Numerical Simulation of Energy Localization in Dynamic Materials
Dynamic materials are artificially constructed in such a way that they may vary their characteristic properties in space or in time, or both, by an appropriate arrangement or control. These controlled changes in time can be provided by the application of an external (non-mechanical) field, or through a phase transition. In principle, all materials change their properties with time, but very slowly and smoothly. Changes in properties of dynamic materials should be realized in a short or quasi-nil time lapse and over a sufficiently large material region. Wave propagation is a characteristic feature for dynamic materials because it is also space and time dependent. As a simple example of the complex behavior of dynamic materials, the one-dimensional elastic wave propagation is studied numerically in periodic structures whose properties (mass density, elasticity) can be switched suddenly in space and in time. It is shown that dynamic materials have the ability to dynamically amplify, tune, and compress initial signals. The thermodynamically consistent high-resolution finite-volume numerical method is applied to the study of the wave propagation in dynamic materials. The extended analysis of the influence of inner reflections on the energy localization in the dynamic materials is presented.
Authors appreciate discussions with Prof. G. A. Maugin, Prof. K. A. Lurie, and Prof. S. Weekes. The first author acknowledges the support from Worcester Polytechnic Institute.
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