On the theory of plane strain in finitely deformed compressible materials

Abstract

In solid mechanics an outstanding lacuna is a general method for solving problems of plane strain for materials other than classically elastic, or visco-elastic, or rigid–plastic. Even with restriction to incrementally linear response, and to infinitesimal deformations superimposed on uniform pre-strains, there is no body of theory with the scope and power of the complex variable approach in isotropic elasticity. This lack has been highlighted recently by the growing interest in bifurcation phenomena in finitely deformed materials. So far, all analytical solutions to plane boundary-value problems with bifurcations (1,2,3,4) have relied on a separation-of-variables technique, which succeeds only for certain types of data.