Approximating dynamic phase-field fracture in viscoelastic materials with a first-order formulation for velocity and stress
Authors
- Thomas, Marita
ORCID: 0000-0001-9172-014X - Tornquist, Sven
- Wieners, Christian
ORCID: 0000-0001-6242-6777
2020 Mathematics Subject Classification
- 74H10 74H20 35M86 35Q74 74J05 65M60
Keywords
- Visco-elastodynamic damage, phase-field method, discontinuous Galerkin method, first-order formulation of momentum balance, elastic waves in solids
DOI
Abstract
We investigate a model for dynamic fracture in viscoelastic materials at small strains. While the sharp crack interface is approximated with a phase-field method, we consider a viscous evolution with a quadratic dissipation potential for the phase-field variable. A non-smooth constraint enforces a unidirectional evolution of the phase-field, i.e. material cannot heal. The viscoelastic equation of motion is transformed into a first order formulation and coupled in a nonlinear way to the non-smooth evolution law of the phase field. The system is fully discretized in space and time with a discontinuous Galerkin approach for the first-order formulation. Based on this, existence of discrete solutions is shown and, as the step size in space and time tends to zero, their convergence to a suitable notion of weak solution of the system is discussed.
Download Documents