A Method of Mechanical Control of Structure-property Relationship in Grains-containing Material Systems

Abstract

Material systems can grow indefinitely large unless there appear some physical restrictions superimposed on them. At first approximation, they can be restricted in their evolution by means of an external mechanical factor such as pressure. If the material system's evolution can be described by a Smoluchowski type equation in the phase space of grain sizes, the average grain size magnitude can be suitably controlled by such mechanical factor. Both magnitude and direction of the factor can render the grain sizes either bigger or smaller than the one expected without any influence of the factor. We propose to embody the mechanical factor in the drift term of the corresponding Smoluchowski equation, in general, derivable from the entropy production principle. Such an embodiment allows one to modify controllably (over certain distinguished time scales of the process) the grain sizes, thus, the mechanically affected material properties such as superplasticity or superconductivity. A simple econophysical example, addressing investment strategies upon random-market tensions, is added to support the overall rationale of the method thus developed.

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