An iteration method to study nonlinear wave propagation for a non-Green elastic 1D bar

The problem of propagation of nonlinear waves in a 1D bar is studied, wherein the linearized strain tensor is considered as a function of the Cauchy stress tensor. Specifically, two constitutive equations for non-Green elastic solids are investigated, introducing a novel numerical iterative method c...

Full description

Saved in:
Bibliographic Details
Published inIMA journal of applied mathematics Vol. 89; no. 2; pp. 426 - 440
Main Authors Bustamante, R, Arrue, P, Orellana, O, Meneses, R
Format Journal Article
LanguageEnglish
Published Oxford University Press 04.08.2024
Subjects
nonlinear elasticity
small gradient of the displacement field
rock mechanics
strain-limiting behaviour
Online AccessGet full text

Cover

More Information
Summary:The problem of propagation of nonlinear waves in a 1D bar is studied, wherein the linearized strain tensor is considered as a function of the Cauchy stress tensor. Specifically, two constitutive equations for non-Green elastic solids are investigated, introducing a novel numerical iterative method capable of obtaining approximate solutions of one nonlinear constitutive equation for rock, and one constitutive equation that shows a strain-limiting behaviour. The numerical results are compared with exact solutions for the case of a linearized elastic solid.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxae017