Open AccessNon‐linear damage rheology and wave resonance in rocks
Author(s) -
Lyakhovsky V.,
Hamiel Y.,
Ampuero J.P.,
BenZion Y.
Publication year - 2009
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.2009.04205.x
Subject(s) - resonance (particle physics) , amplitude , rheology , materials science , brittleness , mechanics , ultimate tensile strength , linear elasticity , wave propagation , elasticity (physics) , physics , composite material , optics , thermodynamics , finite element method , atomic physics
SUMMARY We address various deformational aspects of damaged materials with theoretical analyses and numerical simulations based on a non‐linear continuum damage model. Quasi‐static simulations of damage accumulation under cyclic load reproduce the laboratory‐observed increase in the difference between tensile and compressive elastic moduli with ongoing deformation beyond the elastic regime. Modelling of wave propagation effects reproduces the observed relations between the resonance frequency and wave amplitude. In agreement with laboratory experiments, the simulated resonant curves are asymmetric, with gradual decrease of wave amplitudes for frequencies higher than the resonance value and strong reduction for lower frequencies. The predicted shift of the resonance frequency with increasing wave amplitude under constant material damage is only a few per cent, whereas the resonance frequency shift associated with increasing material damage may reach tens of per cent. The results show that the employed continuum damage rheology model provides a self‐consistent treatment for multiple manifestations of non‐linear elastic and brittle deformation of solids.