Spline model for strain energy

variational formulation
11

Ok, maybe I have to workaround the code a bit and fully understand what’s going on there. On the side note, I tried to plot original data and interpolated data using -

import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import CubicSpline

# Strain data points and energy values
strain_values = [0.0, 0.6, 0.19, 0.25]
energy_values = [0.0, 0.03, 0.005, 0.047]

if any(strain_values[i] >= strain_values[i+1] for i in range(len(strain_values)-1)):
    # If there are repeated or non-unique values, preprocess the data
    unique_strain_values, unique_indices = np.unique(strain_values, return_index=True)
    unique_energy_values = [energy_values[i] for i in unique_indices]
    strain_values = list(unique_strain_values)
    energy_values = list(unique_energy_values)

# Calculate the spline for strain-energy interpolation
spline = CubicSpline(strain_values, energy_values)

# Solve variational problem
store_u = np.linspace(0, -0.4, 50, endpoint=True)

# Calculate energy values using the spline for the given strain values
interpolated_energy_values = spline(store_u)

# Plot the original data points
plt.plot(strain_values, energy_values, 'o', label='Original Data')

# Plot the interpolated data using the spline
plt.plot(store_u, interpolated_energy_values, label='Interpolated Data')

plt.xlabel('Strain')
plt.ylabel('Energy')
plt.title('Strain-Energy Interpolation')
plt.legend()
plt.grid(True)
plt.show()

image
image911×607 57.9 KB

Could you please interpret the plot and tell what you are trying to achieve exactly ?
Also I would strongly suggest you to go through this post Incompressible Humphrey hyperelastic material in Fencis which shows how you can make user-defined functions and use them.