Quasistatic delamination problem

Abstract

We study delamination of two elastic bodies glued together by an adhesive that can undergo a unidirectional inelastic rate-independent process. The quasistatic delamination process is thus activated by time-dependent external loadings, realized through body forces and displacements prescribed on parts of the boundary. The novelty of this work consists of considering the glue as infinitesimally thin and ideally rigid in the sense that a crack in the glue cannot be seen before, speaking "microscopically", all macromolecular links of the adhesive are fully debonded. The concept of energetic solution is applied and existence of such solutions is proved by showing Γ -convergence of a suitable approximation that, in addition, allows for a direct computer implementation, unlike the original problem.

Stress-driven local-solution approach to quasistatic brittle delamination

“…(2.6) and (3.1c) below, differs significantly from the scaling applied in [42] for the setting of energetic solutions. On the first glance, the new scaling even looks rather surprising because asymptotically the fracture toughness tends to 0, and thus, the dissipated energy due to delamination vanishes.…”

“…This last example even exhibits a good qualitative agreement with an everyday experience that, in very brittle materials, like, e.g., glass or, here, the brittle adhesive, the crack propagates very easily if once nucleated. Obviously, the scaling keeping the dissipation fixed as on Figure 2 (left) and as used for the energetic solutions in [42] would give completely wrong response without any delamination in the limit. Conversely, energetic solutions with the scaling as on Figure 2 (right) (3.1c) would give also completely wrong response with delamination at the very beginning.…”

“…[40,41], it is the aim of this paper to establish the notion of stress-driven local solutions also for the setting of brittle delamination. For this, we will valorize the method of an adhesive contact approximation of brittle delamination studied in [42] in the context of energetic solutions. More specifically, in this paper we address a delamination problem of two elastic bodies at small strains glued along a contact boundary Γ C by a brittle adhesive with a prescribed fracture toughness.…”

Quasistatic delamination models for Kirchhoff‐Love plates

“…For ε > 0 the proposition has been proven for the unscaled problem in [35]. The case ε = 0 can be treated similarly.…”

Dimension reduction of a crack evolution problem in a linearly elastic plate

“…In this context crack growth is studied, differently from Griffith's approach, without prescribing the crack path position. Nonetheless in several contexts it is still convenient to start the study within the framework in which the crack path is known in advance, see, e.g., [7,18,19] and references therein.…”