Atomistic-to-continuum convergence for quasi-static crack growth in brittle materials

Friedrich M, Seutter J (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Mathematical Models & Methods in Applied Sciences World Scientific Publishing

DOI: 10.1142/S0218202525500198

Abstract

We study the atomistic-to-continuum limit for a model of quasi-static crack evolution driven by time-dependent boundary conditions. We consider a two-dimensional atomic mass spring system whose interactions are modeled by classical interaction potentials, supplemented by a suitable irreversibility condition accounting for the breaking of atomic bonding. In a simultaneous limit of vanishing interatomic distance and discretized time step, we identify a continuum model of quasistatic crack growth in brittle fracture [G. A. Francfort and J.-J. Marigo, Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids 46 (1998) 1319–1342] featuring an irreversibility condition, a global stability, and an energy balance. The proof of global stability relies on a careful adaptation of the jump-transfer argument in [G. A. Francfort and C. J. Larsen, Existence and convergence for quasi-static evolution in brittle fracture, Commun. Pure Appl. Math. 56 (2003) 1465–1500] to the atomistic setting.

Authors with CRIS profile

Manuel Friedrich Professur für Angewandte Mathematik (Angewandte Analysis) Joscha Seutter Professur für Angewandte Mathematik (Angewandte Analysis)

How to cite

APA:

Friedrich, M., & Seutter, J. (2025). Atomistic-to-continuum convergence for quasi-static crack growth in brittle materials. Mathematical Models & Methods in Applied Sciences. https://doi.org/10.1142/S0218202525500198

MLA:

Friedrich, Manuel, and Joscha Seutter. "Atomistic-to-continuum convergence for quasi-static crack growth in brittle materials." Mathematical Models & Methods in Applied Sciences (2025).

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