Micromechanical Analysis of Thermal Expansion Coefficients

Thermal expansion coefficients play an important role in the design and analysis of composite structures. A detailed analysis of thermo-mechanical distortion can be performed on microscopic level of a structure. However, for a design and analysis of large structures, the knowledge of effective material properties is essential. Thus, either a theoretical prediction or a numerical estimation of the effective properties is indispensable. In some simple cases, exact analytical solutions for the effective properties can be derived. Moreover, bounds on the effective values exist. However, in dealing with complex heterogeneous composites, numerical methods are becoming increasingly important and more widely used, because of the limiting applicability of the existing (semi-)analytical approaches. In this study, finite-element methods for the calculation of effective thermal expansion coefficients of composites with arbitrary geometrical inclusion configurations are discussed and applied to a heterogeneous lightning protection coating made from Dexmet® copper foil 3CU7-100FA and HexPly® epoxy resin M21. A short overview of some often used (semi-)analytical formulas for effective thermal expansion coefficients of heterogeneous composites is given in addition.