Cohesive zone-type delamination in visco-elasticity

Abstract

We study a model for the rate-independent evolution of cohesive zone delamination in a visco-elastic solid, also exposed to dynamics effects. The main feature of this model, inspired by [32], 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 nonpenetration 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 [41] and refined in [38].

Existence, energy identity and higher time regularity of solutions to a dynamic visco-elastic cohesive interface model

“…We conclude this introduction comparing with adhesive interface energies (more details are provided in Remark 4.3); as pointed out in [34], adhesive and cohesive settings are indeed closely related, with some differences which are worth to point out. Although adhesive models cover a vast type of interface energy profiles, see e.g.…”

“…Besides rate-independent evolutions also rate-dependent systems with inertial effects have been considered to describe the motion of visco-elastic bodies together with crack propagation, delamination, debonding and damage evolution; we quote only some important contributions, as [8,14,9,7,32,31,10,34,24] and references therein. In some cases, starting from dynamic models it is possible to recover a quasi-static evolution by time rescaling.…”

“…Let us now describe the model. Following the quasi-static models of [23,22] and the dynamical model of [34] we are here interested in an evolution accounting for visco-elastic and inertial effects, in the bulk, and traction-separation laws with finite activation threshold and different loading-unloading regimes, in the cohesive interface. A closer comparison with the setting and the results of [34] is postponed at the end of the introduction.…”

“…Following the quasi-static models of [23,22] and the dynamical model of [34] we are here interested in an evolution accounting for visco-elastic and inertial effects, in the bulk, and traction-separation laws with finite activation threshold and different loading-unloading regimes, in the cohesive interface. A closer comparison with the setting and the results of [34] is postponed at the end of the introduction. Let Ω ⊂ R 2 represent (the planar section of) our reference configuration, consisting of a couple of elastic bodies in contact along a common interface K, i.e., Ω = Ω + ∪ Ω − and K = ∂Ω + ∩ ∂Ω − .…”

Cohesive Fracture in 1D: Quasi-static Evolution and Derivation from Static Phase-Field Models

“…In these cases the existence of a quasi-static evolution (encoding in the definition the relevant notion of irreversibility) is established. In the cohesive fracture context, further results on evolutions of local minimizers or critical points (rather than global minimizers) are obtained in [4,9,17,45,47].…”