Unit Cell Of Microstructure Research Articles

Concurrent two-scale topological design of multiple unit cells and structure using combined velocity field level set and density model

This paper studies concurrent two-scale design optimization of composite structures filled with multiple microstructural unit cells. The task of the design problem is to simultaneously optimize microstructural configurations of the unit cells and their spatial distribution in the macroscale. To this end, a new topology optimization framework based on combined topology representation of the density model and the level set model is proposed. The homogenization method is used to link the material microstructural design and the macroscale design by evaluating the effective properties of the microstructures. In the microscale, topology optimization of multiple microstructural unit cells is performed with the density-based method. In the macroscale design, the distribution of multiple microstructural unit cells is optimized by the velocity field level set method, which inherits advantages of the implicit geometrical representation of the conventional level set model (relatively clear and smooth material boundaries/interfaces, more natural description of topological evolution). Moreover, the velocity field level set method maps the variational boundary shape optimization problem into a finite-dimensional design space, thus making it relatively easy and efficient to employ general mathematical programming algorithms to handle the multiple constraints and two types of design variables in the concurrent two-scale design problem. Numerical examples show that the present concurrent two-scale design method can generate meaningful designs of hierarchical cellular structures with well-defined boundaries and material interfaces.

Concurrent topology optimization design of structures and non-uniform parameterized lattice microstructures

This paper presents a novel concurrent topology optimization approach for finding the optimum topologies of macrostructures and their corresponding parameterized lattice microstructures in an integrated manner. Considering the manufacturability of the structure designs and computational efficiency, additional parameters are introduced to define the microstructure unit cell patterns and their non-uniform distribution, which avoids expensive iterative numerical homogenization calculations during topology optimization and results in an easier modelling of structure designs as well. It is worth mentioning that the equivalent properties of material microstructures serve as a link between the macro and the micro scale with the help of homogenization theory and the Porous Anisotropic Material with Penalization (PAMP) model. Besides, sensitivities of global structure compliance with respect to the pseudo-density variables and the microstructure parameter variables are derived, respectively. Moreover, several numerical examples are presented and reasonable solutions have been obtained to demonstrate the efficiency of the proposed method. Finally, mechanical testing is conducted to investigate the better performance of the optimized structure which is fabricated by 3D printing.

Multiscale Modeling for Mechanical Properties of Cancellous Bone Based on the Schwarz Surface

Microstructure and the mechanical properties of cancellous bone were modeled by multiscale finite element method in this paper. Microstructure of the cancellous bone determines its mechanical properties and a rational geometry modeling of the cancellous bone is fundamental to predict the material properties. In this paper, we generate a new parameterized microstructural unit cell model based on triple periodic minimal surfaces (TPMS) which is established by the Schwarz surface with various volume fractions. This model truly simulates the microstructure of the cancellous bone and satisfies some biological and mechanical requirements. By using the new unit cell model, the second-order two-scale (SOTS) method is applied to predict the mechanical properties of cancellous bone. The predictive the mechanical properties of numerical results are in good agreement with the experimental data reported in literature, which demonstrate that the established unit cell model is applicable and the second-order two-scale method is valid to predict the mechanical properties of cancellous bone.

Traveling Lamb wave in elastic metamaterial layer

The propagation of traveling Lamb wave in single layer of elastic metamaterial is investigated in this paper. We first categorized the traveling Lamb wave modes inside an elastic metamaterial layer according to different combinations (positive or negative) of effective medium parameters. Then the impacts of the frequency dependence of effective parameters on dispersion characteristics of traveling Lamb wave were studied. Distinct differences could be observed when comparing the traveling Lamb wave along an elastic metamaterial layer with one inside the traditional elastic layer. We further examined in detail the traveling Lamb wave mode supported in elastic metamaterial layer, when the effective P and S wave velocities were simultaneously imaginary. It was found that the effective modulus ratio is the key factor for the existence of special traveling wave mode, and the main results were verified by FEM simulations from two levels: the level of effective medium and the level of microstructure unit cell.

Concurrent topology design of structure and material using a two-scale topology optimization

This paper presents new MIST (moving iso-surface threshold) formulation and algorithm for concurrent design of structural and cellular material topology. The material microstructure is assumed to be uniform in macro-scale, i.e. the macrostructure is composed of periodic unit cells. New formulations for the two physical response functions of macrostructure and microstructure (unit cell) are derived in terms of the results of finite element analyses of structure and material by using the homogenization theory. Several numerical examples are presented for optimum design solutions of the macrostructures and their corresponding material microstructures to illustrate the capability and efficiency of the present approach.

Study on Compressive Properties of Z-pinned Laminates in RTD and Hygrothermal Environment

Compressive tests of [0]12 and [90]12 unidirectional laminates and [45/0/–45/90]2S quasi-isotropic laminates are accomplished in both room-temperature and dry (RTD) and hygrothermal environment. And simulation studies on the compressive strength of Z-pinned laminates of [0]12 and [45/0/–45/90]2S are conducted by using finite element analysis (FEA). A microstructural unit cell for FEA is created to simulate a representative laminates unit with one pin. Within the unit cell, the first directions of the elements' material coordinate systems are changed to simulate the fibres' deflecting around the pin. The hygrothermal effect is simulated by the material properties' adjustments which are determined by the compressive tests of non-pined laminates. The experimental results indicate that the percentage of reduction in the compressive modulus of Z-pinned laminates caused by Z-pin becomes smaller with the percentage of 0° fibres decreasing in the laminates; the compressive strength of quasi-isotropic laminates reduces and the percentage of the reduction in the compressive strength declines with Z-pin volume content increasing, and the moisture absorption ratio of the Z-pinned specimens is greater than that of the non-pinned specimens, because the cracks around Z-pin increase the moisture absorption. In addition, the simulations show that the deflection of fibres around Z-pin is the main factor for the reduction in the compressive strength of Z-pinned unidirectional laminates, the dilution of fibre volume content caused by resin-rich pocket is the principal factor for the decline in the compressive strength of Z-pinned quasi-istropic laminates, and the compressive strength of Z-pinned specimens in hygrothermal environment reduces as the result of superimposition of some factors, including the changes in material properties caused by hygrothermal environment, the deflection of fibres and the resin-rich pocket caused by Z-pin.

Microstructure and unit-cell geometry of four-step three-dimensional rectangular braided composites

This article investigates the microstructure of 3D four-directional rectangular braided composites produced by the four-step 1 × 1 procedure. The planar and spatial yarn paths are analyzed systematically based on 3D braiding process. Three different types of microstructural unit cell models are established with respect to the interior, surface, and corner regions of a braided preform. These models truly simulate the microstructure of the braided composites. Furthermore, they are oriented in the same reference frame of the preform cross-section, which coincides with the actual configuration of composites and suits for the analysis of mechanical properties. The mathematical relationships among the structural parameters, such as braiding dimensions, fiber orientation, braiding pitch, the yarn packing factor, fiber volume fraction, are deduced. The calculated results are in good agreement with the measured values of the geometric characteristics of braided composite samples.

Microstructure and mechanical properties of three-dimensional five-directional braided composites

Three-dimensional (3D) five-directional braided composites are significant structural materials in the fields of astronauts and aeronautics. On the basis of the 3D five-directional braiding process, three types of microstructural unit cell models are established with respect to the interior, surface and corner regions. The mathematical relationships among the structural parameters, such as fiber orientation, fiber volume fraction, the yarn packing factor, are derived. By using these three unit cell models, a micromechanical prediction procedure is described to simulate the stiffness and strength properties of 3D five-directional braided composites. Only the in situ constituent fiber and matrix properties of the composites and the fiber volume proportion are required in the simulation. The stress states generated in the constituent fiber and matrix materials are explicitly correlated with the overall applied load on the composites. The predictive stiffness and strength are in good agreement with available experimental data, which demonstrates the applicability of the present analytical model.

Modeling of the effect of rigid fillers on the stiffness of rubbers

AbstractThe theories that predict the increase in the modulus of elastomers resulting from the presence of a rigid filler are typically derived from Einstein's viscosity law. For example, Guth and Gold used this approach to predict how the Young's modulus of an elastomer is related to the filler volume fraction. Hon et al. have shown using finite element microstructural models that stiffness predictions at small strains were also possible. Here, microstructural finite element models have been used to investigate the modulus of filled elastomer over a wider range of strains than has been possible previously. At larger strains, finite extensibility effects are significant and here an appropriate stored energy function proposed by Gent was adopted. In this work, the effect of spherical MT‐type carbon‐black filler behavior was considered. Different models were made and the results were then compared to experimental measurement of the stiffness taken from the literature. It is shown that the boundary conditions of the microstructural unit cell lie between the two extremes of free surfaces and planar surfaces. Also as the filler volume fraction increases then the number of filler particles required in the representative volume to predict the actual stiffness behavior also increases. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008

Digital image-based modeling applied to the homogenization analysis of composite materials

The systematic methodologies to derive accurate microstructural models are developed for studying the mechanical behaviors of composite materials. Since the geometric information of a microstructure is often given by an image or a set of images, the direct interpretation of the geometry is possibly by digitizing it. By identifying each pixel or voxel with a finite element (FE) and accompanying appropriate image processing, an FE model can be automatically generated. It is also emphasized that the digitized models can be suitable for solving the FE equations by utilizing the uniformity of the FE mesh. The finite element analysis (FEA) with the homogenization method enables the prediction the thermo-mechanical behavior of the periodic microstructure (unit cell) as well as the global mechanical response of a structural component, while we are taking into account the specific effect of the geometric structural configuration of the microstructure through digitization. Several kinds of the digitizing techniques are presented to illustrate the potential of digital image-based (DIB) FE modeling of the unit cell. Keeping the microstructural design in mind, the modification of the plane image is introduced and the virtual realization of the unit cell geometry is presented so that a microstructural analysis utilizing the homogenization method would be realistic.

Macro and micro scale modeling of thermal residual stresses in metal matrix composite surface layers by the homogenization method

The modeling of thermal residual stresses generated in TaC/stellite and TiC/stellite composite surface layers produced by the oscillating electron beam remelting on low alloys steel is presented. The homogenization method is applied to analyze the real composite microstructures by utilizing the digital image-based (DIB) geometric modeling technique. Two scales of elastic stress analysis are studied: macroscopic one referring to the global structure of composite layer produced over the substrate of low alloy steel and microscopic, comprising the selected unit cell of composite microstructure.