Local and global bifurcation phenomena in plane-strain finite elasticity (Q760239)

Bifurcation, global non-uniqueness and stability of solutions to the plane-strain problem of an incompressible isotropic elastic material subject to in-plane dead-load tractions are considered. In particular, for loading in equibiaxial tension, bifurcation from a configuration in which the in-plane principal stretches are equal is shown to occur at a certain critical value of the tension (which depends on the form of strain-energy function). Results concerning the global invertibility of the elastic stress-deformation relations are obtained and then used to derive an equation governing the deformation paths branching from this critical value. The stability of each branch is also examined. The analysis is carried through for a general form of strain-energy function and the results are then illustrated for a particular class of strain- energy functions.