Vladislav Mantic

Tomas Roubicek, Christos G. Panagiotopoulos, Vladislav Mantic

An adhesive unilateral contact of elastic bodies with a small viscosity in the linear Kelvin-Voigt rheology at small strains is scrutinized. The flow-rule for debonding the adhesive is considered rate-independent and unidirectional, and inertia is neglected. The asymptotics for the viscosity approaching zero towards purely elastic material involves a certain defect-like measure recording in some sense natural additional energy dissipated in the bulk due to (vanishing) viscosity, which is demonstrated on particular 2-dimensional computational simulations based on a semi-implicit time discretisation and a spacial discretisation implemented by boundary-element method.

Christos G. Panagiotopoulos, Vladislav Mantic, Tomas Roubicek

Two models for quasistatic adhesive unilateral contact delaminating in mixed fracture mode, i.e. distinguishing the less-dissipative Mode I (opening) from the more-dissipative Mode II (shearing), and allowing rigorous mathematical and numerical analysis, are studied. One model, referred to as Associative Plasticity-based Rate-Independent Model (APRIM), works for purely elastic bodies and involves, in addition to an interface damage variable, an auxiliary variable (representing interfacial plastic slip) to provide a fracture-mode sensitivity. It relies on a particular concept of force-driven local solutions (given by either vanishing-viscosity concept or maximum-dissipation principle). The other model, referred to as Linear Elastic - (perfectly) Brittle Interface Model (LEBIM), works visco-elastic bodies and rely on a conventional concept of weak solution and needs no auxiliary interfacial variable. This model is directly related to a usual phenomenological model of interface fracture by Hutchinson and Suo used in engineering. This paper devises a way how the phenomenology of the LEBIM can be fit to imitate the APRIM under relatively very slow loading, where both models are essentially rate-independent. The so-called effective dissipated energy is partitioned in both formulations to the surface energy and the energy dissipated during the interface debonding process, where the former is independent and the latter dependent on the fracture mode mixity. A numerical comparison of these models, implemented in a Boundary Element Method (BEM) code, is carried out on a suitable two-dimensional example. Furthermore, the computational efficiency and behaviour of the LEBIM is illustrated on another geometrically more complicated numerical example.

Tomas Roubicek, Christos Panagiotopoulos, Vladislav Mantic

The quasistatic rate-independent evolution of a delamination at small strains in the so-called mixed mode, i.e.~distinguishing opening (Mode I) from shearing (Mode II) is rigorously analyzed in the context of a concept of stress-driven local solutions. The model has separately convex stored energy and is associative, namely the 1-homogeneous potential of dissipative force driving the delamination depends only on rates of internal parameters. An efficient fractional-step-type semi-implicit discretisation in time is shown to converge to specific, stress-driven like) local solutions that may approximately obey the maximum-dissipation principle. Making still a spatial discretisation, this convergence as well as relevancy of such solution concept are demonstrated on a nontrivial 2-dimensional example.