Multiscale Reduced Order Modeling and Design of High-Performance Materials: from Metal Fatigue Prediction to Nonlinear Composites Design

Abstract

Computational modeling has long been adopted to facilitate the analysis and design of high-performance materials subjected to extreme conditions, such as those involving fatigue and damage. While progress has been significant, several modeling and design challenges remain, including: 1) finite element discretization of the complex microstructures; 2) capturing the highly nonlinear constituent and interfacial behavior; 3) efficient and accurate upscaling from the microstructure scale to that of a structural component as these phenomena are highly dependent on the underlying microstructure behavior; and 4) addressing the even more computationally prohibitive costs associated with microstructure design, especially those based on gradient-based optimization.

In this presentation, an efficient multiscale reduced order modeling technique based on the eigendeformation-based reduced order homogenization model (EHM) will be discussed, highlighting its potential for addressing some of the challenges above associated with multiscale modeling and design. EHM works in a two-scale computational homogenization setting, leverages the concept of transformation field analysis, and focuses on model order reduction at the microscale, enabling efficient coupling to a structural simulation. EHM first partitions the microstructure into a few sub-domains (also known as parts) and precomputes the so-called coefficient tensors, including each part’s localization tensor and the interaction tensors between parts. By assuming a uniform stress/strain response over each part, a reduced-order nonlinear system can be derived and solved for the part-wise responses to replace the full-field microscale equilibrium problem, achieving high computational efficiency for moderately low levels of error. EHM framework is rather general, and its adaption for metal plasticity and composite damage will be discussed in this presentation, along with several of its major algorithm and implementation advancements. These advancements include achieving sparsity for better scalability, considering multiphysics, adaptive mode order reduction, load-dependent ROM construction, coefficient tensors constructions, and its integration with a gradient-based optimization framework for nonlinear composite design. The accuracy and efficiency characteristics of EHM, for both modeling and design, are fully explored and demonstrated by comparison with direct numerical simulations. 

Biography

Xiang Zhang, assistant professor in the Mechanical Engineering Department at the University of Wyoming, leads the Computations for Advanced Materials and Manufacturing Laboratory. Zhang’s engineering education started at Northeastern University in Shenyang, China, where he received his bachelor’s degree in engineering mechanics. His interest in computational modeling was developed during his master’s study at Beihang University, China. He earned his PhD in civil engineering at Vanderbilt University, followed by a postdoctoral research experience in Aerospace Engineering at the University of Illinois at Urbana-Champaign. Zhang’s research interest is computational mechanics, with a particular focus on developing sophisticated multiscale/multiphysics methods in conjunction with data-driven techniques for the modeling, design, and manufacturing of high-performance materials and advanced manufacturing processes. His work has been recognized by multiple awards, including being a Finalist of the 28th Robert J. Melosh Medal Competition for the Best Student Paper on Finite Element Analysis when he was a graduate student, and the American Society of Mechanical Engineers Materials Division, ORR Early Career Award in 2024.