Anisotropic energies for the variational modeling of cavitation in nonlinear elasticity

2025/03/29 by Marco Bresciani, Bresciani, Marco · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2503.23143

openalex publication_date 2025/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence of minimizers for free-discontinuity functionals in nonlinear elasticity, where discontinuities correspond to the phenomenon of cavitation. The energy comprises two terms: a volume term accounting for the elastic energy; and a surface term concentrated on the boundaries of the cavities in the deformed configuration that depends on their unit normal. While the treatment of the first term in standard, that of the second one relies on the regularity of inverse deformations, their weak continuity properties, and Ambriosio's lower semicontinuity theorem for special functions of bounded variation.

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