Finite-Strain Elastic—Plastic Theory with Application to Plane-Wave Analysis

Abstract

In the generation of plane waves in metal plates by detonation of contact explosives, the pressures reached can be sufficiently high to produce finite elastic and plastic strain components, and appreciable changes in temperature due to thermomechanical coupling effects. A theory of elastic—plastic deformation is developed to include these conditions. Finite elastic and plastic deformations are represented in terms of the initial and final configurations of the body, and an unstressed configuration subject only to plastic flow. In general, this configuration cannot be represented by a continuous displacement function. The analysis of the kinematics of these three states is carried out for general deformation history. The discussion of the application of finite deformation thermoelastic theory is limited to the conditions in a plane wave with fixed principal directions. Plasticity theory with the consideration of variable temperature is also restricted to the plane‐wave situation. The influence of the thermodynamic irreversibility of plastic flow is included in an entropy production term which modifies the temperature variation. Application to the plane‐wave propagation problem is discussed.