Spherical elastic-plastic wave solutions
type: Item
instance of: scholarly article
title: Spherical elastic-plastic wave solutions
zbMATH Open document ID: 0632.73029
DOI: 10.1016/0022-5096(88)90018-X
author: B. George
published in: Journal of the Mechanics and Physics of Solids
publication date: 1988-01-01T00:00:00Z
review text: Two closed-form radially symmetric elastic-plastic wave solutions, corresponding to spherical cavity loadings, are compared to numerical solutions constructed by a finite difference code. An infinitesimal strain theory, with plastic incompressibility, a Mises yield condition and either perfectly plastic flow or parabolic work hardening, allows wave function representations in both elastically and plastically deforming regions. The solutions examined are for (a) the loading problem in which the cavity wall pressure is raised instantaneously to a value \(p_ 0\), sufficient to induce plastic yielding, then maintained at \(p_ 0\), and (b) the unloading problem when the wall pressure is released continuously after the instantaneous step to \(p_ 0\). In the former case there is a region of continuous plastic loading extending from the cavity wall to the diverging plastic discontinuity front which persists for a finite time until the plastic discontinuity is annulled. In the latter case, provided that the initial pressure decrease rate exceeds a critical value, the region behind the diverging plastic discontinuity front is purely elastic. In both cases the numerical solution smears the plastic discontinuity, and while the maintained plastic loading in case (a) allows the maximum pressure to be attained over a finite distance, this is prevented by the elastic unloading in case (b) and the following release wave is significantly distorted. It is shown that suitable ramping of the applied load produces an excellent analytic-numeric agreement unless the continuous unloading is too rapid.
Mathematics Subject Classification ID: 74J99
Mathematics Subject Classification ID: 74C99
zbMATH DE Number: 4029007
zbMATH Keywords: closed-form radially symmetric elastic-plastic wave solutions
zbMATH Keywords: spherical cavity loadings
zbMATH Keywords: finite difference code
zbMATH Keywords: infinitesimal strain theory
zbMATH Keywords: plastic incompressibility
zbMATH Keywords: Mises yield condition
zbMATH Keywords: perfectly plastic flow
zbMATH Keywords: parabolic work hardening
MaRDI profile type: Publication
cites work: The starting problem for spherical elastic-plastic waves of small amplitude
cites work: Existence and uniqueness of elastic-plastic interfaces
cites work: Spherical wave propagation in elastic-plastic work-hardening materials
cites work: PLANE WAVE PROPAGATION IN ANISOTROPIC JOINTED MEDIA
cites work: Existence and uniqueness of solutions to uni-axial elastic-plastic wave interactions
full work available at URL: 0022-5096(88)90018-x
OpenAlex ID: W2033493858
description: scientific article; zbMATH DE number 4029007