Stochastic homogenisation for functionals defined on asymptotically piecewise rigid functions

Donnarumma AF, Friedrich M (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Calculus of Variations and Partial Differential Equations Springer Verlag (Germany)

Book Volume: 64

Article Number: 69

Journal Issue: 2

DOI: 10.1007/s00526-025-02930-w

Abstract

We study stochastic homogenisation of free-discontinuity surface functionals defined on piecewise rigid functions which arise in the study of fracture in brittle materials. In particular, under standard assumptions on the density, we show that there exists a Γ-limit almost surely and that it can be represented by a surface integral. In addition, the effective density can be characterised via a suitable asymptotic cell formula and is deterministic under an ergodicity assumption. We also show via Γ-convergence that the homogenised functional defined on piecewise rigid functions can be recovered from a Griffith-type model by passing to the limit of vanishing elastic deformations.

Authors with CRIS profile

Antonio Flavio Donnarumma Professur für Angewandte Mathematik (Angewandte Analysis) Manuel Friedrich Professur für Angewandte Mathematik (Angewandte Analysis)

How to cite

APA:

Donnarumma, A.F., & Friedrich, M. (2025). Stochastic homogenisation for functionals defined on asymptotically piecewise rigid functions. Calculus of Variations and Partial Differential Equations, 64(2). https://doi.org/10.1007/s00526-025-02930-w

MLA:

Donnarumma, Antonio Flavio, and Manuel Friedrich. "Stochastic homogenisation for functionals defined on asymptotically piecewise rigid functions." Calculus of Variations and Partial Differential Equations 64.2 (2025).

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