On the passage from nonlinear to linearized viscoelasticity

Friedrich M, Kruzik M (2018)

Publication Type: Journal article

Publication year: 2018

Journal

SIAM Journal on Mathematical Analysis Society for Industrial and Applied Mathematics

Book Volume: 50

Pages Range: 4426-4456

Journal Issue: 4

DOI: 10.1137/17M1131428

Abstract

We formulate a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain setting in the Kelvin{Voigt rheology where the viscosity stress tensor complies with the principle of time-continuous frame indifference. We identify weak solutions in the nonlinear framework as limits of time-incremental problems for vanishing time increment. Moreover, we show that linearization around the identity leads to the standard system for linearized viscoelasticity and that solutions of the nonlinear system converge in a suitable sense to solutions of the linear one. The same property holds for time-discrete approximations, and we provide a corresponding commutativity result. Our main tools are the theory of gradient flows in metric spaces and σ-convergence.

Authors with CRIS profile

Manuel Friedrich

Involved external institutions

Westfälische Wilhelms-Universität (WWU) Münster DE Germany (DE) Academy of Sciences of the Czech Republic (ASCR) / Akademie věd České republiky (AVČR) CZ Czech Republic (CZ)

How to cite

APA:

Friedrich, M., & Kruzik, M. (2018). On the passage from nonlinear to linearized viscoelasticity. SIAM Journal on Mathematical Analysis, 50(4), 4426-4456. https://doi.org/10.1137/17M1131428

MLA:

Friedrich, Manuel, and Martin Kruzik. "On the passage from nonlinear to linearized viscoelasticity." SIAM Journal on Mathematical Analysis 50.4 (2018): 4426-4456.

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