Simulation of the propagation of a cylindrical shear wave : non linear and dissipative modelling

TL;DR

This paper presents a numerical method for simulating the propagation of cylindrical shear waves with non-linear and dissipative effects due to hysteresis in the stress-strain relationship, relevant for seismic studies.

Contribution

It introduces a novel numerical process capable of handling non-linear, non-differentiable hysteresis effects in wave propagation simulations.

Findings

Successfully models non-linear wave behavior with hysteresis

Handles non-differentiable points in the stress-strain loop

Provides a tool for seismic wave environment analysis

Abstract

The simulation of a wave propagation caused by seismic stimulation allows to study the behaviour of the environment and to evaluate the consequences. The model involves the wave equation with a hysteresis loop in the stress-strain relationship. This induces non-linearities and, at the vertices of the loop, non-differentiable mathematical operators. This paper offers a numerical process which works out this simulation.