Special Session 126: Defects, Microstructures, and Failure: Multiscale Variational Models

Linearization of Quasistatic Fracture Evolution in Brittle Materials
Pascal Steinke
Institute for Applied Mathematics, University of Bonn
Germany
Co-Author(s):    S. Conti, M. Friedrich, K. Stinson
Abstract:
In this talk, we discuss a linearization result for quasistatic fracture evolution in nonlinear elasticity. As the stiffness of the material tends to infinity, we show that rescaled displacement fields and their associated crack sets converge to a solution of quasistatic crack growth in linear elasticity without any a priori assumptions on the geometry of the crack set. This result corresponds to the evolutionary counterpart of the static linearization result by M. Friedrich, where a Griffith model for nonsimple brittle materials has been considered featuring an elastic energy which also depends suitably on the second gradient of the deformations. The proof relies on a careful study of unilateral global minimality, as determined by the nonlinear evolutionary problem, and its linearization together with a variant of the jump transfer lemma in GSBD proven by M. Friedrich and F. Solombrino. This is a joint project with M. Friedrich (Linz, Austria) and K. Stinson (Salt Lake City, Utah).