Christos G. Panagiotopoulos

BEM solution of delamination problems using an interface damage and plasticity model

The problem of quasistatic and rate-independent evolution of elastic-plastic-brittle delamination at small strains is considered. Delamination processes for linear elastic bodies glued by an adhesive to each other or to a rigid outer surface are studied. The energy amounts dissipated in fracture Mode I (opening) and Mode II (shear) at an interface may be different. A concept of internal parameters is used here on the delaminating interfaces, involving a couple of scalar damage variable and a plastic tangential slip with kinematic-type hardening. The so-called energetic solution concept is employed. An inelastic process at an interface is devised in such a way that the dissipated energy depends only on the rates of internal parameters and therefore the model is associative. A fully implicit time discretization is combined with a spatial discretization of elastic bodies by the BEM to solve the delamination problem. The BEM is used in the solution of the respective boundary value problems, for each subdomain separately, to compute the corresponding total potential energy. Sample problems are analysed by a collocation BEM code to illustrate the capabilities of the numerical procedure developed.

Quasistatic adhesive contact delaminating in mixed mode and its numerical treatment

An adhesive unilateral contact between visco-elastic bodies at small strains and in a Kelvin–Voigt rheology is scrutinized, neglecting inertia. The flow-rule for debonding the adhesive is considered rate independent, unidirectional, and non-associative due to dependence on the mixity of modes of delamination, namely Mode I (opening) needs (= dissipates) less energy than Mode II (shearing). Such mode-mixity dependence of delamination is a very pronounced (and experimentally confirmed) phenomenon typically considered in engineering models. An efficient semi-implicit-in-time FEM discretization leading to recursive quadratic mathematical programs is devised. Its convergence and thus the existence of weak solutions is proved. Computational experiments implemented by BEM illustrate the modeling aspects and the numerical efficiency of the discretization.

Critical Assessment of Penalty-Type Methods for Imposition of Time-Dependent Boundary Conditions in FEM Formulations for Elastodynamics

Recent work by the authors proposes a methodology that avoids ad hoc procedures and is applicable to both linear as well as nonlinear problems and provides a variationally-consistent way for incorporation of time-dependent boundary conditions in problems of elastodynamics. More specifically, an integral formulation of the elastodynamic problem serves as basis for the imposition of the corresponding constraints, which are enforced via the consistent form of the penalty method, e.g., a form that complies with the norm and inner product of the functional space where the weak formulation is mathematically posed. It is shown that well known and broadly implemented modelling techniques in the finite element method such as “large mass” and “large spring” techniques arise as limiting cases of this penalty formulation. In here, we examine the performance and the characteristics of such techniques through some simple examples.