Numerical evaluation of the coefficients of thermal expansion of fibers in composite materials using a lamina-scale cost function with quasi-analytical gradients

Abstract

In this work, the coefficients of thermal expansion (CTEs) of fibers in composite materials that contain microstructures are numerically evaluated using a lamina-scale cost function with quasi-analytical gradients. To consider the effects of fiber arrangements and local defects, such as interface debonding and voids, a variety of representative volume elements are modeled with a number of finite element meshes. Then, the CTEs of fibers are evaluated by minimizing a lamina-scale cost function that represents the difference between the measured CTEs and the computed CTEs by means of a computational homogenization scheme for the composite lamina. The descent direction of the cost function is obtained using quasi-analytical gradients that take partial derivatives from prediction models, such as the Schapery model and Hashin model defined in an explicit manner, which accelerates the minimization procedure. To verify the performance of the proposed scheme in terms of accuracy and efficiency, the CTEs of constituents calculated using the proposed scheme in a unidirectional composite lamina are compared with experimental values reported in the literature. Furthermore, the convergence behavior of the proposed scheme with quasi-analytical gradients is also investigated and compared with other minimization methods.