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arXiv · 2602.11915

Eigenfracture approximation of quasi-static crack growth in brittle materials

Ba Duc Duong·Manuel Friedrich
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Abstract

We study an approximation scheme for a variational theory of quasi-static crack growth based on an eigendeformation approach. We consider a family of energy functionals depending on a small parameter $\varepsilon$ and on two fields, the displacement field and an eigendeformation field that approximates the crack in the material. By imposing a suitable irreversibility condition and adopting an incremental minimization scheme, we define a notion of quasi-static evolution for this model. We then show that, as $\varepsilon \to 0$, these evolutions converge to a quasi-static crack evolution for the Griffith energy of brittle fracture, characterized by irreversibility, global stability, and an energy balance.

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Ba Duc Duong, Manuel Friedrich. 2026-02-12. Eigenfracture approximation of quasi-static crack growth in brittle materials. https://arxiv.org/abs/2602.11915

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