Author Description

Composites have undergone significant growth in recent decades, primarily due to their exceptional strength-to-weight ratio. However, modeling the mechanical behavior of composites with complex microstructures still remains a great challenge. One approach to address this challenge is to utilize direct numerical modeling, which accounts for the intricate microscale details and nonlinear constitutive laws, and leverage advanced numerical techniques, such as the Interface-enriched Generalized Finite Element Method (IGFEM). Nevertheless, the high computational cost associated with this method often becomes a limiting factor. Reduced Order Modeling (ROM) has emerged as a technique to mitigate the computational cost by building upon the Eigendeformation-based reduced-order homogenization model (EHM). This approach significantly reduces the computational cost associated with the microscale problem by developing a reduced-order representation of the full field microscale problem, allowing flexible control of the model order to balance the accuracy and efficiency. This research advances EHM from multiple fronts. Inspired by the adaptive mesh refinement in the finite element method, both uniform and non-uniform adaptive ROMs have been developed. The idea is to start the modeling of microstructure with a coarse ROM, and gradually switch to a finer ROM when localized response starts. The adaptive ROM approach enhances the modeling of composite materials by providing greater flexibility in controlling the order of ROM to balance the computational cost and efficiency. We further developed a load-dependent ROM, which accounts for known characteristics of the loading the microstructure is going to experience, and construct the ROM accordingly. Numerical examples indicate that by incorporating load-dependent information into the EHM, more accurate stress-strain responses can be obtained. Additionally, we adopt the Physics-Informed Neural Network (PINN) to assist the pre-processing i