On a rate-independent damage model for hybrid laminates with cohesive interface

Filippo Riva (Università di Pavia)

Seminario online

Abstract. Rate-independence is the property of a system whose behaviour is preserved by time-reparametrisations. In the framework of mechanical systems this feature is possessed by many different models, assuming that the acting forces are so slow that inertia can be neglected. In this setting, the term quasistatic is also adopted to denote the fact that the system evolves, thus it is not static, but the evolution is not driven by inertia and thus it cannot be dynamic. In this talk I will present a quasistatic damage model for two bars glued together and subjected to a horizontal loading; we assume the adhesive interface connecting the two layers follows a cohesive law.
The approach is based on a phase-field description of the (irreversible) damage variable and on the nowadays consolidated concept of (globally stable) energetic evolution introduced by Mielke, Roubicek and Theil to deal with quasistatic problems. Due to the presence of the cohesive zone, compactness mathematical issues usually lead to the introduction of a fictitious variable replacing the physical one which represents the maximal opening of the interface displacement reached during the evolution. I will illustrate a novel strategy which allows to recover the equivalence between the fictitious and the real variable under general loading-unloading regimes. The argument is based on temporal regularity of energetic evolutions, achieved by means of a careful balance between the convexity of the elastic energy of the layers and the natural concavity of the cohesive energy of the interface.
This is a joint work with E. Bonetti, C. Cavaterra and F. Freddi.