Analysis of stability and stability loss together with associated bifurcation phenomena in elastic and pseudoelastic solids subject to large deformations is given on the base of nonlinear elasticity equations for compessible and incompressible materials. From the viewpoint of inversion of stress-deformation relationships, the author also considers global aspects of the problem. The results obtained are applied to two problems involving homogeneous deformation. An example with bifurcation from a homogeneous state of deformation, which is associated with inhomogeneous incremental modes of deformation, is investigated in detail. The author also develops a new pseudoelasticity theory which takes into account changes in the elastic constitutive law associated with damage. Local and global stability aspects of this theory are discussed, and the theory is applied to a specific model to study the isotropic material response.
For the entire collection see [Zbl 0960.00063].