BurgersElement

Source: models/solid_mechanics/viscoelasticity/BurgersElement.py

Burgers viscoelastic model: a Maxwell element in series with a Kelvin-Voigt element. The shared stress is \(\boldsymbol{\sigma} = E_M (\boldsymbol{\varepsilon} - \boldsymbol{\varepsilon}_{v,M} - \boldsymbol{\varepsilon}_K)\), and the internal strains evolve as \(\dot{\boldsymbol{\varepsilon}}_{v,M} = \boldsymbol{\sigma}/\eta_M\) and \(\dot{\boldsymbol{\varepsilon}}_K = (\boldsymbol{\sigma} - E_K \boldsymbol{\varepsilon}_K) / \eta_K\).

Inputs

strain — input · SR2 · required

Total strain

maxwell_viscous_strain — input · SR2 · required

Viscous strain in the Maxwell branch dashpot

kelvin_voigt_strain — input · SR2 · required

Strain in the Kelvin-Voigt branch

Outputs

stress — output · SR2 · required

Total stress (shared between Maxwell and Kelvin-Voigt elements)

maxwell_viscous_strain_rate — output · SR2 · default maxwell_viscous_strain_rate

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

kelvin_voigt_strain_rate — output · SR2 · default kelvin_voigt_strain_rate

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

Parameters

maxwell_modulus — parameter · Scalar · required

Maxwell branch spring modulus

maxwell_viscosity — parameter · Scalar · required

Maxwell branch dashpot viscosity

kelvin_modulus — parameter · Scalar · required

Kelvin-Voigt branch spring modulus

kelvin_viscosity — parameter · Scalar · required

Kelvin-Voigt branch dashpot viscosity