A mathematical continuum limit of the interaction energy of a random particle chain is shown to yield new insight into the effect of microscopic heterogeneities on macroscopic fracture laws in brittle materials. We derive a formula which yields that either elastic behaviour or a crack is energetically preferred. The formula explicitly shows the dependence on the boundary condition and the microstructure of the chain. The mathematical analysis is based on a variational convergence Γ-convergence of convex-concave potentials together with ergodic theorems which are common tools in stochastic homogenization.
@article{arxiv.2104.08607,
title = {Derivation of a variational model for brittle fracture from a random heterogeneous particle chain},
author = {Laura Lauerbach and Anja Schlömerkemper},
journal= {arXiv preprint arXiv:2104.08607},
year = {2021}
}