• Structural Engineering and Mechanics
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• v.81 no.3
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• pp.267-280
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• 2022

Multiscale structure has attracted significant interest due to its high stiffness/strength to weight ratios and multifunctional performance. However, most of the existing concurrent topology optimization works are carried out under deterministic load conditions. Hence, this paper proposes a robust concurrent topology optimization method based on the bidirectional evolutionary structural optimization (BESO) method for the design of structures composed of periodic microstructures subjected to uncertain dynamic loads. The robust objective function is defined as the weighted sum of the mean and standard deviation of the module of dynamic structural compliance with constraints are imposed to both macro- and microscale structure volume fractions. The polynomial chaos expansion (PCE) method is used to quantify and propagate load uncertainty to evaluate the objective function. The effective properties of microstructure is evaluated by the numerical homogenization method. To release the computation burden, the decoupled sensitivity analysis method is proposed for microscale design variables. The proposed method is a non-intrusive method, and it can be conveniently extended to many topology optimization problems with other distributions. Several numerical examples are used to validate the effectiveness of the proposed robust concurrent topology optimization method.

• Interaction and multiscale mechanics
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• v.5 no.3
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• pp.229-265
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• 2012

Hygroexpansion of wood is a known and undesired characteristic in civil engineering. When wood is exposed to changing environmental humidity, it adsorbs or desorbs moisture and warps. The resulting distortions or - at restrained conditions - cracks are a major concern in timber engineering. We herein present a multiscale model for prediction of the macroscopic hygroexpansion behavior of individual pieces of softwood from their microstructure, demonstrated for spruce. By applying poromicromechanics, we establish a link between the swelling pressure, driving the hygroexpansion of wood at the nanoscale, and the resulting macroscopic dimensional changes. The model comprises six homogenization steps, which are performed by means of continuum micromechanics, the unit cell method and laminate theory, all formulated in a poromechanical framework. Model predictions for elastic properties of wood as functions of the moisture content closely approach corresponding experimental data. As for the hygroexpansion behavior, the swelling pressure has to be back-calculated from macroscopic hygroexpansion data. The good reproduction of the anisotropy of wood hygroexpansion, based on only a single scalar calibration parameter, underlines the suitability of the model. The multiscale model constitutes a valuable tool for studying the effect of microstructural features on the macroscopic behavior and for assessing the hygroexpansion behavior at smaller length scales, which are inaccessible to experiments. The model predictions deliver input parameters for the analysis of timber at the structural scale, therewith enabling to optimize the use of timber and to prevent moisture-induced damage or failure.

• Composites Research
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• v.19 no.1
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• pp.1-8
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• 2006

Prediction of damage caused by low-velocity impact in laminated composite plate is an important problem faced by designers using composites. Not only the inplane stresses but also the interlaminar normal and shear stresses playa role in estimating the damage caused. But it is well known that the conventional approach based on the homogenization has the limit in description of damage. The work reported here is an effort in getting better predictions of dynamic behavior and damage in composite plate using DNS approach. In the DNS model, we discretize the composite plates through separate modeling of fiber and matrix for the local microscopic analysis. In the view of microscopic mechanics with DNS model, interlaminar stress behaviors in the inside of composite materials are investigated and compared with the results of the homogenized model which has been used in the conventional approach to impact analysis. Also the multiscale model based on DNS concept is developed in order to enhance the effectiveness of impact analysis, and we present the results of multiscale analysis considering micro and macro structures simultaneously.

• Interaction and multiscale mechanics
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• v.2 no.1
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• pp.45-68
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• 2009

An aim of the study is to develop an efficient numerical simulation technique that can handle the two-scale analysis of fluid permeation filters fabricated by the partial sintering technique of small spherical ceramics. A solid-fluid mixture homogenization method is introduced to predict the mechanical characters such as rigidity and permeability of the porous ceramic filters from the micro-scale geometry and configuration of partially-sintered particles. An extended finite element (X-FE) discretization technique based on the enriched interpolations of respective characteristic functions at fluid-solid interfaces is proposed for the non-interface-fitted mesh solution of the micro-scale analysis that needs non-slip condition at the interface between solid and fluid phases of the unit cell. The homogenization and localization performances of the proposed method are shown in a typical two-dimensional benchmark problem whose model has a hole in center. Three-dimensional applications to the body-centered cubic (BCC) and face-centered cubic (FCC) unit cell models are also shown in the paper. The 3D application is prepared toward the computer-aided optimal design of ceramic filters. The accuracy and stability of the X-FEM based method are comparable to those of the standard interface-fitted FEM, and are superior to those of the voxel type FEM that is often used in such complex micro geometry cases.

• Advances in biomechanics and applications
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• v.1 no.2
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• pp.111-126
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• 2014

The microarchitecture of trabecular bone plays a significant role in mechanical strength due to its load-bearing capability. However, the complexity of trabecular microarchitecture hinders the evaluation of its morphological characteristics. We therefore propose a new classification method based on static multiscale theory and dynamic finite element method (FEM) analysis to visualize a three-dimensional (3D) trabecular network for investigating the influence of trabecular microarchitecture on load-bearing capability. This method is applied to human vertebral trabecular bone images obtained by micro-computed tomography (micro-CT) through which primary trabecular bone is successfully visualized and extracted from a highly complicated microarchitecture. The morphological features were then analyzed by viewing the percolation of load pathways in the primary trabecular bone by using the stress wave propagation method analyzed under impact loading. We demonstrate that the present method is effective for describing the morphology of trabecular bone and has the potential for morphometric measurement applications.

• Composites Research
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• v.35 no.3
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• pp.188-195
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• 2022

This paper proposes a multiscale process-structural analysis methodology and applies to a battery housing part made of the short fiber-reinforced and fabric-reinforced composite layers. In particular, uncertainties of the material properties within the microscale representative volume element (RVE) were considered. The random spatial distribution of matrix properties in the microscale RVE was realized by the Karhunen-Loeve Expansion (KLE) method. Then, effective properties of the RVE reflecting on spatially varying matrix properties were obtained by the computational homogenization and mapped to a macroscale FE (finite element) model. Morever, through the hybrid process simulation, a FE (finite element) model mapping residual stress and fiber orientation from compression molding simulation is combined with one mapping fiber orientation from the draping process simulation. The proposed method is expected to rigorously evaluate the design requirements of the battery housing part and composite materials having various material configurations.

• Composites Research
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• v.30 no.5
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• pp.323-330
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• 2017

In this study, multiscale analysis in which the information obtained from molecular dynamics simulation is applied to the continuum mechanics level is conducted to investigate the effects of clustering of silicon carbide nanoparticles reinforced into polypropylene matrix on mechanical behavior of nanocomposites. The elastic behavior of polymer nanocomposites is observed for various states of nanoparticulate agglomeration according to the model reflecting the degradation of interphase properties. In addition, factors which mainly affect the mechanical behavior of the nanocomposites are identified, and new index 'clustering density' is defined. The correlation between the clustering density and the elastic modulus of nanocomposites is understood. As the clustering density increases, the interfacial effect decreased and finally the improvement of mechanical properties is suppressed. By considering the random distribution of the nanoparticles, the range of elastic modulus of nanocomposites for same value of clustering density can be investigated. The correlation can be expressed in the form of exponential function, and the mechanical behavior of the polymer nanocomposites can be effectively predicted by using the nanoparticulate clustering density.

• Interaction and multiscale mechanics
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• v.2 no.3
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• pp.321-332
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• 2009

Recent development in composites containing phase-transforming particles, such as vanadium dioxide or barium titanate, reveals the overall stiffness and viscoelastic damping of the composites may be unbounded (Lakes et al. 2001, Jaglinski et al. 2007). Negative stiffness is induced from phase transformation predicted by the Landau phase transformation theory. Although this unbounded phenomenon is theoretically supported with the composite homogenization theory, detailed stress analyses of the composites are still lacking. In this work, we analyze the stress distribution of the Hashin-Shtrikman (HS) composite and its two-dimensional variant, namely a circular inclusion in a square plate, under the assumption that the Young's modulus of the inclusion is negative. Assumption of negative stiffness is a priori in the present analysis. For stress analysis, a closed form solution for the HS model and finite element solutions for the 2D composite are presented. A static loading condition is adopted to estimate the effective modulus of the composites by the ratio of stress to average strain on the loading edges. It is found that the interfacial stresses between the circular inclusion and matrix increase dramatically when the negative stiffness is so tuned that overall stiffness is unbounded. Furthermore, it is found that stress distributions in the inclusion are not uniform, contrary to Eshelby's theorem, which states, for two-phase, infinite composites, the inclusion's stress distribution is uniform when the shape of the inclusion has higher symmetry than an ellipse. The stability of the composites is discussed from the viewpoint of deterioration of perfect interface conditions due to excessive interfacial stresses.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.34 no.1
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• pp.51-58
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• 2021

In this paper, a multi-scale finite element (FE) modeling methodology for three-dimensional (3D) needle-punched (NP) C/SiC with a complex microstructure is presented. The variations of the material properties induced by the needle-punching process and complex geometrical features could pose challenges when estimating the material behavior. For considering these features of composites, a 3D microscopic FE approach is introduced based on micro-CT technology to produce a 3D high fidelity FE model. The image processing techniques of micro-CT are utilized to generate discrete-gray images and reconstruct the high fidelity model. Furthermore, a subcell modeling technique is developed for the 3D NP C/SiC based on the high fidelity FE model to expand to the macro-scale structural problem. A numerical homogenization approach under periodic boundary conditions (PBCs) is employed to estimate the equivalent behavior of the high fidelity model and effective properties of subcell components, considering geometry continuity effects. For verification, proposed models compare excellently with experimental results for the mechanical behavior of tensile, shear, and bending under static loading conditions.

• Composites Research
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• v.36 no.1
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• pp.16-24
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• 2023

This paper presents a multi-scale progressive fatigue damage model incorporating the model for interfacial debonding between fibers and matrix. The micromechanics model for the progressive interface debonding was adopted, which defined the four different interface phases: (1) perfectly bonded fibers; (2) mild imperfect interface; (3) severe imperfect interface; and (4) completely debonded fibers. As the number of cycles increases, the progressive transition from the perfectly bonded state to the completely debonded fiber state occurs. Eshelby's tensor for each imperfect state is calculated by the linear spring model for a damaged interface, and effective elastic properties are obtained using the multi-phase homogenization method. The fatigue damage evolution formulas for fiber, matrix and interface were proposed to demonstrate the fatigue behavior of CFRP laminates under cyclic loading. The material parameters for the fiber/matrix fatigue damage were characterized using the chaotic firefly algorithm. The model was implemented into the UMAT subroutine of ABAQUS, and successfully validated with flat-bar UD laminate specimens ([0]₈,[90]₈, [30]₁₆) of AS4/3501-6 graphite/epoxy composite.