Session: 12-04-01: Multiscale Models and Experimental Techniques for Composite Materials and Structures

Paper Number: 100055

100055 - Adaptive Eigendeformation-Based Reduced-Order Homogenization Model for Composite Materials 

Computational homogenization provides a straightforward way to concurrently couple microscale simulation to a structural simulation, as in FE², and is readily able to model a wide range of materials and structures. However, the inherent computational cost associated with computational homogenization prohibits its wide application, especially in the case of nonlinear constitutive responses. This has led to an emerging effort to develop reduced-order models (ROM) for multiscale modeling. The Eigendeformation-based reduced-order homogenization model (EHM) is an attractive method for this purpose, and has seen significant advancement with applications to metals, composites, and other heterogeneous materials [1-2]. EHM operates in a computational homogenization setting, with a focus on model order reduction of the microscale problem and is based upon precomputing elastic microstructure information.

EHM partitions the microstructure into a number of 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 problem, achieving high computational efficiency for moderately low levels of error. While previous studies have shown a hierarchical sequence of ROMs ranging from low fidelity-high efficiency to high fidelity -low efficiency can be achieved by different microstructure partitioning, typically only a single ROM is used in the same simulation.

In this research, we present an adaptive EHM where the simulation gradually refines the ROM used to better balance efficiency and accuracy. To achieve this adaptivity, we begin with the finest ROM we are considering and compute the coefficient tensors (i.e., localization and interaction tensors). Coarser partitionings are then constructed by combining two finer parts into a single coarser part. This way, coefficient tensors of the coarse parts can be directly computed from the ones associated with the finest ROM. As the initial response is generally near-linear, a coarse ROM is sufficient to capture this response. Once inelastic deformation starts and localization starts to accumulate, the simulation adaptively switches to a finer ROM to improve computational accuracy. The data transferring between the coarse and refined ROM, as well as the switching criteria are discussed. The performance and accuracy of the proposed framework is evaluated by comparison with EHM with a fixed ROM partition and the reference direct numerical simulations. 

References

[1] Zhang, Xiang, and Caglar Oskay. "Eigenstrain based reduced order homogenization for polycrystalline materials." Computer Methods in Applied Mechanics and Engineering 297 (2015): 408-436.

[2]Brandyberry, David R., Xiang Zhang, and Philippe H. Geubelle. "A GFEM-based reduced-order homogenization model for heterogeneous materials under volumetric and interfacial damage." Computer Methods in Applied Mechanics and Engineering 377 (2021): 113690.

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 coming 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 at Urbana-Champaign. His research efforts focus on developing sophisticated multiscale /multiphysics methods in conjunction with data-driven methods for the modeling, design, and manufacturing of high-performance martials and advanced-manufacturing processes.

Authors:

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