Elastic-plastic Deformation at Finite Strains

In some circumstances, elastic-plastic deformation occurs in which both components of strain are finite. Such situations fall outside the scope of classical plasticity theory which assumes either infinitesimal strains or plastic-rigid theory for large strains. The present theory modifies the kinematics to include finite elastic and plastic strain components. For situations requiring this generalization, dilatational influences are usually significant including thermo-mechanical coupling. This is introduced through the consideration of two coupled thermodynamic systems: one comprising thermo-elasticity at finite strain and the other the irreversible process of dissipation and absorption of plastic work. The present paper generalizes a previous theory to permit arbitrary deformation histories. Introduction Fig. 1 shows the stress-strain curve in tension or shear for a ductile metal such as aluminum. Plastic deformation sets in at A , and the material work hardens along ABE . Unloading from B is elastic along BC , and the elastic strain at B , CD in magnitude, Is recovered on unloading down to zero stress at C . The remaining strain OC is the plastic strain associated with loading to the point B . The magnitude of the elastic strain CD is equal to the yield stress divided -3 by the elastic modulus and is of the order 10 . Plastic flow can