Constrained optimization for interface cracks in composite materials subject to non-penetration conditions

Abstract

A constrained problem for a composite material with an interface crack subject to nonpenetration conditions is considered. The response of a composite consisting of two identical homogeneous orthotropic materials is described with respect to in-plane deformation. The coupling of the materials occurs at an interface with angle between their vertical planes of elastic symmetry. The model is not split into independent in-plane and anti-plane states. Well-posedness of the problem is proved by variational methods. For numerical computations, a semi-smooth Newton method is proposed and its convergence is studied. Using the proposed algorithms, numerical experiments for an interface crack under mode-3 loading are presented and analyzed with respect to the half-angle defining the coupling.

A primal-dual active set method for solving multi-rigid-body dynamic contact problems

“…These first encouraging results leads us to envisage taking into account friction, using Coulomb’s law within the framework of the active set method. We refer to Hintermuller et al [26, 27] and Kunisch and Stadler [25] for the treatment of frictional and cohesive contact.…”

“…Dual active set methods for convex quadratic problems generate a sequence of dual feasible iterations until primal feasibility is achieved; hence, an optimal solution is obtained. More recently, primal-dual active set methods have been considered to solve variational problems with unilateral constraints [22][23][24][25][26][27][28]. These approaches are characterized by the fact that the active set is defined by a relation described by both the primal and the dual feasibilities, which are enforced together during each iteration.…”

Optimization in constrained crack problems

“…For numerical implementation, based on the generalized differentiability property, a semi-smooth Newton method proposed in the form of primal-dual active-set strategy (PDAS-method) is used in [2] as the efficient numerical technique for solution of the constrained minimization problems, in particular with cracks, due to the property of its unconditional global and, moreover, monotone convergence.…”

Study of voltage cycling conditions on Pt oxidation and dissolution in polymer electrolyte fuel cells

“…[16,17,18]. For mathematical approaches which are suitable to describe and to test a mechanical degradation due to fracture phenomena, we refer to [19,20,21].…”