Abstract
This chapter introduces bases of nonlinear mesoscopic elasticity and presents a novel approach to model and numerically simulate the dynamical behavior of this class of material. Under dynamical solicitation, these so-called nonclassical materials exhibit two different time-dependent nonlinear mechanisms termed “fast” (nonlinear elasticity) and “slow” (loss of elastic properties and relaxation). A unified model of one-dimensional continuum is presented, which combines all of these phenomena as well as viscoelastic attenuation often neglected. The final set of partial differential equations is a system of conservation laws with relaxation described by a reduced number of parameters to account for all the effects. A numerical scheme based on finite-volume methods is presented which reproduces well the key experimental observations made in Dynamic Acousto Elasticity (DAE) and Nonlinear Resonant Ultrasound Spectroscopy (NRUS) type of experiments.
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