Three-dimensional failure criteria of unidirectional fiber composites are established in terms of quadratic stress polynomials which are expressed in terms of the transversely isotropic invariants of the applied average stress state. Four distinct failure modes—tensile and compressive fiber and matrix modes—are modeled separately, resulting in a piecewise smooth failure surface.
Variational theorems are established and applied to the derivation of bounds for the effective magnetic permeability of macroscopically homogeneous and isotropic multiphase materials. For reasons of mathematical analogy the results are also valid for the dielectric constant, electric conductivity, heat conductivity, and diffusivity of such materials. For the case of two-phase materials, the bounds derived are the most restrictive ones that can be given in terms of the phase permeabilities and volume fractions. Comparison of present theoretical results with existing experimental data shows good agreement.
The purpose of the present survey is to review the analysis of composite materials from the applied mechanics and engineering science point of view. The subjects under consideration will be analysis of the following properties of various kinds of composite materials: elasticity, thermal expansion, moisture swelling, viscoelasticity, conductivity (which includes, by mathematical analogy, dielectrics, magnetics, and diffusion) static strength, and fatigue failure.
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