• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.2
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• pp.199-214
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• 2020

This paper describes the development of a parallel computational algorithm based on the finite element tearing and interconnecting (FETI) method that uses a local Lagrange multiplier. In this approach, structural computational domain is decomposed into non-overlapping sub-domains using local Lagrange multiplier. The local Lagrange multipliers are imposed at interconnecting nodes. 8-node solid element using extra shape function is adopted by using the representative volume element (RVE). The parallel computational algorithm is further established based on message passing interface (MPI). Finally, the present FETI-local approach is implemented on parallel hardware and shows improved performance.

• Interaction and multiscale mechanics
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• v.2 no.4
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• pp.375-396
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• 2009

In the present work, the elasto-viscoplastic behavior, interactions between grains, and the texture evolution in polycrystalline materials subjected to finite deformations are modeled using a multiscale analysis procedure within a finite element framework. Computational homogenization is used to relate the grain (meso) scale to the macroscale. Specifically, a polycrystal is modeled by a material representative volume element (RVE) consisting of an aggregate of grains, and a periodic distribution of such unit cells is considered to describe material behavior locally on the macroscale. The elastic behavior is defined by a hyperelastic potential, and the viscoplastic response is modeled by a simple power law complemented by a work hardening equation. The finite element framework is based on a Lagrangian formulation, where a kinematic split of the deformation gradient into volume preserving and volumetric parts together with a three-field form of the Hu-Washizu variational principle is adopted to create a stable finite element method. Examples involving simple deformations of an aluminum alloy are modeled to predict inhomogeneous fields on the grain scale, and the macroscopic effective stress-strain curve and texture evolution are compared to those obtained using both upper and lower bound models.

• Aerospace Engineering and Technology
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• v.12 no.2
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• pp.48-56
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• 2013

In this paper, the equivalent elastic properties of fiber reinforced plastic laminar are investigated using various homogenization schemes. Although there are several methods for predicting the equivalent elastic properties such as analytical formula or semi-empirical formula, most of them have some limitations or are not much accurate when handling new composite material consisting of various fiber, matrix and fiber-volume fraction ratio. To resolve the issues, computational homogenization scheme is adopted with a representative volume element (RVE) comprised of a set of finite elements. Finally, the equivalent elastic properties are obtained by applying periodic boundary conditions. The obtained results are compared with those by the existing methods and test results. Also its effect on structural analysis results of the composite satellite panel is investigated.

• Composites Research
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• v.33 no.1
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• pp.30-37
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• 2020

Stress distributions dependent on fiber arrangements are studied using the two-dimensional representative volume element (RVE) model for uni-directionally continuous fiber-reinforced composites subjected to transverse tensile loading. It is easily expected that the stresses around the fibers are concentrated mainly due to the stiffness mismatch between the fiber and matrix materials. In this presentation, it is shown that the stresses are not always increased although the distance between two fibers is shortened. The 2D RVE models, originally having a regular hexagonal fiber array, is utilized to study the effect of the fiber locations on the stress distributions. As the central fiber is relocated, the stress distributions around the fiber are obtained through finite element analysis. It is found that the stresses around the fiber are strongly dependent on the fiber distance as well as the angle between the loading direction and the line connecting two fibers.

• Composites Research
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• v.34 no.1
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• pp.70-75
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• 2021

This paper presents a novel algorithm to reconstruct meso-scale representative volume elements (RVE), referring to experimentally observed features of Sheet Molding Compound (SMC) composites. Predicting anisotropic mechanical properties of SMC composites is challenging in the multiscale virtual test using finite element (FE) models. To this end, an SMC RVE modeler consisting of a series of image processing techniques, the novel reconstruction algorithm, and a FE mesh generator for the SMC composites are developed. First, micro-CT image processing is conducted to estimate probabilistic distributions of two critical features, such as fiber chip orientation and distribution that are highly related to mechanical performance. Second, a reconstruction algorithm for 3D fiber chip packing is developed in consideration of the overlapping effect between fiber chips. Third, the macro-scale behavior of the SMC is predicted by the multiscale analysis.

• Journal of the Microelectronics and Packaging Society
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• v.29 no.3
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• pp.43-48
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• 2022

In this study, simulation method was developed to improve the accuracy of the warpage simulation based on the equivalent anisotropic viscoelastic model. First, a package with copper traces and bumps was modeled to implement anisotropic viscoelastic behavior. Then, equivalent anisotropic viscoelastic properties and thermal expansion coefficient for the bump region were derived through the representative volume element model. A thermal cycle of 0 to 125 degrees was applied to the package based on the derived mechanical properties, and the warpage according to the thermal cycle was simulated. To verify the simulation results, the actual package was manufactured, and the warpage with respect to the thermal cycle was measured through shadow moiré interferometer. As a result, by applying the equivalent anisotropic viscoelastic model, it was possible to calculate the warpage of the package within 5 ㎛ error and predict the shape of the warpage.

• Composites Research
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• v.36 no.5
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• pp.329-334
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• 2023

The classical multiscale finite element (FE² ) method involves iterative calculations of micro-boundary value problems for representative volume elements at every integration point in macro scale, making it a computationally time and data storage space. To overcome this, we developed the data-driven multiscale analysis method based on the mean-field homogenization (MFH). Data-driven computational mechanics (DDCM) analysis is a model-free approach that directly utilizes strain-stress datasets. For performing multiscale analysis, we efficiently construct a strain-stress database for the microstructure of composite materials using mean-field homogenization and conduct data-driven computational mechanics simulations based on this database. In this paper, we apply the developed multiscale analysis framework to an example, confirming the results of data-driven computational mechanics simulations considering the microstructure of a hyperelastic composite material. Therefore, the application of data-driven computational mechanics approach in multiscale analysis can be applied to various materials and structures, opening up new possibilities for multiscale analysis research and applications.

• Composites Research
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• v.31 no.5
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• pp.251-259
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• 2018

In this paper, statistical volume element modeling method was developed for multi-scale progressive failure analysis of fiber reinforced composite materials. Big-size statistical volume elements (BSVEs) was considered to minimize the size effect in the micro-scale, by including as many fibers as possible. For that purpose, a mesh cutting method is suggested and adapted into the fiber model generator that creates finite element domain rapidly. The fiber defect model was also developed based on the experimental distribution of the fiber strength. The size effects from the local load sharing (LLS) are evaluated by increasing the fiber inclusion in the micro-scale model. Finally, continuum damage mechanics (CDM) model to the fiber direction was extracted from numerical analysis on BSVEs. And it was compared with strength prediction from typical representative volume element (RVE) model.

• Composites Research
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• v.32 no.5
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• pp.270-278
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• 2019

In this study, the transverse mechanical properties of the unidirectional fiber reinforced composite modeled with fiber, matrix, and interphase is predicted with the representative volume elements and is calibrated by adjusting the properties and thickness of the interphase by referring to the test results. While the conventional representative volume elements modeled with fiber and matrix shows high predictive accuracy for the longitudinal mechanical properties, but it shows some deviations in the transverse mechanical properties. In order to compensate such gaps, the interphase region is employed, and its mechanical properties are adjusted to improve the prediction accuracy according to various elastic modulus, thickness, and strength parameters. As a result, the deviation of the transverse elastic modulus and strength is reduced significantly similar to the test results of the unidirectional composites with the accuracy of the longitudinal mechanical properties preserved.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2002.05a
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• pp.177-180
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• 2002

3-D 원형 브레이드 복합재료의 물리적인 물성을 계산하기 위해서는 실제와 같은 단위구조의 모델링과 이를 통한 RVE(Representative Volume Element)의 구현이 필수적이다. 실제적인 내부구조 모델링을 위해 단위구조를 2가지로 나누었으며, 실의 경로를 3차원 스플라인으로 적합시켰다. 구현한 내부구조를 통하여 공정변수와 구조변수와의 관계를 고찰하였다.