Plane wave simulation of elastic-viscoplastic single crystals

Shock compression modeling of metallic single crystals: comparison of finite difference, steady wave, and analytical solutions

“…[6,10]. Many, if not most, features are also used in the SW and analytical models described later in "Steady wave model" and "Analytical model".…”

“…Advantages of the method developed in Ref. [10], which is the first known implementation of the SW approach for anisotropic elastic-plastic crystals, include the following: a detailed description of the steady shock structure (and associated material state) is obtained, solutions are obtained at relatively low computational cost, no artificial viscosity is used, and sophisticated rate-and temperature-dependent crystal plasticity models are enabled. Disadvantages are that effects of transverse waves for non-symmetric crystal orientations are ignored, unsteady waves cannot be addressed, and material properties must be spatially homogeneous.…”

“…The FD model, the SW model, and the analytical model are described in "Finite difference model", "Steady wave model", and "Analytical model", including governing equations, constitutive theory and parameters, and numerical methods. Because these models have been described at length in prior publications [6,10,15], only essential features are provided herein. Quantitative comparison and evaluation of the numerical approaches (FD and SW) are given in "Numerical methods comparison".…”

“…Although all three models have been presented individually and validated versus experimental data in prior work [6,10,15], previous papers have not included any comparisons of results among the three methods or any evaluations of computational efficiency. Explicit method comparisons identifying material orientations and loading regimes for which each method may be most appropriate are the primary new contributions of this paper.…”

Shock compression of metal single crystals modeled via Finsler-geometric continuum theory

“…Approaches to modeling the response of anisotropic single crystalline metals to planar shock loading include analytical models [1,2,3], steady wave models [4,5], finite difference models [6,7,8], and fully resolved finite element models [9,10,11]. These approaches all tend to adopt continuum crystal plasticity theory [12,13,14] to describe the constitutive response, whereby a flow rule is used to specify the relationship between shear strength and the rate of plastic flow attributed to dislocation glide, for example.…”