Session: 20-17-01: Rising Stars of Mechanical Engineering

Paper Number: 173715

Toward Efficient Multiscale Reduced Order Modeling and Design of Particulate Composite Materials 

Computational modeling and design have long been adopted to facilitate the analysis and design of better and lighter composites for various applications. While progress has been significant, several modeling and design challenges for complex composites remain, including but not limited to: 1) finite element discretization of the complex microstructure; 2) capturing the highly nonlinear constituent and interfacial behavior that involves rate dependency and damage; 3) efficient and accurate upscaling from the microstructure to a structural component; 4) addressing the even more computationally prohibitive costs associated with microstructure (e.g., material and geometrical parameter) design, especially those based on gradient-based optimization.

In this poster presentation, we illustrate our relevant prior and ongoing development, focusing on accelerating the modeling and design of nonlinear composite microstructures. These developments are based on the Eigendeformation-based Receded Order Homogenization Model (EHM). EHM partitions the microstructure into a few sub-domains (also known as parts) and precomputes coefficient tensors, including each part’s localization tensor and the interaction tensors between parts. By assuming a uniform strain response over each part, a reduced-order nonlinear system can be solved for the part-wise responses to replace the full field microscale simulation, achieving high computational efficiency for moderately low levels of error. EHM can be used in a multiscale setting, serving as a microstructure-informed constitutive law for the macroscopic simulation, or as a material point calculation to evaluate the response of a microstructure under a prescribed loading history.

 In the current development, EHM considers both interfacial and volumetric damage in composites, whose efficiency and accuracy are probed against the reference direct numerical simulation using the Interface-Enriched Generalized Finite Element Method. We will present our prior developments related to IGFEM and EHM for the modeling of different composites undergoing both interfacial and volumetric damage, covering the formulation, implementation, and results discussion, emphasizing the efficiency and accuracy characteristics of EHM. We then make transmissions to introduce the sensitivity analysis, which computes the derivative of the overall stress of the microstructure with respect to the nonlinear material parameters (i.e., parameters from the damage law) or geometrical parameters (i.e., diameter of the location of individual fiber/particle) within the EHM framework. The use of this sensitivity analysis to drive the reduced-order design of particulate composite microstructures will be discussed, along with some ongoing developments.  The results suggested that EHM has great potential for accelerating the design of nonlinear composites, especially when used in a gradient-based optimization where a large number of initial conditions need to be studied to avoid falling into a local minimum. 

Presenting Author: Xiang Zhang University of Wyoming

Presenting Author Biography: Dr. Xiang Zhang has been an Assistant Professor in the Mechanical Engineering Department at the University of Wyoming since 2019, leading the Computations for Advanced Materials and Manufacturing Laboratory. 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 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.

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