Calculus of Variations and Geometric Measure Theory

P. M. Mariano - D. Mucci

Cracking brittle thin films

created by mucci on 17 Dec 2020


Submitted Paper

Inserted: 17 dec 2020
Last Updated: 17 dec 2020

Year: 2020


We describe thin films as surfaces endowed with directors satisfying a non-degeneracy condition under large strain. We then consider through-the-thickness descriptors of the material microstructure taking values on a finite-dimensional, complete, differentiable, intrinsic manifold, a choice leading to general results, unifying models of different material classes because they are independent of specific microstructural geometric features. We look at brittle materials. We consider cracks as rectifiable sets supporting appropriate curvature varifolds and containing the jump sets of fields involved. The choice allows us to describe the circumstance in which along the deformation crack margins remain in contact at least partially. We prove existence of energy minima for different (constitutive) functional choices. In all of them we consider deformations as weak diffeomeorphisms modeled over the space of $SBV$ maps satisfying an impenetrability condition.

Keywords: calculus of variations, microstructures, varifolds, shells, fracture, ground states