From nonlinear to linear elasticity in a coupled rate-dependent/independent system for brittle delamination

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Date
2017
Volume
2409
Issue
Journal
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Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract

We revisit the weak, energetic-type existence results obtained in [RT15] for a system for rateindependent, brittle delamination between two visco-elastic, physically nonlinear bulk materials and explain how to rigorously extend such results to the case of visco-elastic, linearly elastic bulk materials. Our approximation result is essentially based on deducing the MOSCO-convergence of the functionals involved in the energetic formulation of the system. We apply this approximation result in two different situations at small strains: Firstly, to pass from a nonlinearly elastic to a linearly elastic, brittle model on the time-continuous level, and secondly, to pass from a time-discrete to a time-continuous model using an adhesive contact approximation of the brittle model, in combination with a vanishing, super-quadratic regularization of the bulk energy. The latter approach is beneficial if the model also accounts for the evolution of temperature.

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Keywords
Adhesive contact, brittle delamination, non-smooth brittle constraint, Kelvin-Voigt visco-elasticity, coupled rate-dependent, rate-independent evolution, semistable energetic solutions
Citation
Rossi, R., & Thomas, M. (2017). From nonlinear to linear elasticity in a coupled rate-dependent/independent system for brittle delamination (Vol. 2409). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2409
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