Finite-strain Poynting-Thomson model: existence and linearization
Analysis of PDEs
2023-12-20 v3
Abstract
We analyze the finite-strain Poynting-Thomson viscoelastic model. In its linearized small-deformation limit, this corresponds to the serial connection of an elastic spring and a Kelvin-Voigt viscoelastic element. In the finite-strain case, the total deformation of the body results from the composition of two maps, describing the deformation of the viscoelastic element and the elastic one, respectively. We prove the existence of suitably weak solutions by a time-discretization approach based on incremental minimization. Moreover, we prove a rigorous linearization result, showing that the corresponding small-strain model is indeed recovered in the small-loading limit.
Cite
@article{arxiv.2303.10933,
title = {Finite-strain Poynting-Thomson model: existence and linearization},
author = {A. Chiesa and M. Kružík and U. Stefanelli},
journal= {arXiv preprint arXiv:2303.10933},
year = {2023}
}