The Method of Failure Paths for Reduced-Order Computational Homogenization

Sparks, Paul A.; Oskay, Caglar

doi:10.1615/intjmultcompeng.2016018702

Cited by 15 publications

(9 citation statements)

References 43 publications

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“…26,27 The proposed modeling approach is a nonlocal generalization of the Eigenstrain-based reduced order computational homogenization modeling (EHM). [27][28][29] In the remainder of this section, we provide an overview of "local" EHM, and generalize it to a nonlocal formulation. The specific features of the nonlocal compression kink-band model are then discussed.…”

Section: Multiscale Compression Kink Band Modelmentioning

confidence: 99%

“…While Figure 2 illustrates partitioning of the microstructure into the matrix and fiber phases, other partitioning strategies are also possible as explored in Ref. 25,29. The kinematic equation that relates the inelastic strain coefficients to the macroscopic strain is expressed asin which boldA^(αΔ) and boldB^(αΔγ) are additional coefficient tensors.…”

Section: Introductionmentioning

confidence: 99%

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Reduced order multiscale model for compression kink-band failure in composites

Faupel

Meshi

Oskay

2022

Journal of Composite Materials

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A multiscale model for compression kink band failure in fibrous composites is presented. The computational model predicts the progression of damage associated with the formation of kink bands, which experiments demonstrate to involve excessive shear straining of the matrix material and fiber fracture. The uniqueness of the study is establishing the concurrent treatment of nonlinear deformation and failure of the composite constituents at the scale of the material microstructure, and the formation of kink bands at the mesoscopic scale. The model incorporates computational homogenization of the material response, a nonlocal gradient regularization scheme, and a curvature-based criterion for macroscopic fiber break to predict kink band formation. The multiscale approach resolves mesoscale mechanisms associated with kink banding while offering computational benefits compared to direct mesomechanical approaches. An accessible implementation within finite element analysis software is presented and the model is verified with analysis of a mesoscale domain incorporating initial fiber waviness. In quasi-static simulations, the kink band initiates due to matrix softening that results in the onset of buckling and is completely formed when fibers break as a result of localized curvature. Results from parametric studies confirm that compression strength is not directly related to measures of the kink band morphology, but it is strongly correlated with the shear strength and initial fiber misalignment angle. The predicted effects of material properties representing various carbon fiber reinforced polymers and a range of fiber misalignment angles on kink band width and failure strength corroborate analytical and experimental results presented in the literature.

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Section: Multiscale Compression Kink Band Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reduced order multiscale model for compression kink-band failure in composites

Faupel

Meshi

Oskay

2022

Journal of Composite Materials

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“…Oskay and Fish (2007) developed a nonlocal eigendeformation homogenization method based on two-scale asymptotic expansion to describe damage in the composite structures. To reduce the computational cost due to solving a system of nonlinear equations, Sparks and Oskay (2016) proposed the method of overlapping failure paths. Ren et al (2011) used enriched reproducing kernel particle methods (RKPMs) to investigate microcracks informed damage models (MIDMs).…”

Section: Unit Conversion Factorsmentioning

confidence: 99%

“…Other efforts in the literature have been devoted to characterizing the damage evolution function by utilizing an arc tangent damage evolution function based on material parameters (Oskay and Fish 2007;Sparks and Oskay 2016). Such efforts provide reasonable approximations to describe the damage evolution at the microscopic and continuum levels, and the reliability of the approach is dependent on fitting the material parameters to experiments.…”

Section: Unit Conversion Factorsmentioning

confidence: 99%

A multiscale meshfree approach to modeling damage of Cor-Tuf without fibers using fracture energy experiments

Sherburn¹,

Heard²,

Williams³

et al. 2019

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Many continuum damage mechanics models for cementitious materials are typically phenomenological in design. Recent work has shown that a physics-based multiscale approach to modeling damage is efficient and effective. In order to use a multiscale approach, appropriate experimental data are necessary to model the microscale calculations that will then inform the continuum-scale calculations. This work uses the multiscale approach and experimentally determines the parameters necessary to model the microscale calculations. Notched three-point beam experiments were performed to determine the fracture energy of the ultra-high performance concrete known as Cor-Tuf. The fracture energy is then used by a simplified microscale calculation to determine a physics-based damage evolution equation that can be used in continuum-scale calculations. A meshfree method is used to show the usefulness of the newly determined damage evolution equation. Both a quasi-static application and a dynamic application are shown as examples. DISCLAIMER: The contents of this report are not to be used for advertising, publication, or promotional purposes. Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products. All product names and trademarks cited are the property of their respective owners. The findings of this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents.

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“…Some additional approaches previously used for identifying the partitioning of the microstructure into reduced bases are discussed in Sparks and Oskay. 47,48 The hybrid integration for ROVME method avoids the hourglassing instabilities using Equation 37 with ng > 1. Since the partition pattern of each of the microstructure, Θ g (g = 1, 2, … , ng), is independent of the other microstructures (as shown in Figure 6 for ng ⩾ 2), it is impossible for the centroid of all parts in the enrichment domain to coincide with the center of the enrichment domain.…”

Section: Hourglassing Controlmentioning

confidence: 99%

Hybrid multiscale integration for directionally scale separable problems

Zhang

Oskay

2017

Numerical Meth Engineering

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This manuscript presents the formulation and implementation of a hybrid multiscale integration scheme for multiscale problems that exhibit different scale separation characteristics in different directions. The proposed approach uses the key ideas of the variational multiscale enrichment at directions that exhibit poor scale separation and computational homogenization at directions with good scale separability. The proposed approach is particularly attractive for surface degradation problems in structures operating in the presence of aggressive environmental agents. Formulated in the context of variational multiscale principles, we develop a novel integration scheme that takes advantage of homogenization-like integration along directions that exhibit scale separation. The proposed integration scheme is applied to the reduced-order variational multiscale enrichment method to arrive at a computationally efficient multiscale solution strategy for surface degradation problems. Numerical verifications are performed to verify the implementation of the hybrid multiscale integrator.The results of the verifications reveal high accuracy and computational efficiency, compared with the direct reduced-order variational multiscale enrichment simulations. A coupled transport-thermomechanical analysis is presented to demonstrate the capability of the proposed computational framework. KEYWORDSmultiscale modeling, reduced-order modeling, variational multiscale enrichment, computational homogenization, hybrid multiscale integration Int J Numer Meth Engng. 2018;113 1755-1778. wileyonlinelibrary.com/journal/nme

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The Method of Failure Paths for Reduced-Order Computational Homogenization

Cited by 15 publications

References 43 publications

Reduced order multiscale model for compression kink-band failure in composites

Reduced order multiscale model for compression kink-band failure in composites

A multiscale meshfree approach to modeling damage of Cor-Tuf without fibers using fracture energy experiments

Hybrid multiscale integration for directionally scale separable problems

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