Coupled time discretisation of dynamic damage models at small strains

TL;DR

This paper introduces a coupled time discretisation scheme for dynamic damage models in viscoelastic materials, ensuring stability, convergence, and eliminating numerical artifacts, thus enabling reliable simulations of dynamic fracture.

Contribution

It presents a novel coupled discretisation scheme with a variational structure that guarantees stability, convergence, and reliable nonlinear solver performance for dynamic damage modeling.

Findings

The scheme suppresses spurious numerical attenuation during vibrations.

It is stable and convergent as the time step approaches zero.

The method enables reliable dynamic fracture simulations using phase-field models.

Abstract

The dynamic damage model in viscoelastic materials in Kelvin-Voigt rheology is discretised by a scheme which is coupled, suppresses spurious numerical attenuation during vibrations, and has a variational structure with a convex potential for small time-steps. In addition, this discretisation is numerically stable and convergent for the time step going to zero. When combined with the FEM spatial discretisation, it leads to an implementable scheme and to that iterative solvers (e.g. the Newton-Raphson) used for the nonlinear algebraic systems at each time level have guaranteed global convergence. Models which are computationally used in some engineering simulations in a non-reliable way are thus stabilized and theoretically justified in this viscoelastic rheology. In particular, this model and algorithm can be used in a reliable way for a dynamic fracture in the usual phase-field approximation.