2021/04/17 by Laura Lauerbach, Lauerbach, Laura, Anja Schlömerkemper +1
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #Enhanced Oil Recovery Techniques #FOS: Mathematics #Rock Mechanics and Modeling
paper · pdf · doi:10.48550/arxiv.2104.08607
openalex publication_date 2021/04/17 · openalex created_date 2022/09/14 · openalex updated_date 2026/07/28
A mathematical continuum limit of the interaction energy of a random particle\nchain is shown to yield new insight into the effect of microscopic\nheterogeneities on macroscopic fracture laws in brittle materials. We derive a\nformula which yields that either elastic behaviour or a crack is energetically\npreferred. The formula explicitly shows the dependence on the boundary\ncondition and the microstructure of the chain. The mathematical analysis is\nbased on a variational convergence \Γ-convergence of convex-concave\npotentials together with ergodic theorems which are common tools in stochastic\nhomogenization.\n