An Eulerian Method for Calculating Strength Dependent Deformation. Part One: A Derivation for the Flow Equations for Strength Dependent Deformation

摘要

Equations for the motion of a continuous medium capable of supporting shear stresses are reported by a number of authors, but the complete set does not appear to have been published in a form suitable for solution by Eulerian hydrodynamic codes. Specifically, the Eulerian equations of motion for a compressible medium acted upon by a general stress tensor are required. In this volume the equations of motion are discussed starting from the principles of mass, momentum and energy conservation for finite masses. From these the differential equations of motion are derived. The constitutive equations relating stress and strain are required to complete the mathematical description. It is also shown that the difference equations for hydrodynamic codes can be conveniently obtained from the integral form of the conservation laws. The nature of a medium is specified by its equation of state, which is used to calculate the pressure from the density and specific internal energy, and a tensor constitutive equation relating deviator stresses, deviator strains and their rates. Constitutive equations for the shear stresses are discussed and the appropriate forms for elastic, elastic-plastic and rigid-plastic solids as well as for viscous fluids are presented. (Author)