Listing 1:

The Python code snippet for the NN material model

def E2S(E_PD, E_XD, E_phi, sigma, W0, b0, W1, b1, W2, b2):

″″″Compute the stress components using the NN material model.

Wi and bi (i = 0,1,2) are the weights and biases of the NN model.″″″

# An element–wise softplus function

def softplus (x, beta = 1., threshold = 20.):

def _elem_softplus (x, beta=beta, threshold=threshold):

return 1./beta*ln(exp(beta*x) + 1)

y = elem_op (_elem_softplus, x)

return y

# The NN model prediction

inputs = as_vector ([E_PD, E_XD, E_phi, sigma])

y1 = softplus (dot(W0, inputs) + b0)

y2 = softplus (dot(W1, y1) + b1)

outputs = dot (W2, y2) + b2

# Impose zero shear stresses for zero shear strains

multiplier = as_vector ([1., 1., E[2]])

S = elem_mult (multiplier, outputs)

return S