Dynamic Materials As Media Natural for Dynamics

Abstract eng:
Heterogeneous material structures assembled in space and time - dynamic materials (DM) - have received a systematic investigation starting from the late nineties [1, 2] when it was realized that such formations generate a novel material concept. An idea of spatial-temporal variability of material properties may seem unusual to a conservative mind. Though this principle has been implemented for ages in living organisms, its technological implementation has become achievable relatively recently. At the same time, viewed as a material concept, this idea goes far and wide: it may also be perceived, in a broader context, as environmental concept that embraces phenomena that are at first sight very diverse. Among them, one can mention the traffic flow, the picture dynamics observed on a television screen, the patterns of material properties in mechanical devices, specifically on a nanoscale [3, 4]. An attentive observer will find indications of this concept in mechanics of bodies of variable mass, specifically, in the rocket flight; many illustrations also come from vibrational mechanics [5]. A classical example that ``lies on the surface'' is set by electrodynamics of moving media: the material relations introduced by Minkowski are explicitly affected by the material motion. Generally speaking, electrodynamics offers an ideal embodiment for the concept of dynamic materials. The tensor formulation of electrodynamics has revealed a natural classification of dynamic materials, such as dielectrics and conductors, into activated and kinetic [1, 2]. Though it originally appeared in the context of electrodynamics [6], such classification is quite universal. The activated DM are defined as substances that expose spatio-temporal variability of their property patterns alone, with no presence of actual material motion. The kinetic DM are specified as assemblages of material fragments that participate in relative mechanical motion: the Minkowski's material relations clearly illustrate this possibility. Various means can be used to maintain the property patterns variable in space and time. In electromagnetic applications, such variability can be achieved by the material, or network switching artificially implemented in both radio and optical frequency ranges [7, 8]. In the traffic flow, the property pattern is not a material one: it is a velocity chart introduced by traffic regulations and implemented through the use of traditional signals, such as traffic lights and road signs, applied wherever and whenever necessary. We will nevertheless preserve the term DM in this case, too. Regardless of the implementation, all of the DM share a common universal feature: such materials appear to be thermodynamically open systems. To secure their existence, a non-stop exchange of energy and momentum should be maintained between the DM formation and the environment. In other words, an external agent should necessarily be involved as a factor that supports a spatial-temporal property structure. Mathematically, the DM concept is expressed through linear hyperbolic equations with variable coefficients. When such coefficients take at each point of space-time one out of two admissible systems of values, then we speak about ``two materials'' that may be distributed in space-time to form various layouts. Depending on the layouts' geometry, the problems of wave propagation through DM were classified [9] into two major categories. One of them, termed regular, is characterized by the absence of collisions

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