A second-order algorithm for the dynamic response of soils
In this paper we describe a formally second-order algorithm for the dynamic response of one-dimensional soils and rock. There are two kinds of equations describing the motion of the material: the partial differential equations expressing conservation of momentum, and the kinetic equation of state relating the stress to the deformation. The stress-rate equations for the kinetic equation of state are formulated as a constrained system of ordinary differential equations and are integrated implicitly in time, both for stability and for satisfaction of the yield constraints. The equations of motion are formulated as a first-order system of hyperbolic conservation laws and integrated explicitly by means of a second-order version of Godunov's method. Because the motion can develop both smooth waves and shocks, special care has been taken to design a numerical method that is second-order in smooth waves and yet reduces to a stable low-order method near discontinuities. We present numerical results for both the integration of the equation of state and the equations of motion, in order to demonstrate the features of the method. © 1990.
