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math.AP2025
Hausdorff dimension of the singular set for Griffith almost-minimizers in the plane
Manuel Friedrich, Camille Labourie, Kerrek Stinson
We consider regularity of the crack set associated to a minimizer of the Griffith fracture energy, often used in modeling brittle materials. We show that the crack is uniformly rec…
math.AP2025
Adaptive finite element approximation for quasi-static crack growth
Vito Crismale, Manuel Friedrich, Joscha Seutter
We provide an adaptive finite element approximation for a model of quasi-static crack growth in dimension two. The discrete setting consists of integral functionals that are define…
math.AP2024
Linearization of quasistatic fracture evolution in brittle materials
Manuel Friedrich, Pascal Steinke, Kerrek Stinson
We prove a linearization result for quasistatic fracture evolution in nonlinear elasticity. As the stiffness of the material tends to infinity, we show that rescaled displacement f…