An energy based formulation of a quasi-static interface damage model with a multilinear cohesive law

Abstract

A new quasi-static and energy based formulation of an interface damage model which provides interface traction-relative displacement laws like in traditional trilinear (with bilinear softening) or generally multilinear cohesive zone models frequently used by engineers is presented. This cohesive type response of the interface may represent the behaviour of a thin adhesive layer. The level of interface adhesion or damage is defined by several scalar variables suitably defined to obtain the required traction-relative displacement laws. The weak solution of the problem is sought numerically by a semi-implicit timestepping procedure which uses recursive double minimization in displacements and damage variables separately. The symmetric Galerkin boundary-element method is applied for the spatial discretization. Sequential quadratic programming is implemented to resolve each partial minimization in the recursive scheme applied to compute the time-space discretized solutions. Sample 2D numerical examples demonstrate applicability of the proposed model.

A boundary element approach for an interface visco-damage model exposed to cyclic shear load

“…We use the model to find solutions for various amplitudes and various maxima of the same load type applied to the domain shown in Fig. 3 (see also [6][7][8]). The model formulation is implemented in a MATLAB computer code.…”

“…The data from Table 1 can be used to calculate the parameters of the crack-growth power law known for fatigue processes, see [22]. Linearised regression is used to obtain Δa/ ΔN = 2.71×10 8 , where the maximum of the applied force is used as the independent variable. The damage evolution in Fig.…”

“…The fourth-order tensor C h includes elastic constants for the domain Ω η and e is the small strain tensor. The interface integral defines stored energy of the adhesive, depending on the initial undamaged interface stiffnesses k n and k s , and on the actual state of damage controlled by the degradation function Φ(ζ) as in [7,8] ⋅ n , denoting the negative part of the relative normal displacement, reflects the normal-compliance contact condition being understood as a reasonable approximation of Signorini contact conditions due to asperities of the contacting surfaces.…”

“…To simulate the fatigue processes, the dissipation potential has a rate-dependent form with hysteresis associated to damage, see also [4][5][6]. The CZMs in the context of the energy evolution were implemented in [7,8] and a simple viscous term was also tested in [9]. In the present implementation, the viscous term and also the damage triggering term of dissipation are formulated as state dependent in order to provide a better control of the hysteretic model so that the unloading and reloading paths were non-coincident.…”

“…The solution evolution is approximated by an appropriate time stepping algorithm which is capable of providing a variational structure to the solved problem by two recursively solved minimisations with respect to variables of deformation separated from damage variables as it was devised in [10,11]. Similar methodology was also described and implemented in the previous author's works [7,8,12]. The variational character of the solved problem requires algorithms of energy minimisation.…”