Design of reinforced composites with a given set of effective thermophysical characteristics and some adjoining problems of diagnostics of their properties

Definition of effective coefficients of thermal conductivity in spatially reinforced composites on the basis of energy criterion of equivalence

“…This makes the problem of modeling of heat transfer processes in elements with spatial reinforcement (and random orientation of anisotropy of composite-making components) a topical problem for investigation. This problem is a subject of this publication, and it continues the study published in [2], where we had considered the particular case of reinforcement, i.e., the case of fiber orientation along three orthogonal directions.…”

“…Due to definitions for matrices , Κ Λ (see (2), (21)) and taking (33), we have a simple relation: 1 .…”

“…Axes Since the actual distribution of heat fluxes and temperature field in the spatially reinforced material is typically unknown, the problem of finding suitable relations for six independent thermophysical characteristics in the form of components of linear thermal conductivity ij λ ( , ij ji λ λ = i, j = 1, 2, 3) moves us to several assumptions; these assumptions are similar to ideas used in [2,5] for deriving of formulas for effective coefficients of thermal conductivity in composites with collinear and orthogonal reinforcement: 1. Reinforcement material is a continuous macroscopically quasi-uniform anisotropic body.…”

“…The formula for Fourier law (2) in this case is rewritten in the following form: 3×3 symmetric matrices inverse to 0 , , , k Λ Λ Λ and the elements in matrices are known, but the elements of matrix Κ are to be determined. According to assumption 5, also with regard for (21), we have instead of (18) the following expression [6]:…”

“…In industry, the traditional structure of composite materials is multilaminar structure (for example, in thin-wall elements like shells and plates), so the reinforcement trajectory is in the layers plane, and the layers are put together through the binding sublayers (as for critical analysis of structural models and thermophysical behavior of that type of composites, we recommend papers [1,2]). However, composites with spatial (3D) reinforcement are of special interest for industry.…”