Calculus of Variations and Geometric Measure Theory

D. Knees - R. Rossi - C. Zanini

A vanishing viscosity approach to a rate-independent damage model

created by rossi on 31 Aug 2011
modified by knees on 19 Dec 2017


Published Paper

Inserted: 31 aug 2011
Last Updated: 19 dec 2017

Journal: Mathematical Models and Methods in Applied Sciences
Volume: 23
Number: 4
Pages: 565-616
Year: 2013


We analyze a rate-independent model for damage evolution in elastic bodies. The central quantities are a stored energy functional and a dissipation functional, which is assumed to be positively homogeneous of degree one. Since the energy is not simultaneously (strictly) convex in the damage variable and the displacements, solutions may have jumps as a function of time. The latter circumstance makes it necessary to recur to suitable notions of weak solution. However, the by-now classical concept of global energetic solution fails to describe accurately the behavior of the system at jumps.

Hence, we consider rate-independent damage models as limits of systems driven by viscous, rate-dependent dissipation. We use a technique for taking the vanishing viscosity limit, which is based on arc-length reparameterization. In this way, in the limit we obtain a novel formulation for the rate-independent damage model, which highlights the interplay of viscous and rate-independent effects in the jump regime, and provides a better description of the energetic behavior of the system at jumps.