WiechertElement

Source: models/solid_mechanics/viscoelasticity/WiechertElement.py

Wiechert (generalized Maxwell) viscoelastic model with two Maxwell branches in parallel with an equilibrium spring. Total stress is \(\boldsymbol{\sigma} = (E_\infty + E_1 + E_2) \boldsymbol{\varepsilon} - E_1 \boldsymbol{\varepsilon}_{v,1} - E_2 \boldsymbol{\varepsilon}_{v,2}\), with each viscous strain evolving according to \(\dot{\boldsymbol{\varepsilon}}_{v,i} = E_i (\boldsymbol{\varepsilon} - \boldsymbol{\varepsilon}_{v,i}) / \eta_i\).

Inputs

strain — input · SR2 · required

Total strain

viscous_strain_1 — input · SR2 · required

Viscous strain in the first Maxwell branch

viscous_strain_2 — input · SR2 · required

Viscous strain in the second Maxwell branch

Outputs

stress — output · SR2 · required

Total stress

viscous_strain_1_rate — output · SR2 · default viscous_strain_1_rate

Optional name for the derived output (defaults to ‘viscous_strain_1_rate’, i.e. the ‘viscous_strain_1’ variable name with the ‘_rate’ suffix).

viscous_strain_2_rate — output · SR2 · default viscous_strain_2_rate

Optional name for the derived output (defaults to ‘viscous_strain_2_rate’, i.e. the ‘viscous_strain_2’ variable name with the ‘_rate’ suffix).

Parameters

equilibrium_modulus — parameter · Scalar · required

Equilibrium spring modulus

modulus_1 — parameter · Scalar · required

Spring modulus of the first Maxwell branch

viscosity_1 — parameter · Scalar · required

Dashpot viscosity of the first Maxwell branch

modulus_2 — parameter · Scalar · required

Spring modulus of the second Maxwell branch

viscosity_2 — parameter · Scalar · required

Dashpot viscosity of the second Maxwell branch