Please cite this article as: Luscher, D.J., Mayeur, J.R., Mourad, H.M., Hunter, A., Kenamond, M.A., Coupling continuum dislocation transport with crystal plasticity for application to shock loading conditions AbstractWe have developed a multi-physics modeling approach that couples continuum dislocation transport, nonlinear thermoelasticity, crystal plasticity, and consistent internal stress and deformation fields to simulate the single-crystal response of materials under extreme dynamic conditions. Dislocation transport is modeled by enforcing dislocation conservation at a slip-system level through the solution of advection-diffusion equations. Nonlinear thermoelasticity provides a thermodynamically consistent equation of state to relate stress (including pressure), temperature, energy densities, and dissipation. Crystal plasticity is coupled to dislocation transport via Orowan's expression where the constitutive description makes use of recent advances in dislocation velocity theories applicable under extreme loading conditions. The configuration of geometrically necessary dislocation density gives rise to an internal stress field that can either inhibit or accentuate the flow of dislocations. An internal strain field associated with the internal stress field contributes to the kinematic decomposition of the overall deformation. The paper describes each theoretical component of the framework, key aspects of the constitutive theory, and some details of a one-dimensional implementation. Results from single-crystal copper plate impact simulations are discussed in order to highlight the role of dislocation transport and pile-up in shock loading regimes. The main conclusions of the paper reinforce the utility of the modeling approach to shock problems.

This work presents an extension of a second order cell-centered hydrodynamics scheme on unstructured polyhedral cells [13] toward higher order. The goal is to reduce dissipation, especially for smooth flows. This is accomplished by multiple piecewise linear reconstructions of conserved quantities within the cell. The reconstruction is based upon gradients that are calculated at the nodes, a procedure that avoids the least-square solution of a large equation set for polynomial coefficients. Conservation and monotonicity are guaranteed by adjusting the gradients within each cell corner. Results are presented for a wide variety of test problems involving smooth and shock-dominated flows, fluids and solids, 2D and 3D configurations, as well as Lagrange, Eulerian, and ALE methods. stress and momentum are solved on offset control volumes such that the logical center of each lies on the boundary of the other. Cell-centered hydrodynamics schemes (CCH) in which all conservation equations are solved on a common control volume have been widely applied to Eulerian methods, but only recently widely applied to Lagrange. A cell-centered Lagrange method was first suggested by Godunov [49,48]. Early implementations such as that in the CAVEAT code [2,39] solved an approximate Riemann problem at cell faces rather than at the nodes. It was not until the seminal work of Després and Mazeran [33] that a solution at the nodes was found. Since then, interest in CCH methods has increased and at least three additional formulations have arisen [74,3,13] giving rise to extensions in many areas [25,32,58,75,76,71,77,70,46,45,73,72,21,14,81,15,80]. Although the discussion in this paper is centered about the CCH2 formulation of [13,15], it is relevant to all.We begin with an overview of the CCH2 method. Details are in the cited references that we summarize here in very general terms. Reference [13] describes the basic XY formulation while [15] describes an RZ formulation based on conservative fluxes that preserves symmetry on equiangular polar meshes. The cyclic ordering of the steps depends upon the particular implementation. For purposes of discussion, we begin with the finite volume integration.Finite volume integration. The extensive evolution or rate equations for momentum, deformation, and total energy are expressed as surface integralsUin which M z is the cell mass and {u z ,γ z ,τ z } are respectively specific cell average rates of change of velocity, deformation, and total energy. The fundamental challenge in CCH is the determination of the surface fluxes u p and σ p that are solutions to a Riemann problem. The decomposition of the total energy into kinetic and internal rates k z ,ė z will be discussed later in Section 2.1. A stress rateσ z is derived from the internal energy rate and deformation rate through a constitutive model such as that described in Appendix A. The rate equations are integrated to yield new values for velocity, stress, and total energy.Conservative reconstruction. The finite volume method provides no direct infor...

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