevars_new = None
+        else:
+            σ, statevars_new = res
+
+        # first Piola-Kirchhoff stress tensor
+        J = jnp.linalg.det(F)
+        P = J * σ @ jnp.linalg.inv(F).T
+
+        if statevars_new is None:
+            return P
+        else:
+            return P, statevars_new
+
+    return first_piola_kirchhoff_stress
diff --git a/src/felupe/constitution/jax/models/hyperelastic/__init__.py b/src/felupe/constitution/jax/models/hyperelastic/__init__.py
@@ -0,0 +1,9 @@
+from ._mooney_rivlin import mooney_rivlin
+from ._third_order_deformation import third_order_deformation
+from ._yeoh import yeoh
+
+__all__ = [
+    "mooney_rivlin",
+    "third_order_deformation",
+    "yeoh",
+]
diff --git a/src/felupe/constitution/jax/models/hyperelastic/_mooney_rivlin.py b/src/felupe/constitution/jax/models/hyperelastic/_mooney_rivlin.py
@@ -0,0 +1,31 @@
+# -*- coding: utf-8 -*-
+"""
+This file is part of FElupe.
+
+FElupe is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+FElupe 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 General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with FElupe.  If not, see <http://www.gnu.org/licenses/>.
+"""
+from functools import wraps
+
+from ....tensortrax.models.hyperelastic import mooney_rivlin as mooney_rivlin_docstring
+
+
+@wraps(mooney_rivlin_docstring)
+def mooney_rivlin(C, C10, C01):
+    from jax.numpy import trace
+    from jax.numpy.linalg import det
+
+    J3 = det(C) ** (-1 / 3)
+    I1 = J3 * trace(C)
+    I2 = (I1**2 - J3**2 * trace(C @ C)) / 2
+    return C10 * (I1 - 3) + C01 * (I2 - 3)
-Original file line number
+Diff line change
@@ Expand Up / @@ -21,6 +21,7 @@ @@
     .. image:: ../../examples/ex02_plate-with-hole_sketch.svg
        :width: 400px
     """
     # sphinx_gallery_thumbnail_number = -2
     h = 1
     L = 2
@@ Expand Down @@