A Nonlinear Theory of Plasticity for Plane Strain*

A nonlinear theory of plasticity is proposed which facilitates the solution of a restricted class of plane strain problems. An anisotropic approximation to a real material is utilized with the characteristic directions chosen a priori. The formulation is in terms of displacements and sufficient displacement boundary conditions must be prescribed in order to solve the resulting classical wave equation. Subsequently, the stress field is determined, corresponding to any nonlinear monotonic relation between shear stress and strain, by direct integration of the equilibrium equations. Uniqueness restricts the class of problems suitable to the theory. Classical isotropic theory will be closely approximated in problems where the deviatoric stress field is predominantly uniform. The theory is illustrated by the solution of an indentation problem.