Add the Van-der-Waals model for JAX

docs/felupe/constitution/autodiff/jax.rst

@@ -52,6 +52,7 @@ These material model formulations are defined by a strain energy density functio
    mooney_rivlin
    storakers
    third_order_deformation
+   van_der_waals
    yeoh
 
 **Material Models for** :class:`felupe.constitution.jax.Material`
@@ -101,6 +102,8 @@ formulations in :class:`~felupe.constitution.jax.Material`.
 
 .. autofunction:: felupe.constitution.jax.models.hyperelastic.third_order_deformation
 
+.. autofunction:: felupe.constitution.jax.models.hyperelastic.van_der_waals
+
 .. autofunction:: felupe.constitution.jax.models.hyperelastic.yeoh
 
 .. autofunction:: felupe.constitution.jax.models.lagrange.morph

src/felupe/constitution/jax/models/hyperelastic/__init__.py

@@ -3,6 +3,7 @@
 from ._mooney_rivlin import mooney_rivlin
 from ._storakers import storakers
 from ._third_order_deformation import third_order_deformation
+from ._van_der_waals import van_der_waals
 from ._yeoh import yeoh
 
 __all__ = [
@@ -11,6 +12,7 @@
     "mooney_rivlin",
     "storakers",
     "third_order_deformation",
+    "van_der_waals",
     "yeoh",
 ]
 
@@ -20,4 +22,5 @@
 mooney_rivlin.kwargs = dict(C10=0, C01=0)
 storakers.kwargs = dict(mu=[0], alpha=[2], beta=[1])
 third_order_deformation.kwargs = dict(C10=0, C01=0, C11=0, C20=0, C30=0)
+van_der_waals.kwargs = dict(mu=0, beta=0, a=0, limit=100)
 yeoh.kwargs = dict(C10=0, C20=0, C30=0)

src/felupe/constitution/jax/models/hyperelastic/_van_der_waals.py

@@ -0,0 +1,37 @@
+# -*- 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 jax.lax import select
+from jax.numpy import isclose, log, sqrt, trace
+from jax.numpy.linalg import det
+
+from ....tensortrax.models.hyperelastic import van_der_waals as van_der_waals_docstring
+
+
+@wraps(van_der_waals_docstring)
+def van_der_waals(C, mu, limit, a, beta):
+    J3 = det(C) ** (-1 / 3)
+    I1 = J3 * trace(C)
+    I2 = (trace(C) ** 2 - J3**2 * trace(C @ C)) / 2
+    Im = (1 - beta) * I1 + beta * I2
+    Im = select(isclose(Im, 3), Im + 1e-6, Im)
+    eta = sqrt((Im - 3) / (limit**2 - 3))
+    return mu * (
+        -(limit**2 - 3) * (log(1 - eta) + eta) - 2 / 3 * a * ((Im - 3) / 2) ** (3 / 2)
+    )

src/felupe/constitution/tensortrax/models/hyperelastic/_van_der_waals.py

@@ -24,11 +24,11 @@
 def van_der_waals(C, mu, limit, a, beta):
     r"""Strain energy function of the
     `Van der Waals <https://doi.org/10.1016/0032-3861(81)90200-7>`_ [1]_ material
-    formulation.,
+    formulation.
 
     Parameters
     ----------
-    C : tensortrax.Tensor
+    C : tensortrax.Tensor or jax.Array
         Right Cauchy-Green deformation tensor.
     mu : float
         Initial shear modulus.
@@ -42,12 +42,22 @@ def van_der_waals(C, mu, limit, a, beta):
 
     Examples
     --------
+    First, choose the desired automatic differentiation backend
+
+    ..  pyvista-plot::
+        :context:
+
+        >>> # import felupe.constitution.jax as mat
+        >>> import felupe.constitution.tensortrax as mat
+
+    and create the hyperelastic material.
+
     ..  pyvista-plot::
         :context:
 
         >>> import felupe as fem
         >>>
-        >>> umat = fem.Hyperelastic(fem.van_der_waals, mu=1.0, beta=0.1, a=0.5, limit=5.0)
+        >>> umat = mat.Hyperelastic(fem.van_der_waals, mu=1.0, beta=0.1, a=0.5, limit=5.0)
         >>> ax = umat.plot(incompressible=True)
 
     ..  pyvista-plot::

tests/test_constitution_jax.py

@@ -68,6 +68,7 @@ def test_hyperelastic_jax():
         md.third_order_deformation,
         md.miehe_goektepe_lulei,
         md.storakers,
+        md.van_der_waals,
         md.blatz_ko,
     ]:
         umat = mat.Hyperelastic(W, **W.kwargs)