Speaker
Description
We give a brief overview of our previous work analyzing models for dynamic phase-field fracture in viscoelastic materials under small strains [1]. Building on this, the initial steps towards an extension of the framework to finite strains are addressed. In this context, we adopt a first-order formulation for the momentum balance to describe the dynamics of the elastic solid. To model the material response, a polyconvex stored elastic energy density W = W(F, H, J) is employed, depending on the gradient of the deformation F, its cofactor H, and Jacobian J. For a fully discrete approximation scheme, existence, stability, and consistency conditions for the discrete solutions are established, and convergence to a measure-valued limit in the sense of [2] and [3] are discussed.
This work is financially supported by the German Research Foundation (DFG) in the priority programme “Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials” (SPP 2256) within the project “Nonlinear Fracture Dynamics: Modeling, Analysis, Approximation, and Applications”.
References:
[1] M. Thomas, S. Tornquist, C. Wieners, Approximating dynamic phase-field fracture in viscoelastic materials with a first-order formulation for velocity and stress. Preprint, Weierstraß-Institut für Angewandte Analysis und Stochastik Leibniz-Institut im Forschungsverbund Berlin eV, 2023.
[2] S. Demoulini, D. M. A. Stuart, A. E. Tzavaras, A variational approximation scheme for three-dimensional elastodynamics with polyconvex energy, Arch. Rational Mech. Anal. 157 (2001), no. 4, 325-344
[3] E. Feireisl, M. Lukáčová-Medvid'ová, H. Mizerová, K-convergence as a new tool in numerical analysis, IMA J. Num. Anal. 40 (2020), 2227–2255.
