Core-Radius Approximation of Singular Minimizers in Nonlinear Elasticity

Bresciani M, Friedrich M (2026)

Publication Type: Journal article

Publication year: 2026

Journal

Applied Mathematics and Optimization Springer Verlag (Germany)

Book Volume: 93

Article Number: 21

Journal Issue: 1

DOI: 10.1007/s00245-025-10376-x

Abstract

We study a variational model in nonlinear elasticity allowing for cavitation which penalizes both the volume and the perimeter of the cavities. Specifically, we investigate the approximation of the energy (in the sense of -convergence) by means of functionals defined on perforated domains. Perforations are introduced at flaw points where singularities are expected and, hence, the corresponding deformations do not exhibit cavitation. Notably, those points are not prescribed but rather selected by the variational principle. Our analysis is motivated by the numerical simulation of cavitation and extends previous results on models which solely accounted for elastic energy without contributions related to the formation of cavities.

Authors with CRIS profile

Marco Bresciani Department Mathematik

Involved external institutions

Johannes Kepler Universität (JKU) Linz

Austria (AT)

How to cite

APA:

Bresciani, M., & Friedrich, M. (2026). Core-Radius Approximation of Singular Minimizers in Nonlinear Elasticity. Applied Mathematics and Optimization, 93(1). https://doi.org/10.1007/s00245-025-10376-x

MLA:

Bresciani, Marco, and Manuel Friedrich. "Core-Radius Approximation of Singular Minimizers in Nonlinear Elasticity." Applied Mathematics and Optimization 93.1 (2026).

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