Calculus of Variations and Geometric Measure Theory

M. Friedrich

A derivation of linearized Griffith energies from nonlinear models

created by friedrich on 26 Jun 2015



Inserted: 26 jun 2015
Last Updated: 26 jun 2015

Year: 2015


We derive Griffith functionals in the framework of linearized elasticity from nonlinear and frame indifferent energies in brittle fracture via Gamma-convergence. The convergence is given in terms of rescaled displacement fields measuring the distance of deformations from piecewise rigid motions. The configurations of the limiting model consist of partitions of the material, corresponding piecewise rigid deformations and displacement fields which are defined separately on each component of the cracked body. Apart from the linearized Griffith energy the limiting functional comprises also the segmentation energy which is necessary to disconnect the parts of the specimen.

Keywords: Gamma-convergence, functions of bounded variation, free discontinuity problems, Brittle materials, variational fracture , Geometric rigidity, Griffith energies