WIAS Preprint No. 2409, (2017)

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


  • Rossi, Riccarda
    ORCID: 0000-0002-7808-0261
  • Thomas, Marita
    ORCID: 0000-0001-9172-014X

2010 Mathematics Subject Classification

  • 49J53 49J45 74H20 74C05 74C10 74M15 74R10


  • Adhesive contact, brittle delamination, non-smooth brittle constraint, Kelvin-Voigt visco-elasticity, coupled rate-dependent/rate-independent evolution, semistable energetic solutions




We revisit the weak, energetic-type existence results obtained in [Rossi/Thomas-ESAIM-COCV-21(1):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: 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.

Appeared in

  • Proceedings of the INdAM-ISIMM Workshop on Trends on Applications of Mathematics to Mechanics, Rome, Italy, September 2016, E. Rocca, U. Stefanelli, L. Truskinovsky, A. Visintin, eds., vol. 27 of Springer INdAM Series, Springer International Publishing, Cham, 2018, pp. 127--157, DOI 10.1007/978-3-319-75940-1_7 .

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