Merge pull request #111 from adtzlr/add-template-materials

Add template tensor-based materials

README.md

@@ -252,7 +252,7 @@ dWdF, dWdp, statevars_new = NH.function([defgrad, pressure, statevars])
 d2WdFdF, d2WdFdp, d2Wdpdp = NH.gradient([defgrad, pressure, statevars])
 ```
 
-**Hint**: *The state variable concept is also implemented for the `Material` class.*
+**Hint**: *The above Neo-Hooke as well as the MORPH material model formulation within the u/p-framework are available as template-materials in `matadi.models` as `NeoHookeOgdenRoxburgh()`and `Morph()`. The state variable concept is also implemented for the `Material` class.*
 
 Simple examples for using `matadi` with [`scikit-fem`](https://github.com/adtzlr/matadi/discussions/14#) as well as with [`felupe`](https://github.com/adtzlr/matadi/discussions/22) are shown in the Discussion section.
 

matadi/__about__.py

@@ -1 +1 @@
-__version__ = "0.1.8"
+__version__ = "0.1.9"

matadi/models/__init__.py

@@ -28,3 +28,5 @@
 
 from . import microsphere
 from .microsphere.nonaffine import miehe_goektepe_lulei
+
+from ._templates import NeoHookeOgdenRoxburgh, Morph

matadi/models/_misc.py

@@ -17,7 +17,7 @@
 
 
 def morph(x, p1, p2, p3, p4, p5, p6, p7, p8):
-    "MORPH consitututive material formulation."
+    "MORPH consitutive material formulation."
 
     # split input into the deformation gradient and the vector of state variables
     F, statevars = x[0], x[-1]

matadi/models/_templates.py

@@ -0,0 +1,83 @@
+from ._misc import morph
+from ._hyperelasticity_isotropic import neo_hooke
+from ._pseudo_elasticity import ogden_roxburgh
+from ._helpers import volumetric, displacement_pressure_split
+from ..math import det, gradient
+from .._material import MaterialTensor
+from .. import Variable
+
+
+class NeoHookeOgdenRoxburgh(MaterialTensor):
+    "Neo-Hooke and Ogden-Roxburgh material formulations within the u/p framework."
+
+    def __init__(self, C10=0.5, r=3, m=1, beta=0, bulk=5000):
+        @displacement_pressure_split
+        def fun(x, C10, r, m, beta, bulk):
+
+            # split `x` into the deformation gradient and the state variable
+            F, Wmaxn = x[0], x[-1]
+
+            # isochoric and volumetric parts of the hyperelastic
+            # strain energy function
+            W = neo_hooke(F, C10)
+            U = volumetric(det(F), bulk)
+
+            # pseudo-elastic softening function
+            eta, Wmax = ogden_roxburgh(W, Wmaxn, r, m, beta)
+
+            # first Piola-Kirchhoff stress and updated state variable
+            # for a pseudo-elastic material formulation
+            return eta * gradient(W, F) + gradient(U, F), Wmax
+
+        F = Variable("F", 3, 3)
+        p = fun.p
+        z = Variable("z", 1, 1)
+
+        kwargs = {"C10": C10, "r": r, "m": m, "beta": beta, "bulk": bulk}
+
+        super().__init__(x=[F, p, z], fun=fun, triu=True, statevars=1, kwargs=kwargs)
+
+
+class Morph(MaterialTensor):
+    "MORPH consitutive material formulation within the u/p framework."
+
+    def __init__(
+        self,
+        p1=0.035,
+        p2=0.37,
+        p3=0.17,
+        p4=2.4,
+        p5=0.01,
+        p6=6.4,
+        p7=5.5,
+        p8=0.24,
+        bulk=4050,
+    ):
+        @displacement_pressure_split
+        def fun(x, p1, p2, p3, p4, p5, p6, p7, p8, bulk):
+
+            F = x[0]
+            J = det(F)
+
+            P, statevars = morph(x, p1, p2, p3, p4, p5, p6, p7, p8)
+            U = volumetric(J, bulk)
+
+            return P + gradient(U, F), statevars
+
+        F = Variable("F", 3, 3)
+        p = fun.p
+        z = Variable("z", 13, 1)
+
+        kwargs = {
+            "p1": p1,
+            "p2": p2,
+            "p3": p3,
+            "p4": p4,
+            "p5": p5,
+            "p6": p6,
+            "p7": p7,
+            "p8": p8,
+            "bulk": bulk,
+        }
+
+        super().__init__(x=[F, p, z], fun=fun, triu=True, statevars=1, kwargs=kwargs)

pyproject.toml

@@ -1,6 +1,6 @@
 [project]
 name = "matadi"
-version = "0.1.8"
+version = "0.1.9"
 description = "Material Definition with Automatic Differentiation"
 readme = "README.md"
 requires-python = ">=3.6"

setup.cfg

@@ -1,6 +1,6 @@
 [metadata]
 name = matadi
-version = 0.1.8
+version = 0.1.9
 author = Andreas Dutzler
 author_email = [email protected]
 description = Material Definition with Automatic Differentiation

tests/test_template-materials.py

@@ -0,0 +1,29 @@
+import numpy as np
+
+from matadi.models import NeoHookeOgdenRoxburgh, Morph
+
+
+def test_up_templates():
+
+    for MaterialUP in [NeoHookeOgdenRoxburgh, Morph]:
+
+        # Material as a function of `F` and `p`
+        # with additional state variables `z`
+        M = MaterialUP()
+
+        FF = (np.random.rand(3, 3, 8, 100) - 0.5) / 2
+        pp = np.random.rand(1, 8, 100)
+        zz = np.random.rand(*M.x[-1].shape, 8, 100)
+
+        for a in range(3):
+            FF[a, a] += 1
+
+        P = M.function([FF, pp, zz])  # stress, constraint, statevars_new
+        A = M.gradient([FF, pp, zz])
+
+        assert len(P) == 3
+        assert len(A) == 3
+
+
+if __name__ == "__main__":
+    test_up_templates()