2024/11/20 by Manuel Friedrich, Friedrich, Manuel, Pascal Steinke +3
Engineering · Materials Science · #49J45 #70G75 #74B10 #74B20 #74G65 #74R10 #Analysis of PDEs (math.AP) #Elasticity and Wave Propagation #FOS: Mathematics #Functional Analysis (math.FA) #Geotechnical and Geomechanical Engineering #High-Velocity Impact and Material Behavior
paper · pdf · doi:10.48550/arxiv.2411.13446
openalex publication_date 2024/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove 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 the first author, 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.