add plane-stress material for linear-elasticity

fixes #62

README.md

@@ -64,7 +64,7 @@ A = Mat.hessian([defgrad])[0]
 ```
 
 ## Template classes for hyperelasticity
-matADi provides several simple template classes suitable for simple hyperelastic materials. Some isotropic hyperelastic material formulations are located in `matadi.models` (see list below). These strain energy functions have to be passed as the `fun` argument into an instance of `MaterialHyperelastic`. Usage is exactly the same as described above. To convert a hyperelastic material based on the deformation gradient into a mixed three-field formulation suitable for nearly-incompressible behavior (*displacements*, *pressure* and *volume ratio*) an instance of a `MaterialHyperelastic` class has to be passed to `ThreeFieldVariation`. For *plane strain* or *plane stress* use `MaterialHyperelasticPlaneStrain` or `MaterialHyperelasticPlaneStressIncompressible` instead of `MaterialHyperelastic`.
+matADi provides several simple template classes suitable for simple hyperelastic materials. Some isotropic hyperelastic material formulations are located in `matadi.models` (see list below). These strain energy functions have to be passed as the `fun` argument into an instance of `MaterialHyperelastic`. Usage is exactly the same as described above. To convert a hyperelastic material based on the deformation gradient into a mixed three-field formulation suitable for nearly-incompressible behavior (*displacements*, *pressure* and *volume ratio*) an instance of a `MaterialHyperelastic` class has to be passed to `ThreeFieldVariation`. For *plane strain* or *plane stress* use `MaterialHyperelasticPlaneStrain`, `MaterialHyperelasticPlaneStressIncompressible` or `MaterialHyperelasticPlaneStressLinearElastic` instead of `MaterialHyperelastic`.
 
 ```python
 

matadi/__about__.py

@@ -1 +1 @@
-__version__ = "0.0.22"
+__version__ = "0.0.23"

matadi/__init__.py

@@ -17,6 +17,7 @@
     MaterialComposite,
     MaterialHyperelasticPlaneStrain,
     MaterialHyperelasticPlaneStressIncompressible,
+    MaterialHyperelasticPlaneStressLinearElastic,
 )
 from ._lab import Lab
 

matadi/_templates.py

@@ -66,6 +66,22 @@ def _fun_wrapper(self, x, **kwargs):
         return self.fun(F, **kwargs)
 
 
+class MaterialHyperelasticPlaneStressLinearElastic(MaterialHyperelasticPlaneStrain):
+    def __init__(self, fun, **kwargs):
+        super().__init__(fun, **kwargs)
+
+    def _fun_wrapper(self, x, **kwargs):
+        F = horzcat(vertcat(x[0], zeros(1, 2)), zeros(3, 1))
+        # stress-free thickness ratio for linear elastic material
+        # s_33 != 0 = 2 mu e_33 + lmbda (e_11 + e_22 + e_33)
+        # e_33 = - (e_11 + e_22) * lmbda / (2 mu + lmbda)
+        # F_33 = 1 + e_33
+        F[2, 2] = 1 - (F[0, 0] + F[1, 1] - 2) * (
+            kwargs["lmbda"] / (2 * kwargs["mu"] + kwargs["lmbda"])
+        )
+        return self.fun(F, **kwargs)
+
+
 class MaterialComposite:
     def __init__(self, materials):
         "Composite Material as a sum of a list of materials."

pyproject.toml

@@ -1,6 +1,6 @@
 [project]
 name = "matadi"
-version = "0.0.22"
+version = "0.0.23"
 description = "Material Definition with Automatic Differentiation"
 readme = "README.md"
 requires-python = ">=3.6"

setup.cfg

@@ -1,6 +1,6 @@
 [metadata]
 name = matadi
-version = 0.0.22
+version = 0.0.23
 author = Andreas Dutzler
 author_email = a.dutzler@gmail.com
 description = Material Definition with Automatic Differentiation

tests/test_plane.py

@@ -3,8 +3,9 @@
 from matadi import (
     MaterialHyperelasticPlaneStrain,
     MaterialHyperelasticPlaneStressIncompressible,
+    MaterialHyperelasticPlaneStressLinearElastic,
 )
-from matadi.models import neo_hooke
+from matadi.models import neo_hooke, linear_elastic
 
 
 def pre():
@@ -40,7 +41,7 @@ def test_plane_strain():
     assert DW[0].shape == (2, 2, 2, 2, 8, 1000)
 
 
-def test_plane_stress():
+def test_plane_stress_incompr():
 
     # data
     FF = pre()
@@ -64,6 +65,32 @@ def test_plane_stress():
     assert DW[0].shape == (2, 2, 2, 2, 8, 1000)
 
 
+def test_plane_stress_linear():
+
+    # data
+    FF = pre()
+
+    # init Material
+    W = MaterialHyperelasticPlaneStressLinearElastic(
+        fun=linear_elastic,
+        mu=1.0,
+        lmbda=200.0,
+    )
+
+    W0 = W.function([FF])
+    dW = W.gradient([FF])
+    DW = W.hessian([FF])
+
+    assert W0[0].shape == (8, 1000)
+    assert dW[0].shape == (2, 2, 8, 1000)
+    assert DW[0].shape == (2, 2, 2, 2, 8, 1000)
+
+    assert W0[0].shape == (8, 1000)
+    assert dW[0].shape == (2, 2, 8, 1000)
+    assert DW[0].shape == (2, 2, 2, 2, 8, 1000)
+
+
 if __name__ == "__main__":
     test_plane_strain()
-    test_plane_stress()
+    test_plane_stress_incompr()
+    test_plane_stress_linear()