WIAS Preprint No. 1889, (2013)

Stress-driven local-solution approach to quasistatic brittle delamination


Authors

  • Roubíček, Tomáš
    ORCID: 0000-0002-0651-5959
  • Thomas, Marita
    ORCID: 0000-0001-9172-014X
  • Panagiotopoulos, Christos

2010 Mathematics Subject Classification

  • 35K86 35R35 47J20 49J45 49J40 49S05 65M38 65Z05 74M15 74R10

Keywords

  • unilateral adhesive contact, brittle limit, rate-independent processes, semi-implicit time discretisation, finite perimeter, property a, (d-1)-thick set, lower density estimate, Hardy's inequality, computational simulations

DOI

10.20347/WIAS.PREPRINT.1889

Abstract

A unilateral contact problem between elastic bodies at small strains glued by a brittle adhesive is addressed in the quasistatic rate-independent setting. The delamination process is modelled as governed by stresses rather than by energies. This results in a specific scaling of an approximating elastic adhesive contact problem, discretised by a semi-implicit scheme and regularized by a BV-type gradient term. An analytical zero-dimensional example motivates the model and a specific local-solution concept. Two-dimensional numerical simulations performed on an engineering benchmark problem of debonding a fiber in an elastic matrix further illustrate the validity of the model, convergence, and algorithmical efficiency even for very rigid adhesives with high elastic moduli.

Appeared in

  • Nonlinear Anal. Real World Appl., 22 (2015) pp. 645--663.

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