On shock waves in elastic-plastic solids

Mathematical modelling of elastoplasticity at high stress

“…However, there is disagreement in the literature about how to distinguish the elastic and plastic components of the macroscopic displacement and stress (see Ilyushin 1963;Howell et al 2009;Davison 2010, for discussion). These and related issues have also been approached from the rational mechanics viewpoint by many authors, including Willis (1969), Germain & Lee (1973) and Wang et al (1995).…”

“…When we use the multiplicative decomposition proposed by Lee (1969) and others (see Germain & Lee 1973; who specifically address elastoplastic shock waves), the one-dimensional deformation gradient tensor reads…”

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

“…The relative velocity of the material with respect to the shock is v = υ − D. Internal energy per unit mass is u = U /ρ 0 . Using (37), (38) can be rewritten as [12] The downstream state is defined by the set of variables (υ − , ρ − , σ − , u − ). The RankineHugoniot conditions give three equations for determining this state; in order to fully define the downstream state, a fourth equation is supplied by the constitutive model.…”

“…Previous work includes [12][13][14][15]. The present method, which can be applied only for symmetric crystal orientations (e.g., shocks propagating along [100] and [111] directions in FCC crystals), essentially reduces the problem to simultaneous solution of the yield condition and energy balance for the cumulative plastic slip and entropy, with the remaining conservation and constitutive laws sufficient for determination of the downstream material state.…”

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.…”