Nonlinear Partial Differential Equations

Date: March 25, 2025

Time: 3:00PM - 4:00PM

Location: Blocker 302

Speaker: Marita Thomas, Freie Universitaet - Berlin

Title: First-order formulation for dynamic phase-field fracture in viscoelastic materials

Abstract: We investigate a model for dynamic fracture in viscoelastic materials. The sharp crack interface is regularized with a phase-field approximation, and for the phase-field variable a viscous evolution with a quadratic dissipation potential is employed. A non-smooth penalization prevents material healing.The viscoelastic momentum balance is formulated as a first order system and coupled in a nonlinear way to the non-smooth evolution equation of the phase field. We give a full discretization in time and space, using a discontinuous Galerkin method for the first order system. Based on this, we show the existence of discrete solutions and, as the step size in space and time tends to zero, we prove their convergence to a suitable notion of weak solution of the system. We discuss our modeling approach both at small and at finite strains and point out mathematical challenges. **This is joint work with Sven Tornquist (FUB), Christian Wieners (Karlsruhe), and Kerstin Weinberg (Siegen).