Nonclassical nonlinear elasticity of crystalline structures.

Abstract

Hysteretic elastic nonlinearity has been shown to result in a dynamic nonlinear response which deviates from the known classical nonlinear response; hence this phenomenon was termed nonclassical nonlinearity. Metallic structures, which typically exhibit weak nonlinearity, are typically categorized as classical nonlinear materials. This article presents a material model which derives stress amplitude dependent nonlinearity and damping from the mesoscale dislocation pinning and breakaway to show that the lattice defects in crystalline structures can give rise to nonclassical nonlinearity. The dynamic nonlinearity arising from dislocations was evaluated using resonant frequency shift and higher order harmonic scaling. The results show that the model can capture the nonlinear dynamic response across the three stress ranges: linear, classical nonlinear, and nonclassical nonlinear. Additionally, the model also predicts that the amplitude dependent damping can introduce a softening-hardening nonlinear response. The present model can be generalized to accommodate a wide range of lattice defects to further explain nonclassical nonlinearity of crystalline structures.