Analysis of Elastic Nonlinearity Using Continuous Waves: Validation and Applications

Propagation Characteristics of Rotation Waves in Transversely Isotropic Granular Media Considering Microstructure Effect

The purpose of this study is to develop a micromechanical-based microstructure model for transversely isotropic granular media and then use it to investigate the propagation characteristics of particle rotation waves. In this paper, the particle translation and rotation are selected as basic independent variables and the particle displacement at contact due to particle rotation is ignored. The relative deformation tensors are introduced to describe the local deformational fluctuation because of their discrete nature and microstructure effect. Based on micro–macro deformation energy conservation, the constitutive relations are derived through transferring the summation into an integral and introducing the contact fabric tensor. The governing equations and corresponding boundary conditions can then be obtained based on Hamilton’s principle. Subsequently, the dispersion characteristics and bandgap features of particle rotation waves in transversely isotropic granular media are analyzed based on the present model. The research shows that: the present microstructure model can predict 12 particle rotation waves and reflect 8 dispersion relations; the effect of the change in fabric on the dispersion relation of particle rotation waves can be mainly attributed to the effect of equivalent stiffness on frequency; and the degree of anisotropy has significant effects on the width of frequency bandgap of longitudinal waves, while it has little effect on the width of frequency bandgap of transverse and in-plane shear waves.

Elastic Slow Dynamics in Polycrystalline Metal Alloys

Elastic slow dynamics, consisting in a reversible softening of materials when an external strain is applied, was experimentally observed in polycrystalline metals and presents analogies with the same phenomenon more widely observed in consolidated granular media. Since the effect is extremely small in metals, precise experimental techniques are needed. Reliable measurement of relative velocity variations of the order of 10−7 is crucial to perform the analysis. In addition, the grain structure and the nature of grain boundaries in metals is very different from that in rocks or concrete. Therefore, linking relaxation elastic effects to the microstructure is needed to understand the physical origin of slow dynamics in metals. Here, interpreting the relaxation phenomenon as a multirelaxation process, we show that it is sensitive to the spatial scale at the microstructural level, up to the point of allowing the identification of the existence of features at different spatial scales, particularly distinguishing damage from microstructural inhomogeneities.