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Pascal Steinke

Publications and source records attributed to Pascal Steinke.

5 recordsLinked to original sources
arXiv2026

Homogenization of Interaction Energy of Dislocation Loops

We consider the sum of interaction energies of an array of dislocation loops placed on a homogenization lattice as the lattice spacing and diameter of the loops tend to zero. Under suitable well-separation and L2 -boundedness assumptions, a formula for the limit of the total interaction energy is derived in terms of the weak limit, the generated H-measure and the generated Wigner measure of the associated Burgers vectors and oriented surface areas.

math.AP↗
arXiv2024

Linearization of quasistatic fracture evolution in brittle materials

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 fields and their associated crack sets converge to a solution of quasistatic crack growth in linear elasticity without any a priori assumptions on the geometry of the crack set. This result corresponds to the evolutionary counterpart of the static linearization result by the first author, where a Griffith model for nonsimple brittle materials has been considered featuring an elastic energy which also depends suitably on the second gradient of the deformations. The proof relies on a careful study of unilateral global minimality, as determined by the nonlinear evolutionary problem, and its linearization together with a variant of the jump transfer lemma in GSBD.

math.AP↗
arXiv2023

Convergence of Allen-Cahn equations to De Giorgi's multiphase mean curvature flow

This paper presents a conditional convergence result of solutions to the Allen--Cahn equation with arbitrary potentials to a De Giorgi type $ \mathrm{BV} $-solution to multiphase mean curvature flow. Moreover we show that De Giorgi type $\mathrm{BV} $-solutions are De Giorgi type varifold solutions, and thus our solution is unique in a weak-strong sense.

math.AP↗