Table 2.

Finite element implementation of the anisotropic ensemble fibre potential.

given:

isochoric deformation gradient F̄ = J−1/3F

orientation distribution data

algorithm:

define integration order t b,W̄fa⇒t

load spherical design M(α), α ∈ {1 … N}

initialize stress and elasticity tensors

DO α = 1, N

compute spatial isochoric fibre direction m̄(α) = F̄M(α)

compute spatial isochoric structure tensor ā(α) = m̄(α) ⊗ m̄(α)

compute fourth invariant Ī4(α) = m̄(α) · m̄(α) = tr(ā(α))

compute co-latitude angle Θ(α) = arccos(K · M(α))

IF (Ī4(α) > 1) THEN

compute orientation density

IF (ρ(α) > ε) THEN

compute W̄ea contribution of stress and elasticity tensors

update W̄ea contribution of stress and elasticity tensors

ENDIF

ENDIF

ENDDO