Calculus of Variations and Geometric Measure Theory

M. Bresciani - M. Friedrich

Quasistatic growth of cavities and cracks in the plane

created by bresciani on 19 Jun 2024
modified on 10 Mar 2025

[BibTeX]

Accepted Paper

Inserted: 19 jun 2024
Last Updated: 10 mar 2025

Journal: SIAM Journal of Mathematical Analysis
Year: 2024

ArXiv: 2406.11293 PDF

Abstract:

We propose a model for quasistatic growth of cavities and cracks in two-dimensional nonlinear elasticity. Cavities and cracks are modeled as discrete and compact subsets of a planar domain, respectively, and deformations are defined only outside of cracks. The model accounts for the irreversibility of both processes of cavitation and fracture and it allows for the coalescence of cavities into cracks. Our main result shows the existence of quasistatic evolutions in the case of a finite number of cavities, under an a priori bound on the number of connected components of the cracks.