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Erschienen in:
2018 | OriginalPaper | Buchkapitel
From Nonlinear to Linear Elasticity in a Coupled Rate-Dependent/Independent System for Brittle Delamination
verfasst von : Riccarda Rossi, Marita Thomas
Erschienen in: Trends in Applications of Mathematics to Mechanics
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Abstract
We revisit the weak, energetic-type existence results obtained in (Rossi and Thomas, ESAIM Control Optim. Calc. Var. 21, 1–59, (2015)) for a system for rate-independent, 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.