On the scaling of steady structured waves in heterogeneous materials

Abstract

Large amplitude steady waves in materials have been observed to display certain scaling relationships between the strain rate and the stress amplitude. In many homogeneous materials, strain rate scales with stress to the fourth power. However, scaling of strain rate with stress to the first, second, and fourth power has been found for different classes of heterogeneous materials. We examine wave structures for three classes of heterogeneous materials through mesoscale simulations that resolve the scale of heterogeneity explicitly. We utilize these simulations to gain insight into the scaling phenomena observed and to identify the critical non-dimensional parameters for the phenomena. These parameters are then applied to the available experimental data for the three classes. The same set of non-dimensional groups is found to be appropriate for layered and particulate composite materials, while somewhat different groups are found for granular materials. Two different types of simulations lead to different conclusions on the need for the inclusion of strength in the non-dimensionalization for granular materials. The groups formed are found to collapse the experimental data quite well when the strength parameter is not included. Finally, a simple model for granular materials demonstrates that the crucial aspect of their behavior that controls the scaling of waves is the need for mass transfer to close voids in the material. V C 2012 American Institute of Physics. [http://dx.[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 130.88.90.110 On: Sat, 20 Dec 2014 10:42:31 FIG. 11. Relationship between stress and strain rate for simulations of 2-D particulate composites in which (a) particle diameter and (b) materials are varied. Also shown for comparison is a power-law scaling relationship of stress to the fourth power.

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