Special fiber elements for thermal analysis of fiber‐reinforced composites

The purpose of this paper is to present a new special element model for thermal analysis of composites.

A hybrid finite element formulation taking the fundamental solution as kernel function is presented in this work for analyzing the thermal behavior and predicting the effective thermal conductivity of fiber‐reinforced composites. A representative volume cell containing single or multiple fibers (or inclusions) is considered to investigate the overall temperature distribution affected by the inclusions and the interactions among them, and to evaluate the effective thermal conductivity of the composites using the presented algorithm with special‐purpose inclusion elements. Numerical examples are presented to demonstrate the accuracy and applicability of the proposed method in analyzing fiber‐reinforced composites.

The independent intra‐element field and frame field, as well as the newly‐developed hybrid functional, make the algorithm versatile in terms of element construction, with the result that the related variational functional involves the element boundary integral only. All numerical results are compared with the solutions from ABAQUS and good agreement is observed for all cases, clearly demonstrating the potential applications of the proposed approach to large‐scale modeling of fiber‐reinforced composites. The usage of special inclusion element can significantly reduce model meshing effort and computing cost, and simultaneously avoid mesh regeneration when the fiber volume fraction is changed.

Due to the fact that the established special elements exactly satisfy the interaction of matrix and fiber within the element, only element boundary integrals are involved, thus the algorithm can significantly reduce modeling effort and computing cost with less elements, and simultaneously avoid mesh regeneration when the fiber volume fraction is changed.

Based on the special fundamental solution, a newly‐constructed inclusion element is applied to a number of test problems involving unit RVCs with multiple fibers to access the accuracy of the model. The effective thermal conductivity of the composites is evaluated for cases of single and multiple fibers using the average temperatures at certain points on a data‐collection surface. A new algorithm for evaluating effective properties with special elements is presented.