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search.filters.applied.f.access: openAccess × Subject: rate-independent processes ×

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    Cohesive zone-type delamination in visco-elasticity : to the occasion of the 60th anniversary of Tomaš Roubícek
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Thomas, Marita; Zanini, Chiara
    We study a model for the rate-independent evolution of cohesive zone delamination in a viscoelastic solid, also exposed to dynamics effects. The main feature of this model, inspired by [OP99], is that the surface energy related to the crack opening depends on the history of the crack separation between the two sides of the crack path, and allows for different responses upon loading and unloading. Due to the presence of multivalued and unbounded operators featuring non-penetration and the memory-constraint in the strong formulation of the problem, we prove existence of a weaker notion of solution, known as semistable energetic solution, pioneered in [Rou09] and refined in [RT15a].
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    Stress-driven local-solution approach to quasistatic brittle delamination
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Roubíček, Tomáš; Thomas, Marita; Panagiotopoulos, Christos
    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.
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    Error estimates for space-time discretizations of a rate-independent variational inequality
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Mielke, Alexander; Paoli, Laetitia; Petrov, Adrien; Stefanelli, Ulisse
    This paper deals with error estimates for space-time discretizations in the context of evolutionary variational inequalities of rate-independent type. After introducing a general abstract evolution problem, we address a fully-discrete approximation and provide a priori error estimates. The application of the abstract theory to a semilinear case is detailed. In particular, we provide explicit space-time convergence rates for the isothermal Souza-Auricchio model for shape-memory alloys.