Cellular automaton model of damage

Abstract

We investigate the role of equilibrium methods and stress transfer range in describing the process of damage. We find that equilibrium approaches are not applicable to the description of damage and the catastrophic failure mechanism if the stress transfer is short ranged. In the long range limit, equilibrium methods apply only if the healing mechanism associated with ruptured elements is instantaneous. Furthermore we find that the nature of the catastrophic failure depends strongly on the stress transfer range. Long range transfer systems have a failure mechanism that resembles nucleation. In short range stress transfer systems, the catastrophic failure is a continuous process that, in some respects, resembles a critical point.

A damage-mechanics model for fracture nucleation and propagation

“…For ρ=3 the failure takes place at ν 0 t gf =1/3 and for ρ=6 at ν 0 t gf =1/6 as predicted by Eq. (14). The behavior for the two values of ρ is quite similar except for the reduction in the time to failure for larger ρ as well as a sharper transition from nucleation to propagation.…”

A damage model based on failure threshold weakening

“…In particular, we compare values of scaling exponents we obtain from the simulations to values for mean-field percolation and spinodal nucleation. We also place our results into the context of other recent work on similar models, with particular attention to the question of punctuated ergodicity [32,8,33,34] which has been observed in both models as well as in natural earthquake fault systems.…”

A possible mechanism for aftershocks: time-dependent stress relaxation in a slider-block model

“…However, the RJB model is advantageous to research the basic physical principles contributing to earthquake scaling laws due to its simple rules, ease of programming and speed of simulations. For these reasons it has often been used to test additional physical principles, such as damage and threshold weakening (Serino et al 2010; Gran et al 2011).…”