The remarkable nature of radially symmetric equilibrium states of aeolotropic nonlinearly elastic bodies
type: Item
instance of: scholarly article
title: The remarkable nature of radially symmetric equilibrium states of aeolotropic nonlinearly elastic bodies
zbMATH Open document ID: 0631.73016
DOI: 10.1007/BF00127554
author: Stuart S. Antman
author: Pablo V. Negrón-Marrero
published in: Journal of Elasticity
publication date: 1987-01-01T00:00:00Z
review text: The radially symmetric equilibrium states of nonlinear, aelotropic, elastic cylinders and balls under constant normal forces on their boundaries are investigated. It is demonstrated that solutions describing both intact and cavitating states are possible because of aeolotropy. These solutions exhibit new phenomena, which does not seem to exist for isotropic bodies, e.g., it is shown that there are materials for which there exists a critical pressure, i.e., if the forces on the boundary are below the critical pressure, then the normal pressures at the center are zero, however if the forces at the boundary are above the critical value then the normal pressure at the center increases indefinitely. It is also shown that there are materials for which there is no equilibrium state with center intact when the boundary is subjected to uniform tension.
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74E10
zbMATH DE Number: 4026906
zbMATH Keywords: radially symmetric equilibrium states
zbMATH Keywords: aelotropic
zbMATH Keywords: elastic cylinders
zbMATH Keywords: balls
zbMATH Keywords: constant normal forces
zbMATH Keywords: intact
zbMATH Keywords: cavitating states
zbMATH Keywords: critical pressure
zbMATH Keywords: uniform tension
reviewed by: Pratap Puri
MaRDI profile type: Publication
cites work: The eversion of thick spherical shells
cites work: Regular and singular problems for large elastic deformations of tubes, wedges, and cylinders
cites work: Discontinuous equilibrium solutions and cavitation in nonlinear elasticity
cites work: Hodograph method of nonlinear stress analysis of thick-walled cylinders and spheres, including porous materials
cites work: Membrane buckling: A study of solution multiplicity
cites work: Sur le polygone de Newton
cites work: Q5576462
cites work: Large thermal buckling of nonuniform beams and plates
cites work: Q3263386
cites work: A bifurcation problem for a compressible nonlinearly elastic medium: Growth of a micro-void
cites work: Discontinuous energy minimizers in nonlinear elastostatics: An example of J. Ball revisited
cites work: Q5724467
cites work: Uniqueness of regular and singular equilibria for spherically symmetric problems of nonlinear elasticity
cites work: Radially symmetric cavitation for hyperelastic materials
cites work: Q4023641
description: scientific article; zbMATH DE number 4026906