Update README.md and add ustruct test case. ustruct result is fairly different from struct result, so could not use result_002.vtu from the struct case

Author: aabrown100-git

tests/cases/struct/spatially_variable_robin/README.md

@@ -1,22 +1,25 @@
-This test case simulates a spatially variable Robin boundary condition on a slab of material described by the Guccione material model. Primary fibers run along the length of the slab (z-direction) and secondary fibers run across the width of the slab
+This test case simulates a spatially variable Robin boundary condition on a slab of material described by the Guccione material model. This case is identical to `ustruct/spatially_variable_robin`, except it uses `struct` physics.
+
+- Primary fibers run along the length of the slab (z-direction) and secondary fibers run across the width of the slab
 (x-direction).
 
-The slab is loaded on the +Y surface with a uniform pressure load. The load profile is a ramp to 10 dynes/cm^2 over 0.5 seconds, then held there until
+- The slab is loaded on the +Y surface with a uniform pressure load. The load profile is a ramp to 10 dynes/cm^2 over 0.5 seconds, then held there until
 2 seconds. The load is defined in `load.dat`, which can be generated with
 `generate_load.py`. The load tends to push the slab downward. 
 
 ![Load Profile](load.png)
 
-This is resisted by a spatially varying Robin boundary condition on the -Y surface. The stiffness is 0 at z = 0, and 50 at the far end.
+- This is resisted by a spatially varying Robin boundary condition on the -Y surface. The stiffness is 0 at z = 0, and 50 at the far end.
 
 ![Spatially varying Robin BC](Y0_spatially_varying_robin.png)
 
 
-The slab is also constrained by Dirichlet boundary conditions on the +-X and +-Z
+- The slab is also constrained by Dirichlet boundary conditions on the +-X and +-Z
 surfaces, applied in the normal direction. These prevent the slab from moving
 in the x and z directions.
 
-The resulting deformation is shown in the video below:
+- The resulting deformation is shown in the video below:
 ![Deformation](animation.gif)
 The black outline shows the initial configuration. As you can see, the displacement of the slab is greatest at z = 0, where the Robin BC stiffness is zero. At the far end of the slab, the displacement is very little, where the stiffness is greatest. The oscillations are due to the absence of any damping in the Robin BC.
 
+- Note, the deformation is fairly different from `ustruct/spatially_variable_robin`, like due to the different underlying physics formulation and the coarse mesh. Therefore, the `result_002.vtu` files are not identical.

tests/cases/struct/spatially_variable_robin/solver.xml

@@ -4,7 +4,7 @@
 <GeneralSimulationParameters>
   <Continue_previous_simulation> 0 </Continue_previous_simulation>
   <Number_of_spatial_dimensions> 3 </Number_of_spatial_dimensions> 
-  <Number_of_time_steps> 2 </Number_of_time_steps> 
+  <Number_of_time_steps> 200 </Number_of_time_steps> 
   <Time_step_size> 0.01 </Time_step_size> 
   <Spectral_radius_of_infinite_time_step> 0.50 </Spectral_radius_of_infinite_time_step> 
   <Searched_file_name_to_trigger_stop> STOP_SIM </Searched_file_name_to_trigger_stop> 

tests/cases/ustruct/spatially_variable_robin/README.md

@@ -0,0 +1,26 @@
+This test case simulates a spatially variable Robin boundary condition on a slab of material described by the Guccione material model. This case is identical to `struct/spatially_variable_robin`, except it uses `ustruct` physics.
+
+- Primary fibers run along the length of the slab (z-direction) and secondary fibers run across the width of the slab
+(x-direction).
+
+- The slab is loaded on the +Y surface with a uniform pressure load. The load profile is a ramp to 10 dynes/cm^2 over 0.5 seconds, then held there until
+2 seconds. The load is defined in `load.dat`, which can be generated with
+`generate_load.py`. The load tends to push the slab downward. 
+
+![Load Profile](load.png)
+
+- This is resisted by a spatially varying Robin boundary condition on the -Y surface. The stiffness is 0 at z = 0, and 50 at the far end.
+
+![Spatially varying Robin BC](Y0_spatially_varying_robin.png)
+
+
+- The slab is also constrained by Dirichlet boundary conditions on the +-X and +-Z
+surfaces, applied in the normal direction. These prevent the slab from moving
+in the x and z directions.
+
+- The resulting deformation is shown in the video below:
+![Deformation](animation.gif)
+The black outline shows the initial configuration. As you can see, the displacement of the slab is greatest at z = 0, where the Robin BC stiffness is zero. At the far end of the slab, the displacement is very little, where the stiffness is greatest. The oscillations are due to the absence of any damping in the Robin BC.
+
+- Note, the deformation is fairly different from `struct/spatially_variable_robin`, like due to the different underlying physics formulation and the coarse mesh. Therefore, the `result_002.vtu` files are not identical.
+

tests/cases/ustruct/spatially_variable_robin/Y0_spatially_varying_robin.png

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5b7fae7ab8ac1ba68df93cb69d6e427a9151148ab4e608bef4763fe09fd26642
+size 6131

tests/cases/ustruct/spatially_variable_robin/Y0_spatially_varying_robin.vtp

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1e25dd76f4e87c6e84d8ac4311709e8869351d2aba525f238627d9e56a217733
+size 6777356

tests/cases/ustruct/spatially_variable_robin/animation.avi

@@ -0,0 +1,32 @@
+import numpy as np
+import os
+
+# Go to directory of this script
+os.chdir(os.path.dirname(os.path.realpath(__file__)))
+
+# Number of timesteps and number of Fourier modes
+n_timesteps = 101
+n_modes = 64
+
+# Generate time values from 0 to 2
+time = np.linspace(0, 2, n_timesteps)
+
+# Generate ramp from 0 to 10 in 0.5 seconds, then hold until 2 seconds.
+load = np.zeros(n_timesteps)
+load[time < 0.5] = 10 * time[time < 0.5] / 0.5
+load[(time >= 0.5)] = 10
+
+
+# Write the time and stress values to a text file
+with open("load.dat", "w") as file:
+    file.write(f"{n_timesteps} {n_modes}\n")
+    for t, s in zip(time, load):
+        file.write(f"{t:.3f} {s:.3f}\n")
+
+# Plot the stress values
+import matplotlib.pyplot as plt
+plt.plot(time, load)
+plt.xlabel("Time (s)")
+plt.ylabel("Load (dynes/cm^2)")
+plt.title("Load")
+plt.savefig("load.png")