Small strain material models and minor improvements (#18)

* added youngs modulus plotting to dash

* added nonlinear pseudo plastic hardening (not working yet)

* rate independent J2 plasticity added

* visco plastic models

* refactorted J2 plasticity

* Formatting

* Disambiguate mandel notation definition in readme.md #17

* renamed internal variable in J2plasticity.h

---------

Co-authored-by: Ishaan Desai <[email protected]>

.gitignore

@@ -201,7 +201,7 @@ test/input_files/**/*.json
 !sphere.h5
 
 # Test input files
-!test_LinearElasticIsotropic.json
-!test_LinearThermalIsotropic.json
-!test_PseudoPlasticLinearHardening.json
-!test_VonMisesPlasticLinearIsotropicHardening.json
+!test_LinearElastic.json
+!test_LinearThermal.json
+!test_PseudoPlastic.json
+!test_J2Plasticity.json

CMakeLists.txt

@@ -135,8 +135,8 @@ set_property(TARGET FANS_FANS PROPERTY PUBLIC_HEADER
 
         include/material_models/LinearThermalIsotropic.h
         include/material_models/LinearElasticIsotropic.h
-        include/material_models/PseudoPlasticLinearHardening.h
-        include/material_models/VonMisesPlasticLinearIsotropicHardening.h
+        include/material_models/PseudoPlastic.h
+        include/material_models/J2Plasticity.h
 )
 
 # ##############################################################################

FANS_Dashboard/FANS_Dashboard.ipynb

@@ -133,8 +133,8 @@
    "outputs": [],
    "source": [
     "# Specify which microstructures, load cases, and quantities to load\n",
-    "microstructures_to_load = ['/sphere/32x32x32/ms']\n",
-    "load_cases_to_load = ['load0']\n",
+    "microstructures_to_load = list(hierarchy.keys())\n",
+    "load_cases_to_load = list(hierarchy[microstructures_to_load[0]].keys())\n",
     "quantities_to_load = ['strain_average', 'stress_average', 'phase_stress_average_phase0', \"stress\"]\n",
     "time_steps_to_load = []\n",
     "\n",
@@ -143,7 +143,11 @@
     "                                 quantities_to_load, \n",
     "                                 microstructures_to_load, \n",
     "                                 load_cases_to_load, \n",
-    "                                 time_steps_to_load)"
+    "                                 time_steps_to_load)\n",
+    "\n",
+    "strain_average = data[microstructures_to_load[0]][load_cases_to_load[0]]['strain_average']  \n",
+    "stress_average = data[microstructures_to_load[0]][load_cases_to_load[0]]['stress_average']\n",
+    "time_steps     = data[microstructures_to_load[0]][load_cases_to_load[0]]['time_steps']\n"
    ]
   },
   {
@@ -164,10 +168,6 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "strain_average = data['/sphere/32x32x32/ms']['load0']['strain_average']\n",
-    "stress_average = data['/sphere/32x32x32/ms']['load0']['stress_average']\n",
-    "time_steps = data['/sphere/32x32x32/ms']['load0']['time_steps']\n",
-    "\n",
     "# Specify measures to compute\n",
     "measures_to_compute = ['von_mises', 'hydrostatic', 'deviatoric', 'principal', \n",
     "                       'max_shear', 'I_invariants', 'J_invariants', 'eigenvalues',\n",
@@ -209,8 +209,8 @@
     "# Postprocessing and writing to h5 file\n",
     "quantities_to_postprocess = ['stress_average', 'stress']\n",
     "measures_to_postprocess = ['deviatoric', 'von_mises']\n",
-    "microstructures_to_postprocess = ['/sphere/32x32x32/ms']\n",
-    "load_cases_to_postprocess = ['load0']\n",
+    "microstructures_to_postprocess = microstructures_to_load[0]\n",
+    "load_cases_to_postprocess = load_cases_to_load[0]\n",
     "\n",
     "processed_data = postprocess_and_write_to_h5(file_path, hierarchy, quantities_to_postprocess, measures_to_postprocess, \n",
     "                                             microstructures_to_postprocess, load_cases_to_postprocess)"

FANS_Dashboard/PlotYoungsModulus.py

@@ -0,0 +1,110 @@
+import numpy as np
+import plotly.graph_objs as go
+
+
+def compute_3d_youngs_modulus(C):
+    """
+    Compute Young's modulus for all directions in 3D.
+
+    Parameters:
+    C : ndarray
+        Stiffness tensor in Mandel notation.
+
+    Returns:
+    E: ndarray
+        Young's modulus in all directions.
+    X, Y, Z: ndarrays
+        Coordinates for plotting the modulus surface.
+    """
+
+    n_theta = 180
+    n_phi = 360
+    theta = np.linspace(0, np.pi, n_theta)  # Polar angle
+    phi = np.linspace(0, 2 * np.pi, n_phi)  # Azimuthal angle
+
+    S = np.linalg.inv(C)
+
+    E = np.zeros((n_theta, n_phi))
+
+    for i in range(n_theta):
+        for j in range(n_phi):
+            d = np.array(
+                [
+                    np.sin(theta[i]) * np.cos(phi[j]),
+                    np.sin(theta[i]) * np.sin(phi[j]),
+                    np.cos(theta[i]),
+                ]
+            )
+
+            N = np.array(
+                [
+                    d[0] ** 2,
+                    d[1] ** 2,
+                    d[2] ** 2,
+                    np.sqrt(2.0) * d[0] * d[1],
+                    np.sqrt(2.0) * d[0] * d[2],
+                    np.sqrt(2.0) * d[2] * d[1],
+                ]
+            )
+
+            E[i, j] = 1.0 / (N.T @ S @ N)
+
+    X = E * np.sin(theta)[:, np.newaxis] * np.cos(phi)[np.newaxis, :]
+    Y = E * np.sin(theta)[:, np.newaxis] * np.sin(phi)[np.newaxis, :]
+    Z = E * np.cos(theta)[:, np.newaxis]
+
+    return X, Y, Z, E
+
+
+def plot_3d_youngs_modulus_surface(C, title="Young's Modulus Surface"):
+    """
+    Plot a 3D surface of Young's modulus.
+
+    Parameters:
+    C : ndarray
+        Stiffness tensor in Mandel notation.
+    title : str
+        Title of the plot.
+
+    """
+    X, Y, Z, E = compute_3d_youngs_modulus(C)
+
+    surface = go.Surface(x=X, y=Y, z=Z, surfacecolor=E, colorscale="Viridis")
+
+    layout = go.Layout(
+        title=title,
+        scene=dict(
+            xaxis=dict(title="X"),
+            yaxis=dict(title="Y"),
+            zaxis=dict(title="Z"),
+            aspectmode="auto",
+        ),
+    )
+
+    fig = go.Figure(data=[surface], layout=layout)
+    fig.show()
+
+
+def demoCubic():
+    """
+    Demonstrates the Young's modulus surface plotting routine for a cubic material (Copper)
+
+    Returns
+    -------
+    None.
+
+    """
+    P1 = np.zeros((6, 6))
+    P1[:3, :3] = 1.0 / 3.0
+    D = np.diag([1, 1, 1, 0, 0, 0])
+    P2 = D - P1
+    P3 = np.eye(6) - D
+
+    # generate stiffness for a cubic material: copper
+    l1, l2, l3 = 136.67, 46, 150
+    C = 3 * l1 * P1 + l2 * P2 + l3 * P3
+
+    print(C)
+
+    # show the 3D Young's modulus plot for copper
+    plot_3d_youngs_modulus_surface(C, title="Young's Modulus Surface for Copper")

README.md

@@ -10,6 +10,7 @@ Fourier Accelerated Nodal Solvers (FANS) is an FFT-based homogenization solver d
 - [Input File Format](#input-file-format)
 - [Examples](#examples)
 - [Acknowledgements](#acknowledgements)
+- [Contributors](#contributors)
 
 ## Installation
 
@@ -159,8 +160,8 @@ Example input files can be found in the [`test/input_files`](test/input_files)
 ```
 
 - `problem_type`: This defines the type of physical problem you are solving. Common options include "thermal" problems and "mechanical" problems.
-- `matmodel`: This specifies the material model to be used in the simulation. Examples include `LinearThermalIsotropic` for isotropic linear thermal problems, `LinearElasticIsotropic` for isotropic linear elastic mechanical problems, `PseudoPlasticLinearHardening` for plasticity mimicking model with linear hardening, and `VonMisesPlasticLinearIsotropicHardening` for rate independent J2 plasticity model with linear isotropic hardening.
-- `material_properties`: This provides the necessary material parameters for the chosen material model. For thermal problems, you might specify `conductivity`, while mechanical problems might require `bulk_modulus`, `shear_modulus`, `yield_stress`, and `hardening_parameter`. These properties can be defined as arrays to represent multiple phases within the microstructure.
+- `matmodel`: This specifies the material model to be used in the simulation. Examples include `LinearThermalIsotropic` for isotropic linear thermal problems, `LinearElasticIsotropic` for isotropic linear elastic mechanical problems, `PseudoPlasticLinearHardening`/`PseudoPlasticNonLinearHardening` for plasticity mimicking model with linear/nonlinear hardening, and `J2ViscoPlastic_LinearIsotropicHardening`/`J2ViscoPlastic_NonLinearIsotropicHardening` for rate dependent J2 plasticity model with linear/nonlinear isotropic hardening.
+- `material_properties`: This provides the necessary material parameters for the chosen material model. For thermal problems, you might specify `conductivity`, while mechanical problems might require `bulk_modulus`, `shear_modulus`, and more properties for advanced material models. These properties can be defined as arrays to represent multiple phases within the microstructure.
 
 ### Solver Settings
 
@@ -194,9 +195,8 @@ Example input files can be found in the [`test/input_files`](test/input_files)
 ```
 
 - `macroscale_loading`: This defines the external loading applied to the microstructure. It is an array of arrays, where each sub-array represents a loading condition applied to the system. The format of the loading array depends on the problem type:
-
-  - For `thermal` problems, the array typically has 3 components, representing the temperature gradients in the x, y, and z directions.
-  - For `mechanical` problems, the array must have 6 components, corresponding to the components of the strain tensor in Mandel notation (e.g., [[ε11, ε22, ε33, ε12, ε13, ε23]]).
+- For `thermal` problems, the array typically has 3 components, representing the temperature gradients in the x, y, and z directions.
+- For `mechanical` problems, the array must have 6 components, corresponding to the components of the strain tensor in Mandel notation (e.g., [[ε_11, ε_22, ε_33, √2 ε_12, √2 ε_13, √2 ε_23]]).
 
 In the case of path/time-dependent loading as shown, for example as in plasticity problems, the `macroscale_loading` array can include multiple steps with corresponding loading conditions.
 
@@ -216,16 +216,23 @@ In the case of path/time-dependent loading as shown, for example as in plasticit
   - `displacement`: The displacement fluctuation field (for mechanical problems) and temperature fluctuation field (for thermal problems).
   - `stress` and `strain`: The stress and strain fields at each voxel in the microstructure.
 
-- Additional material model specific results, such as `plastic_flag`, `plastic_strain`, and `hardening_variable`, can be included depending on the problem type and material model.
+- Additional material model specific results can be included depending on the problem type and material model.
 
 ### Examples
 
 If you would like to run some example tests, you can execute the [`run_tests.sh`](test/run_tests.sh) file. For example to run a linear elastic mechanical homogenization problem for a 6 othonormal load cases on a microstructure image of size `32 x 32 x 32` with a single spherical inclusion,
 
 ```bash
-mpiexec -n 2 ./FANS input_files/test_LinearElasticIsotropic.json test_results.h5
+mpiexec -n 2 ./FANS input_files/test_LinearElastic.json test_results.h5
 ```
 
 ## Acknowledgements
 
 Funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC 2075 – 390740016. Contributions by Felix Fritzen are funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) within the Heisenberg program - DFG-FR2702/8 - 406068690; DFG-FR2702/10 - 517847245 and through NFDI-MatWerk - NFDI 38/1 - 460247524. We acknowledge the support by the Stuttgart Center for Simulation Science (SimTech).
+
+## Contributors
+
+- [Sanath Keshav](https://github.com/sanathkeshav)
+- [Florian Rieg](about:blank)
+- [Ishaan Desai](https://github.com/IshaanDesai)
+- [Moritz Sigg](https://github.com/siggmo)