Session: 12-22-01: Multiscale Models and Experimental Techniques for Composite Materials and Structures

Paper Number: 146045

146045 - Achieving Adaptive Model Order Reduction in Eigendeformation-Based Reduced Order Homogenization Model With Volumetric and Interfacial Damage 

Composite materials have been playing an increasingly important role in various engineering applications especially those involving extreme conditions. Computational modeling of composite materials under these extreme loading conditions, to achieve predictive analysis and design, is an important but challenging task. The challenges particularly come from capturing highly nonlinear behaviors at the microstructural scale and efficiently upscaling from material microstructures to structural components. Among the existing modeling techniques, reduced order modeling (ROM) has gained significant attention due to its ability to balance computational cost and efficiency for simulating complex composite materials. The eigendeformation-based reduced-order homogenization model (EHM) has proven to be effective in capturing inelastic responses of complex microstructures, which originates from the concept of transformation field analysis, and approximate the microscale problem with a much-reduced basis spanning over partitioned subdomains of the microstructures, where the response of each subdomain is assumed to be uniform. While EHM delivers a hierarchy of gradually refining ROMs ranging from low-fidelity-high-efficiency to high-fiddley-low-efficiency by increase the number of subdomains (order of the ROM) used to partition the microstructure, a fixed partitioning of the microstructure is still challenging when involving highly complex geometries and nonlinear behaviors. Efforts have been made to enhance the efficiency of EHM through a Uniform Adaptive Reduced Order Modeling (UAROM) approach, where the simulation switches between a series of pre-defined gradually and uniformly refining ROMS, as the loading and the localization in subdomains continues. However, the ROM order increases substantially, and it becomes hard to control since refining happens in all subdomains uniformly. This limitation restricts the flexibility of the method, hindering its applications in modeling highly complex damage initiation and propagation where adaptability and fine control are essential. To tackle these challenges, we propose the Non-uniform Adaptive Reduced Order Model (NUAROM), which draws inspiration from Adaptive Finite Element Methods (AFEMs). In contrast to the uniform approach, the NUAROM only selectively refine the subdomains that has localization reached to a certain criterion, similar to the concept of mesh refining around propagating crack tip in AFEM. The applicability and accuracy of NUAROM are verified through numerical examples involving single or multiple inclusion particulate composite microstructures with phase continuum damage and/or cohesive interface damage. It demonstrates that NUAROM possesses flexibility in offering various adaptive refinement strategies through the selection of hyperparameters. The investigation into different partitioning strategies also offers valuable insights into how hyperparameters impact the accuracy of NUAROM. Furthermore, an intriguing discovery indicates that employing fewer adaptive refinements at an opportune moment, even with a smaller number of subdomains, can yield superior results compared to a greater number of refinements with a higher number of subdomains. By introducing this flexibility and controllability in NUAROM, NUAROM can improve the accuracy and efficiency of the reduced order modeling technique, facilitating more accurate predictions of composite material behavior.

Presenting Author: Xiang Zhang University of Wyoming

Presenting Author Biography: Dr. Xiang Zhang joined the Mechanical Engineering Department at the University of Wyoming in 2019, leading the Computations for Advanced Materials and Manufacturing Laboratory. Prior to UW, he earned his Ph.D. in Civil Engineering at Vanderbilt University, followed by a postdoctoral research experience in Aerospace Engineering at the University of Illinois and Urbana-Champaign. His research focuses on developing sophisticated multiscale /multiphysics methods in conjunction with data-driven methods for the modeling, design, and manufacturing of high-performance materials and advanced-manufacturing process.

Authors:

Min Lin University of Wyoming
David Brandyberry University of Illinois Urbana-Champaign.
Xiang Zhang University of Wyoming