SHOCK COMPRESSION OF METAL CRYSTALS: A COMPARISON OF EULERIAN AND LAGRANGIAN ELASTIC-PLASTIC THEORIES

Abstract

An unconventional nonlinear elastic theory is advocated for solids undergoing large compression as may occur in shock loading. This theory incorporates an Eulerian strain measure, in locally unstressed material coordinates. Analytical predictions of this theory and conventional Lagrangian theory for elastic shock stress in anisotropic single crystals of aluminum, copper and magnesium are compared. Eulerian solutions demonstrate greater accuracy compared to atomic simulation (aluminum) and faster convergence with increasing order of elastic constants entering the internal energy. A thermomechanical framework incorporating this Eulerian strain and accounting for elastic and plastic deformations is outlined in parallel with equations for Lagrangian finite strain crystal plasticity. For several symmetric crystal orientations, predicted values of volumetric compression at the Hugoniot elastic limit of the two theories begin to differ substantially when octahedral or prismatic slip system strengths exceed about 1% of the shear modulus. Predicted pressures differ substantially for volumetric compression in excess of 5%. Predictions of Eulerian theory are closer to experimental shock data for aluminum, copper, and magnesium polycrystals.