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Journal of Elasticity

, Volume 109, Issue 2, pp 235–273 | Cite as

From Damage to Delamination in Nonlinearly Elastic Materials at Small Strains

  • Alexander Mielke
  • Tomáš Roubíček
  • Marita Thomas
Article

Abstract

Brittle Griffith-type delamination of compounds is deduced by means of Γ-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 suppressed. Noninterpenetration- and transmission-conditions along the interface are obtained.

Keywords

Rate-independent systems Brittle damage Γ-convergence for evolutionary systems Brittle delamination 

Mathematics Subject Classification

74R05 74R10 49J45 49S05 

Notes

Acknowledgements

The authors are thankful to Dr. D. Knees for many fruitful discussions and valuable comments. The article arose out of M.T.’s visit of the ‘Nečas center for mathematical modeling’, supported by LC 06052 (MŠMT ČR). M.T. was also supported by the DFG within the RTG 1128 ‘Analysis, Numerics and Optimization of Multiphase problems’. T.R. was supported by grants A 100750802 (GA AV ČR), 201/10/0357 and 201/09/0917 (GA ČR), MSM 21620839, and 1M06031 (MŠMT ČR), and from the research plan AV0Z20760514 (ČR). The research of A.M. was partially supported by DFG within the subproject C18 of Matheon.

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Alexander Mielke
    • 1
    • 2
  • Tomáš Roubíček
    • 3
    • 4
  • Marita Thomas
    • 1
  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany
  2. 2.Institut für MathematikHumboldt Universität zu BerlinBerlinGermany
  3. 3.Mathematical InstituteCharles UniversityPraha 8Czech Republic
  4. 4.Institute of Thermomechanics of the ASCRPraha 8Czech Republic

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