Repository: Freie Universität Berlin, Math Department

Thermoviscoelasticity in Kelvin-Voigt rheology at large strains.

Mielke, A. and Roubícek, T. (2020) Thermoviscoelasticity in Kelvin-Voigt rheology at large strains. Arch. Rational Mech. Anal., 238 . pp. 1-45.

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The frame-indifferent thermodynamically-consistent model of thermoviscoelasticity at large strain is formulated in the reference configuration by 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 to the reference configuration. The existence of weak solutions in the quasistatic setting, that is inertial forces are ignored, is shown by time discretization

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2475
Deposited By: Monika Drueck
Deposited On:19 Oct 2020 14:58
Last Modified:19 Oct 2020 14:58

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