Multiscale Mathematical Modeling and Simulation of Coupled Thermo-Mechanical Behavior in Advanced Composite Materials

Abstract

Developing composite technologies, such as carbon fiber-reinforced polymers (CFRPs) and ceramic matrix composites (CMCs) are being applied in the aerospace, automotive, and energy systems sectors to a large extent because of their high strength-to-weight ratios, thermal resistance, and durability. Although these have the following advantages, their coupled thermo-mechanical behavior has become a significant challenge to predict and is of concern primarily because of the heterogeneous microstructures and multiscale interactions. The framework in this paper constructs a multiscale mathematical model and computer simulation to study thermo-mechanical reactions of high-tech composites by combining microstructural characterization, homogenization theory, and continuum mechanics. Particular equations of heat conduction, thermal strain and stress equilibrium are transformed into governing equations, and a coupled system is solved using finite element analysis (FEA). At the microscale, fiber-matrix interactions, interfacial debonding, and void effects are modeled by representative volume elements (RVEs). The mesoscale is homogenized by using homogenization methods to correlate microstructural characteristics to ply-level anisotropy. On a macro scale, continuum simulations are made to predict structural response to combined thermal and mechanical loading. A case study of CFRP laminates illustrates the ability of the framework to predict. The proposed multiscale model enhanced thermal expansion coefficient (CTE) estimation with a 12% high accuracy than the traditional unidimensional FEM. It was also able to trace residual stress distributions at fiber-matrix interfaces with high fidelity and early-stage failure mechanisms including delamination which are otherwise invisible to continuum-only models. Adaptive meshing and reduced-order homogenization maintained computational efficiency by reducing simulation run time by 30 percent and accuracy. The findings reaffirm the importance of multiscale modeling in the development of the next-generation composites in mission-critical applications. The work provides a serious mathematical and computational framework that interpolates microstructural physics, with engineering-scale simulations, which allows making predictions of performance more reliably and designing materials more optimally.