Calculus of Variations and Geometric Measure Theory

F. Maddalena - D. Percivale - F. Tomarelli

Local and non-local energies in adhesive interaction

created by tomarelli1 on 10 Oct 2017


Published Paper

Inserted: 10 oct 2017
Last Updated: 10 oct 2017

Journal: IMA Journal of Applied Mathematics
Volume: 81
Number: 6
Pages: 1051-1075
Year: 2016
Doi: doi:10.1093/imamat/hxw044
Links: link to the article online: IMA Journal of Applied Mathematics


We introduce and study a variational model describing a reinforcing sheet, which is glued to an elastic-breakable matrix: the glue and the matrix react elastically to deformations up to a finite threshold. The analysis is performed in linear and nonlinear elasticity. The adhesion energy density is allowed to be neither convex nor differentiable. We provide a description of the conditions characterizing debonding and global collapse of the structure. A detailed analysis is performed in the case of a ring-shaped geometry.

Keywords: calculus of variations, Thin films, elasticity, adhesion, elastic-brittle materials, collapse