Curvature-dependent Eulerian interfaces in elastic solids

Abstract

We propose a sharp-interface model for a hyperelastic material consisting of two phases. In this model, phase interfaces are treated in the deformed configuration, resulting in a fully Eulerian interfacial energy. In order to penalize large curvature of the interface, we include a geometric term featuring a curvature varifold. Equilibrium solutions are proved to exist via minimization. We then utilize this model in an Eulerian topology optimization problem that incorporates a curvature penalization.

References in corpus (5)

• Second order rectifiability of integral varifolds of locally bounded first variation
• A phase-field approach to Eulerian interfacial energies
• Li-Yau inequalities for the Helfrich functional and applications
• Lower-semicontinuity for the Helfrich problem
• Crack occurrence in bodies with gradient polyconvex energies

Cited by in corpus (1)

• Variational models with Eulerian-Lagrangian formulation allowing for material failure