A GFEM-based reduced-order homogenization model for heterogeneous materials under volumetric and interfacial damage

Brandyberry, David; Zhang, X.; Geubelle, Philippe H.

doi:10.1016/j.cma.2021.113690

Cited by 6 publications

(2 citation statements)

References 45 publications

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“…The existing partitioning strategies can be generally classified into two categories: (1) geometry‐based strategy 51‐55 uses internal features such as grains in the polycrystalline microstructures or inclusions in the particulate composites to define the partitions; and (2) response‐based strategy 43,44,56‐58 groups the subdomains of the microstructure with similar responses into the same parts when the microstructure is subjected to a given loading. In this work, we propose a mixed approach: The partitioning is initiated by ensuring that each grain in the polycrystalline volume is represented by at least one part (i.e.,

n\ge {n}_{\mathrm{grain}}

).…”

Section: Reduced Basis Construction For the Phasesmentioning

confidence: 99%

“…In the context of inclusion and fiber reinforced composites, Oskay and Fish 42 proposed the eigendeformation‐based homogenization approach (EHM) approach, which is a generalization of the eigenstrain‐based homogenization to account for interfacial cracks. Brandyberry et al 43 recently implemented a generalized FEM version of the formulation to study interface damage. Liu 44 proposed the use of a deep material network to represent progressive interface debonding in unidirectional fiber‐reinforced composites.…”

Section: Introductionmentioning

confidence: 99%

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Reduced order mathematical homogenization method for polycrystalline microstructure with microstructurally small cracks

Xia

Oskay

2023

Numerical Meth Engineering

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In this manuscript, a reduced order homogenization model is developed for polycrystalline microstructures with microstructurally small cracks. The proposed approach employs and advances the eigendeformation‐based homogenization method to account for the plastic deformation within the microstructure and the presence of cracks. A novel approach to construct the reduced order basis for the separation field is proposed for approximating crack opening profiles of kinked cracks. To capture the variable stress fields around the crack tips, a domain partitioning strategy that automatically refines the reduced order parts in these regions is proposed. The model performance is evaluated against reference crystal plasticity finite element (CPFE) simulations under various loading conditions and crack configurations. Both the overall and local response predictions show reasonable accuracy with only a fraction of the computational cost of the reference simulations.

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n\ge {n}_{\mathrm{grain}}

).…”

Section: Reduced Basis Construction For the Phasesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reduced order mathematical homogenization method for polycrystalline microstructure with microstructurally small cracks

Xia

Oskay

2023

Numerical Meth Engineering

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A reduced order variational spectral method for efficient construction of eigenstrain‐based reduced order homogenization models

Nasirov,

Oskay

2024

Numerical Meth Engineering

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Reduced order models (ROMs) are often coupled with concurrent multiscale simulations to mitigate the computational cost of nonlinear computational homogenization methods. Construction (or training) of ROMs typically requires evaluation of a series of linear or nonlinear equilibrium problems, which itself could be a computationally very expensive process. In the eigenstrain‐based reduced order homogenization method (EHM), a series of linear elastic microscale equilibrium problems are solved to compute the localization and interaction tensors that are in turn used in the evaluation of the reduced order multiscale system. These microscale equilibrium problems are typically solved using either the finite element method or semi‐analytical methods. In the present study, a reduced order variational spectral method is developed for efficient computation of the localization and interaction tensors. The proposed method leads to a small stiffness matrix that scales with the order of the reduced basis rather than the number of degrees of freedom in the finite element mesh. The reduced order variational spectral method maintains high accuracy in the computed response fields. A speedup higher than an order of magnitude can be achieved compared to the finite element method in polycrystalline microstructures. The accuracy and scalability of the method for large polycrystals and increasing phase property contrast are investigated.

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Multiscale design of nonlinear materials using reduced-order modeling

Brandyberry

Zhang

Geubelle

2022

Computer Methods in Applied Mechanics and Engineering

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A GFEM-based reduced-order homogenization model for heterogeneous materials under volumetric and interfacial damage

Cited by 6 publications

References 45 publications

Reduced order mathematical homogenization method for polycrystalline microstructure with microstructurally small cracks

Reduced order mathematical homogenization method for polycrystalline microstructure with microstructurally small cracks

A reduced order variational spectral method for efficient construction of eigenstrain‐based reduced order homogenization models

Multiscale design of nonlinear materials using reduced-order modeling

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