WIAS Preprint No. 2584, (2019)

Thermoviscoelasticity in Kelvin--Voigt rheology at large strains


  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Roubíček, Tomáš
    ORCID: 0000-0002-0651-5959

2010 Mathematics Subject Classification

  • 35K55 35Q74 74A15 74A30 80A17


  • Finite-strain elasticity, static frame indifference, time-dependent frame indifference, balance of total energy, energy estimates, hyperstress regularization, uniform positive of determinant, viscous heating, staggered time-incremental minimization scheme




The frame-indifferent thermodynamically-consistent model of thermoviscoelasticity at large strain is formulated in the reference configuration with using the concept of the second-grade nonsimple materials. We focus on physically correct viscous stresses that are frame indifferent under time-dependent rotations. Also elastic stresses are frame indifferent under rotations and respect positivity of the determinant of the deformation gradient. The heat transfer is governed by the Fourier law in the actual deformed configuration, which leads to a nontrivial description when pulled back into the reference configuration. Existence of weak solutions in the quasistatic setting, i.e. inertial forces are ignored, is shown by time discretization.

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