WIAS Preprint No. 1542, (2010)

From damage to delamination in nonlinearly elastic materials at small strains



Authors

  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Roubíček, Tomáš
  • Thomas, Marita

2010 Mathematics Subject Classification

  • 74R05 74R10 49J45 49S05

Keywords

  • Rate-independent systems, brittle damage, Gamma-convergence for evolutionary systems, brittle delamination

Abstract

Brittle Griffith-type delamination of compounds is deduced by means of Gamma-convergence from partial, isotropic damage of three-specimen-sandwich-structures by flattening the middle component to the thickness 0. The models used here allow for nonlinearly elastic materials at small strains and consider the processes to be unidirectional and rate-independent. The limit passage is performed via a double limit: first, we gain a delamination model involving the gradient of the delamination variable, which is essential to overcome the lack of a uniform coercivity arising from the passage from partial damage to delamination. Second, the delamination-gradient is supressed. Noninterpenetration- and transmission-conditions along the interface are obtained.

Appeared in

  • J. Elasticity, 109 (2012) pp. 235--273.

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