Calculus of Variations and Geometric Measure Theory

R. Alessi - V. Crismale - G. Orlando

Fatigue effects in elastic materials with variational damage models: A vanishing viscosity approach

created by crismale on 13 Jul 2018
modified on 13 Dec 2019


Published Paper

Inserted: 13 jul 2018
Last Updated: 13 dec 2019

Journal: J. Nonlinear Sci.
Volume: 29
Number: 3
Pages: 1041-1094
Year: 2019
Doi: 10.1007/s00332-018-9511-9

ArXiv: 1807.04675 PDF


We study the existence of quasistatic evolutions for a family of gradient damage models which take into account fatigue, that is the process of weakening in a material due to repeated applied loads. The main feature of these models is the fact that damage is favoured in regions where the cumulation of the elastic strain (or other relevant variables, depend on the model) is higher. To prove the existence of a quasistatic evolution, we follow a vanishing viscosity approach based on two steps: we first let the time-step $\tau$ of the time-discretisation and later the viscosity parameter $\epsilon$ go to zero. As $\tau \to 0$, we find $\epsilon$-approximate viscous evolutions; then, as $\epsilon \to 0$, we find a rescaled approximate evolution satisfying an energy-dissipation balance.