Marita Thomas: Approximating dynamic phase-field fracture with a first-order formulation for velocity and stress

Vortragender/Speaker: Prof. Dr. Marita Thomas (WIAS - Berlin)
Ansprechpartner/Contact: Jun. Prof. Dr. Markus Schmidtchen
Videostream (BBB): (on request)

Titel/Title:
Approximating dynamic phase-field fracture with a first-order formulation
for velocity and stress

Zusammenfassung/Abstract:
We investigate a model for dynamic fracture at small strains. The sharp
crack interface is regularized with a phase-field approximation. For the
phase-field variable a viscous evolution with a quadratic dissipation
potential is employed and a non-smooth penalization prevents material
healing. For the solid material both the case of a visco-elastic and of a
purely elastic constitutive law is considered. The 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 variable. We introduce 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. We discuss their convergence to a suitable notion of
weak solution of the system as the step size in space and time tends to
zero and give a comparison to other formulations existing in literature.
Simulation results are presented.

This is joint work with Sven Tornquist (Berlin) and Christian Wieners
(Karlsruhe) and also based upon collaboration with Kerstin Weinberg and
Kai Friebertshäuser (both Siegen) within the priority programme
“Variational Methods for Predicting Complex Phenomena in Engineering
Structures and Materials” (SPP 2256), project “Nonlinear Fracture
Dynamics: Modeling, Analysis, Approximation, and Applications”,
financially supported by the German Research Foundation (DFG).