Stress-driven local-solution approach to quasistatic brittle delamination
- Roubíček, Tomáš
- Thomas, Marita
- Panagiotopoulos, Christos
2010 Mathematics Subject Classification
- 35K86 35R35 47J20 49J45 49J40 49S05 65M38 65Z05 74M15 74R10
- 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
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.
- Nonlinear Anal. Real World Appl., 22 (2015) pp. 645--663.