Derivation of a variational model for brittle fracture from a random heterogeneous particle chain

Laura Lauerbach; Anja Schlömerkemper

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arXiv · 2104.08607

Derivation of a variational model for brittle fracture from a random heterogeneous particle chain

Laura Lauerbach·Anja Schlömerkemper

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Abstract

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 $\Gamma$-convergence of convex-concave potentials together with ergodic theorems which are common tools in stochastic homogenization.

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Laura Lauerbach, Anja Schlömerkemper. 2021-04-17. Derivation of a variational model for brittle fracture from a random heterogeneous particle chain. https://arxiv.org/abs/2104.08607

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