Stability of homogeneous deformation of an incompressible elastic body under dead-load surface tractions

DOI10.1007/BF00049454zbMath0634.73025MaRDI QIDQ1097077

Yi-Chao Chen

Publication date: 1987

Published in: Journal of Elasticity (Search for Journal in Brave)

zbMATH Keywords

minimization problemglobal stabilityhomogeneous deformationlocally stablebiaxial dead-load surface tractionsbiaxial stretch problemisotropic, incompressible materialslocally neutrally stablenecessary and sufficient condition for local stabilityunaxial

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Dynamical problems in solid mechanics (74H99) Equilibrium (steady-state) problems in solid mechanics (74G99)

Related Items

Constitutive Models and Singularity Types for an Elastic Biaxially Loaded Rubber Sheet, Axisymmetric necking versus Treloar–Kearsley instability in a hyperelastic sheet under equibiaxial stretching, Asymmetric equilibrium configurations of hyperelastic cylindrical bodies under symmetric dead loads, Singularities of homogeneous deformations in finite elasticity, Stability of homogeneous deformations in nonlinear elasticity, A decomposition depended on directions for nonsingular linear transformation, Conditions for the onset of elastic and material instabilities in hyperelastic materials, Equilibrium paths of a hyperelastic body under progressive damage, On the relative energies of the Rivlin and cavitation instabilities for compressible materials, Bifurcation and stability of homogeneous deformations of an elastic body under dead load tractions with \(Z_ 2\) symmetry, Instabilities in Biaxially Loaded Rectangular Membranes and Spherical Balloons Made of Compressible Isotropic Hyperelastic Materials, The formation of filamentary voids in solids, A Simple Model of the Treloar—Kearsley Instability, Phase Transformations in Isotropic Elastic Materials Induced by Shear Stress States, Homogeneous equilibrium configurations of a hyperelastic compressible cube under equitriaxial dead-load tractions, Equilibrium configurations and stability of a damaged body under uniaxial tractions, On the dead load boundary value problem

Cites Work

• Unnamed Item
• Unnamed Item
• Some static and dynamic implications of the general theory of elastic stability
• On uniqueness in finite elasticity with general loading
• Minimization in incompressible nonlinear elasticity theory
• On the stability of finitely deformed elastic membranes. I: Stability of a uniformly deformed plane membrane
• Discontinuous equilibrium solutions and cavitation in nonlinear elasticity
• Bifurcation and stability of homogeneous equilibrium configurations of an elastic body under dead-load tractions
• ENERGY-MINIMAL FINITE DEFORMATIONS OF A SYMMETRICALLY LOADED ELASTIC SHEET
• STABILITY OF PURE HOMOGENEOUS DEFORMATIONS OF AN ELASTIC PLATE WITH FIXED EDGES
• Stability of pure homogeneous deformations of an elastic cube under dead loading
• Large elastic deformations of isotropic materials. I. Fundamental concepts