Macroscale constitutive modeling of kinking nonlinear elastic solids

A large class of solids has recently been identified as kinking nonlinear elastic (KNE) solids because they deform predominantly by the formation of dislocation-based, incipient and regular kink bands [M.W. Barsoum, A. Murugaiah, S.R. Kalidindi, T. Zhen, Phys. Rev. Lett. 92 (2004) 255508 1–4; M.W. Barsoum, T. Zhen, A. Zhou, S. Basu, S.R. Kalidindi, Phys. Rev. B (2005) 134101 1–8]. The incipient kink bands are fully reversible and have been shown to be the hysteretic mesoscopic units invoked to explain the nonlinear elastic deformation in rocks. In this paper, we present a theoretical framework to model the macroscale aspects of the nonlinear elastic behavior of KNE solids in a uniaxial stress state. The theory assumes that the probability of kinking is given by Weibull statistics. Despite its simplicity, the model captures reasonably well the fully reversible, hysteretic, rate-independent, and discrete memory aspects of the macroscale behavior of KNE solids in the nonlinear elastic regime.