2 research outputs found
Γ-Limits of convolution functionals
We compute the Γ-limit of a sequence of non-local integral functionals depending on a regularization of the gradient term by means of a convolution kernel. In particular, as Γ-limit, we obtain free discontinuity functionals with linear growth and with anisotropic surface energy density
Eigendamage: an Eigendeformation model for the variational approximation of cohesive fracture -- a one-dimensional case study
We study an approximation scheme for a variational theory of cohesive
fracture in a one-dimensional setting. Here, the energy functional is
approximated by a family of functionals depending on a small parameter 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 , the approximate functionals -converge to
a cohesive zone model.Comment: Comments are welcome