We set up and investigate an approximation scheme for a variational theory of cohesive fracture in antiplane shear deformations. We consider a family of functionals acting on scalar valued functions in general dimensions depending on a small parameter $0<\varepsilon \ll 1$ and on two fields: the elastic part of the displacement field and an eigendeformation field that describes the inelastic response of the material beyond the elastic regime. We measure the inelastic contributions of the latter in terms of a non-local energy functional. Our main result shows that, as $\varepsilon \to 0$, the approximate functionals $\Gamma$-converge to a cohesive zone model.
We study the $\Gamma$-convergence of a general class of anisotropic phase-field functionals modelling cohesive fracture in the multidimensional, vector-valued, and geometrically nonlinear setting. The limiting energy comprises a quasiconvexified bulk term, a Cantor part governed by its recession function, and a cohesiv...
Yield point phenomena in metals, anticracks in soils and snows, or planewise collapses in lattice metamaterials, are different manifestations of plastic instabilities characterized by stress softening and strain localization. Several independent constitutive descriptions exist and suffer from similar challenges: experi...
Linearization is a classical tool in continuum mechanics that connects nonlinear models of solids to their linear counterparts through the small-strain limit, as in the passage from finite to linear elasticity. Here, we study a nonlocal analogue of this limit process in the context of state-based peridynamics, starting...
Carolin Kreisbeck, C. Mora-Corral, Felix Seifert· 0 citations
An interior penalty nonconforming finite element method is developed for a strain gradient elasticity (SGE) model in arbitrary dimensions, using an $H^1$-nonconforming displacement element built from vector-valued quadratic polynomials enriched by divergence-free face bubbles. Rigorous analysis establishes optimal and...
We consider a problem in the inelastic deformation theory. There is a body consisted of a viscoplastic material, which is deformed in a quasistatic process i.e. the movement varies slowly. Additionally we assume that the body has a contact with a rigid foundation: the body moves on the foundation with a friction modell...
Łukasz Gleń· Journal of Convex Analysis· 0 citations
