Finite Strain Elastic-Plastic Theory

Summary

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 thermo-mechanical 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 at the constant base temperature 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 elastic strain component is related to the stress through thermo-elastic theory for finite strains. A plasticity law is developed which includes the influence of temperature change and the finite elastic strain existing during the duration of plastic deformation. Thermo-mechanical coupling is included in the plasticity theory according to experiments on the dissipation of mechanical work into heat energy during plastic flow. Following plastic flow the internal energy and the entropy are greater than in a body of the same material under the same stress and at the same temperature, but not subject to plastic flow. However, these contributions are not considered to modify the elastic law appreciably, as has been found experimentally.

Application of this law to the theory of the propagation of plane waves of one-dimensional strain is discussed.