Mathematical model of non-local thermal viscoelastic medium. Part 3. Equations of motion

Modern structural and functional materials presenting an aggregate of micro- and nanostructured elements find wide application in technology. An important stage in creating and using the class of materials under consideration is the construction of mathematical models providing the description of behavior of these materials within a broad range of variations in exposure conditions. However the general methodology for mathematical model construction is still far from being complete. Here a derivation of equations of motion is offered taking into account the features of small-size materials (continuum non-locality, momentary stress states). For deducing the equations, the relationships of rational thermodynamics of irreversible processes with internal state parameters, as well as the method of continuous approximation of the generalized mechanics of continuum are used. The obtained forms for writing equations ofmotion make it possible to take into consideration the main peculiarities in nonstationary deforming of materials with the small-size structure.

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