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We propose in this paper analytical and numerical models that describe the in-plane uniaxial elastic properties (Young's moduli and Poisson's ratios) of a honeycomb structure with curved walls. We perform a parametric analysis of the mechanical performance of this honeycomb also by taking into account the different types of deformations acting inside the cell walls. The curved wall honeycomb possesses higher magnitudes of the Poisson's ratio ν12 in the auxetic configuration compared to classical center symmetric configuration with straight cell wall. The presence of the curvature also allows creating configurations with positive Poisson's ratio even for negative internal cell angles, and makes this honeycomb design attractive for mechanical tailoring. [ABSTRACT FROM AUTHOR]

In this paper, a novel three-dimensional (3D) cellular structure with negative Poisson's ratio was designed by alternating cuboid surface indents on the vertical ribs of the unit cells. The Poisson's ratio and Young's modulus of structures with different geometric parameters were determined using the finite element method (FEM) as a function of these parameters. Samples with identical geometric variables were fabricated via 3D printing, and their through-thickness direction Poisson's ratios were measured and compared with simulation results. Results showed that the Poisson's ratio of the 3D cellular structures can be tuned from positive to negative and can reach a minimal value of −0.958. Good agreement was found between the experimental results and the simulation. This lattice structure is considerably stiffer than re-entrant negative Poisson's ratio foam with the same solid phase. The design concept developed here can be optimized for specific applications via geometric parameters manipulation. [ABSTRACT FROM AUTHOR]

This paper presents an analysis on the elastic characteristics of luffa and palm natural fiber composites (NFC) with epoxy and ecopoxy matrixes, taking into account the impact of fiber volume fractions. Furthermore, longitudinal modulus, transverse modulus, shear modulus, and Poisson's ratio were predicted using representative volume elements (RVEs) with chopped random and unidirectional fiber arrangements. However, analytical approaches such as rule of mixture, Chamis, Halpin–Tsai, and Nielsen were considered for validating and comparing the findings of finite element analyses. Hence, it was found that increasing fiber volume fraction increased the elastic properties of palm/epoxy, palm/ecopoxy, and luffa/epoxy NFCs, but decreased that of luffa/ecopoxy NFC. Addition of palm fibers in ecopoxy and epoxy had stronger effect than luffa on enhancing the elastic properties of the final structure. However, greatest elastic characteristics observed through analytical and numerical models were obtained for ecopoxy matrix with 0.5 palm fibers. A strong agreement was observed between the results obtained from analytical approaches and RVE unidirectional model. Chamis model exhibited higher outcomes compared to the considered analytical techniques, while Halpin–Tsai model showed the least values. [ABSTRACT FROM AUTHOR]

Based on the auxiliary space method, a preconditioner is studied in this paper for linear systems of equations arising from higher order finite element (FEM) discretizations of linear elasticity equations. The main idea, which is proposed by Xu ( Computing 1996; 56:215-235) for the scalar PDE, is to construct the preconditioner as a combination of a smoother and a coarse level solver, where the systems of equations arising from lower order FEM discretizations are used in the coarse level solver. It is theoretically shown that the condition number of the preconditioned systems is uniformly bounded with respect to both the problem size and moderate Poisson's ratio. When the Poisson's ratio is near the limit of 0.5, we have presented some numerical tests for the case of fourth-order FEM discretization in a combination with quadratic conforming FEM as a coarse space. The results are almost robust when Poisson's ratio is near the limit of 0.5. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Most of the electromagnetic devices, especially electrical machines, have the disadvantage to be exposed to high vibrations caused by magnetic forces. The aim of this study is to propose a methodology to optimize the cylindrical stators generally used in electrical machines regarding the vibration phenomena. Techniques for vibration reduction require knowledge of the proper frequencies, which depend on mechanical shapes and dimensions as well as material properties such as mass density, Young's modulus and Poisson's ratio. This paper proposes a new approach which is based on the identification of mass density (lamination stacking factor) and Young's modulus in the goal to minimize the vibratory behavior of electrical machines. In this goal, we have used artificial intelligent and finite element method (FEM) analysis to solve the magneto-mechanical inverse problem (IP). In the proposed approach, a Multilayer Perceptron Neural Network (MLPNN) is used as a forward model in order to decrease the FEM time consuming. Thus, a Genetic Algorithm (GA) is used to solve the IP in a reasonable time of running. An example study of an induction machine proves that the developed approach may be applied in both design and identification applications. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Finite element method (FEM) is considered as a powerful tool for predicting the mechanical behavior of complex structures. However, the commercially available numerical packages based on FEM are mainly limited to the evaluation of multiphysical properties at the continuum scale and are unable to accurately evaluate the response of nanomaterials since the dominant surface effects in nanoscale analysis are overlooked. In this study, our introduced numerical methodology not only incorporates the effects of surface residual stress and surface tensile stiffness based on the Gurtin–Murdoch surface elasticity but also takes into account the bending stiffness of nanosurfaces in the numerical analysis. The computational results reveal that the stress concentration in nanoporous metallic materials is affected by the void geometry and is enhanced by the surface bending stiffness. In addition, the effect of void geometrical parameters on the elastic properties of nanoporous metallic metamaterials with negative Poisson's ratio is studied and the mechanism of surface tensile/bending stiffness is revealed in detail. The results show that the surface bending stiffness increases the effective Young's modulus of nanoarchitected metallic materials with negative Poisson's ratio and randomly distributed nanopores. [ABSTRACT FROM AUTHOR]

A stiff tubular cellular structure topology is designed by alternatively indenting rectangular contour patterns on the cell ribs. Modified topologies can be obtained by tailoring the geometric parameters. The Poisson's ratios and elastic moduli of the proposed tubular structures with various geometric parameters are determined using finite element method (FEM). Results show that the minimum Poisson's ratio of the proposed structures can reach −0.28. The unit cell topology and orientation can significantly affect the structures deformation behaviors. The structures exhibit mixed mode of bending‐ and stretching‐dominated deformation responses, and show improved specific elastic moduli compared with traditional open‐cell stochastic foams with positive Poisson's ratios. 3D‐printed samples with identical geometric variables to those of the FE models are fabricated, and their Poisson's ratios and stress–strain relationships are determined experimentally, and compared with simulation results. Excellent agreement is achieved between measurements and simulations. The design concept proposed here can be optimized for specific applications via geometric parameters manipulation. [ABSTRACT FROM AUTHOR]

Chiral materials may exhibit negative Poisson's ratio and deformation‐mode coupling phenomena. The finite element numerical method is adopted to analyze a class of 2D chiral and nonchiral materials and to show the effects of microstructural geometry on their effective elastic properties and coupling between tension/compression and bending. With the same area fraction (AF), nonchiral samples show larger effective moduli than chiral ones. The number of unit cells may reduce negativity in effective Poisson's ratio of the chiral samples due to nonuniform lateral deformation under uniaxial straining. Increasing AF in a hierarchical pattern in the chiral samples makes their Poisson's ratio more negative. Bending occurs in the chiral samples when they are under uniform, uniaxial, tensile, or compressive straining due to the coupling of deformation modes. The sensibility of tension–bending coupling may be controlled by the chiral microstructure. Optimization of the coupling sensitivity may help develop novel mechanical sensors. [ABSTRACT FROM AUTHOR]

Chiral hyper‐structure is a family of lightweight structure with negative Poisson's ratio, which leads benefit in mechanical properties and designability. In order to further improve some mechanical properties of chiral hyper‐structures, the concept of gradient is introduced into the structure. Five groups of gradient tetra‐chiral hyper‐structure with different gradient factors are fabricated based on waterjet cutting technology, and the in‐plane quasi‐static lateral compression tests are carried out. Finite element models are developed for the in‐plane linear elastic mechanical properties and plastic deformation modes under lateral compression condition. Theoretical prediction models of elastic modulus in gradient direction and Poisson's ratio of the gradient tetra‐chiral hyper‐structure is derived based on geometric assumptions and inhomogeneous deformation mode which are verified by experiments and finite element analysis. Simultaneously, the effects of gradient factors on the deformation characteristics and mechanical behaviors of the tetra‐chiral hyper‐structure are discussed and analyzed. A kind of gradient tetra‐chiral hyper structure has been proposed, and its elastic‐plastic mechanical properties have been studied by FEA, experimental and theoretical methods. The results show that the structure has good functionality and application prospects which proves that the gradient of the chiral structure is a meaningful exploration. [ABSTRACT FROM AUTHOR]

Microstructured plates, consisting of various conventional and re-entrant cells, are numerically constructed and analyzed for their effective elastic properties under in-plane deformation. The finite element numerical method is adopted. The calculated effective Poisson's ratios of the plates are found to be in the range between −1 and 1, in consistency with the theory of two-dimensional elasticity. Auxetic angles need to be greater than about 20° in order to obtain negative Poisson's ratio. Increasing the auxetic angles reduces the effective pure shear modulus. Elastically anisotropic characteristics of the homogenized plate are analyzed with the calculated effective Young's modulus, Poisson's ratio, and pure shear modulus. [ABSTRACT FROM AUTHOR]

Purpose: Respiratory motion introduces uncertainties in tumor location and lung deformation, which often results in difficulties calculating dose distributions in thoracic radiation therapy. Deformable image registration (DIR) has ability to describe respiratory-induced lung deformation, with which the radiotherapy techniques can deliver high dose to tumors while reducing radiation in surrounding normal tissue. The authors' goal is to propose a DIR method to overcome two main challenges of the previous biomechanical model for lung deformation, i.e., the requirement of precise boundary conditions and the lack of elasticity distribution. Methods: As opposed to typical methods in biomechanical modeling, the authors' method assumes that lung tissue is inhomogeneous. The authors thus propose a DIR method combining a varying intensity flow (VF) block-matching algorithm with the finite element method (FEM) for lung deformation from end-expiratory phase to end-inspiratory phase. Specifically, the lung deformation is formulated as a stress-strain problem, for which the boundary conditions are obtained from the VF block-matching algorithm and the element specific Young's modulus distribution is estimated by solving an optimization problem with a quasi-Newton method. The authors measure the spatial accuracy of their nonuniform model as well as a standard uniform model by applying both methods to four-dimensional computed tomography images of six patients. The spatial errors produced by the registrations are computed using large numbers (>1000) of expert-determined landmark point pairs. Results: In right-left, anterior-posterior, and superior-inferior directions, the mean errors (standard deviation) produced by the standard uniform FEM model are 1.42(1.42), 1.06(1.05), and 1.98(2.10) mm whereas the authors' proposed nonuniform model reduces these errors to 0.59(0.61), 0.52(0.51), and 0.78(0.89) mm. The overall 3D mean errors are 3.05(2.36) and 1.30(0.97) mm for the uniform and nonuniform models, respectively. Conclusions: The results indicate that the proposed nonuniform model can simulate patient-specific and position-specific lung deformation via spatially varying Young's modulus estimates, which improves registration accuracy compared to the uniform model and is therefore a more suitable description of lung deformation. [ABSTRACT FROM AUTHOR]

Purpose: A novel technique is proposed to characterize lung tissue incompressibility variation during respiration. Estimating lung tissue incompressibility parameter variations resulting from air content variation throughout respiration is critical for computer assisted tumor motion tracking. Continuous tumor motion is a major challenge in lung cancer radiotherapy, especially with external beam radiotherapy. If not accounted for, this motion may lead to areas of radiation overdosage for normal tissue. Given the unavailability of imaging modality that can be used effectively for real-time lung tumor tracking, computer assisted approach based on tissue deformation estimation can be a good alternative. This approach involves lung biomechanical model where its fidelity depends on input tissue properties. This investigation shows that considering variable tissue incompressibility parameter is very important for predicting tumor motion accurately, hence improving the lung radiotherapy outcome. Methods: First, an in silico lung phantom study was conducted to demonstrate the importance of employing variable Poisson's ratio for tumor motion predication. After it was established that modeling this variability is critical for accurate tumor motion prediction, an optimization based technique was developed to estimate lung tissue Poisson's ratio as a function of respiration cycle time. In this technique, the Poisson's ratio and lung pressure value were varied systematically until optimal values were obtained, leading to maximum similarity between acquired and simulated 4D CT lung images. This technique was applied in an ex vivo porcine lung study where simulated images were constructed using the end exhale CT image and deformation fields obtained from the lung's FE modeling of each respiration time increment. To model the tissue, linear elastic and Marlow hyperelastic material models in conjunction with variable Poisson's ratio were used. Results: The phantom study showed that the tumor motion trajectory and its final locations obtained from simulations with and without considering tissue incompressibility variation were very different. For example, tumor displacements in the z direction were -11.23 and -38.10 mm obtained with the Marlow hyperelastic material model in conjunction with constant and variable Poisson's ratio, respectively. By comparing the acquired 4D-CT image sequence of the porcine lung with their image sequence counterparts obtained from the hyperelastic model with constant and variable Poisson's ratio, it was shown that using variable tissue incompressibility reduced errors significantly in tumor motion prediction. Conclusions: This investigation demonstrates the importance of incompressibility variation estimation and utilization for accurate tumor tracking in computer assisted lung external beam radiation therapy. An optimization framework was developed to estimate a Poisson's ratio function in terms of respiration cycle time using experimental image data of the lung. Utilizing this function along with respiratory system FE modeling may lead to more effective tumor targeting, hence potentially improving the outcome of lung external beam radiation therapy techniques. This is particularly true for stereotactic body radiation therapy where only one or a few fraction treatments are applied, precluding the possibility of averaging out dosimetric deviations introduced by the respiratory motion. [ABSTRACT FROM AUTHOR]

K-dominance of static crack tip in functionally gradient materials (FGMs) with a crack oriented along the direction of the elastic gradient is studied through coherent gradient sensing (CGS), digital speckle correlation method (DSCM) and finite element method (FEM). In the direction of crack propagation, the shear modulus has a linear variation with constant mass density and Poisson's ratio. First, the CGS and DSCM governing equations related to the measurements and the elastic solutions at mode I crack in FGMs are obtained in terms of the stress intensity factor, material constants and graded index. Secondly, two kinds of FGMs specimens and one homogenous specimen are prepared to observe the influences of the property variation on the K-dominance. Then, CGS and DSCM experiments using three-point-bending of FGMs and homogenous beams are performed. Thirdly, based on the results of the experiments, the stress intensity factors of three kinds of specimens are calculated by CGS and DSCM. Meanwhile, the stress intensity factors are obtained by FEM. Finally, comparing the results from CGS, DSCM and FEM, the K-dominance of mode-I static crack tip in FGMs is discussed in detail. [ABSTRACT FROM AUTHOR]