A Geometric Theory of Plasticity

A new geometric formulation of rate-independent generalized plasticity is presented. The formulation relies crucially on the consideration of the physical (referential) metric as a primary internal variable and does not invoke any decomposition of the kinematical quantities into elastic and plastic parts. On the basis of a purely geometrical argument the transition to classical plasticity is demonstrated. The covariant balance of energy is systematically employed for the derivation of the mechanical state equations. It is shown that unlike the case of finite elasticity, in finite plasticity, the covariant balance of energy does not yield the Doyle-Ericksen formula, unless a further assumption is made. As an application, a new material model is developed and is tested numerically for the solution of several problems of large scale plastic flow.