Bifurcation and stability of homogeneous equilibrium configurations of an elastic body under dead-load tractions
- 1 September 1983
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 94 (2) , 315-339
- https://doi.org/10.1017/s030500410006117x
Abstract
In this paper we consider the equilibrium configurations of a homogeneous, incompressible, isotropic elastic body subjected to a uniform dead load surface traction of magnitude T whose direction is normal to the surface of the body in the reference configuration, and to no other forces. We concentrate on homogeneous equilibrium solutions, that is those for which the deformation gradient F is constant, and we study their bifurcations and stability (with respect to an appropriate static criterion) as T varies. Since it turns out that the equations for homogeneous equilibrium solutions, and the stability properties that we consider of these solutions, are independent of the shape of the body in the reference configuration, we can suppose if desired that this shape is a cube. (See Fig. 1.1.)Keywords
This publication has 20 references indexed in Scilit:
- Discontinuous equilibrium solutions and cavitation in nonlinear elasticityPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1982
- Imperfect bifurcation in the presence of symmetryCommunications in Mathematical Physics, 1979
- A theory for imperfect bifurcation via singularity theoryCommunications on Pure and Applied Mathematics, 1979
- Stability of an elastic cube under dead loading: Two equal forcesInternational Journal of Non-Linear Mechanics, 1976
- A basic open problem in the theory of elastic stabilityPublished by Springer Nature ,1976
- The properties of rubber in pure homogeneous strainJournal of Physics D: Applied Physics, 1975
- Internal rupture of bonded rubber cylinders in tensionProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1959
- On uniqueness and stability in the theory of finite elastic strainJournal of the Mechanics and Physics of Solids, 1957
- Large elastic deformations of isotropic materials. II. Some uniqueness theorems for pure, homogeneous deformationPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1948
- Torsion of a Rubber CylinderJournal of Applied Physics, 1947