Search

This paper investigates the thermo-elastoplastic sliding frictional contact and wear problem of a functionally graded material (FGM) coated homogeneous half-plane subjected to a rigid cylindrical punch. The coating has arbitrarily varying material properties including elastic modulus, Poisson's ratio, thermal expansion coefficient, wear coefficient, etc. The graded layer is modeled using a thermo-elastoplastic constitutive model of FGM to evaluate the contact pressure, in-plane stress, and temperature field. A modified Archard model is used to characterize the wear behavior of FGM coating, and the influence of wear on the stress and strain behavior is considered. The constitutive model and wear model are implemented in the finite element method (FEM) to study the thermo-elastoplastic sliding frictional contact and wear behavior of FGM coating. After the validation of the numerical approach, the effects of plasticity, wear, cycle number, gradient index, and gradient form are discussed. Simulation results show that changing the gradient form and gradient index can prevent contact damage and reduce frictional wear. [ABSTRACT FROM AUTHOR]

This paper deals with solving the problem of constructing two-level computational models relating the stress-strain state at the microscale to the stress-strain state of the structural component at the macroscale for layered polymer composite materials with unidirectional fiber stacking in a monolayer. The paper presents a two-level computational mechanical model of a ten-layer cross-ply fiberglass-reinforced polymer composite with (0/90) laying patterns. The model is based on microindentation data. The model is constructed using the finite element method. The constructed model has allowed us to predict the elastic properties of the composite and to calculate stresses at the microscale and macroscale levels of a specimen prior to fracture under tensile conditions. The elastic properties of the polymer composite material predicted by the computational model are compared with the properties obtained from real experiments. Calculated for fiberglass, the elasticity modulus and Poisson's ratio are 31 GPa and 0.11, respectively. Similar elastic properties obtained from real experiments are 28 GPa and 0.10. The technique used in the paper can be applied to computational experiments with an actual structural component made of a multilayer polymer composite in order to determine the stress-strain state at the micro- and macroscale under external mechanical impact on the structure. [ABSTRACT FROM AUTHOR]

The recyclability of wastes, especially mining waste, is one of the current challenges. Mines are subject to a well-defined life cycle planning to allow sustainable exploitation and development for the next generations. Mining techniques have developed considerably, so mining waste has become highly concentrated on pebbles. To build embankments and spoil heaps, it is necessary to know the mechanical properties of the composite mixture forming the mining waste. This paper tackles the calculation of the mechanical properties of highly heterogeneous mining wastes using a linear elasticity homogenization approach. Numerical models based on the finite element method are developed to determine the elastoplastic properties of the mixture. A first model enables the calculation of the Young's modulus and the Poisson's ratio of the mixture; then, based on an identification technique, a second model calculates the Mohr–Coulomb plasticity parameters. The obtained results show that the mixture is isotropic, and the mixture rigidity increases when the pebble concentration increases from 10 to 50%. Conversely, the volume maneuverability displayed by the Poisson's ratio decreases when the pebble concentrate increases. For the identified coefficients using Mohr–Coulomb model, the cohesion decreases from 9.13 to 5.59 kPa when the pebble concentration increases from 10 to 40%. The cohesion of the mixture remains higher compared to the cohesion of the limestone up to a concentration of 40%; it becomes 3.58 kPa. The mixture friction angle is always higher than the limestone friction angle. [ABSTRACT FROM AUTHOR]

Extracting the mechanical properties of a composite hydrogel; e.g., bioglass (BG)–collagen (COL), is often difficult due to the complexity of the experimental procedure. BGs could be embedded in the COL and thereby improve the mechanical properties of COL for bone tissue engineering applications. This paper proposed a deep-learning-based approach to extract the mechanical properties of a composite hydrogel directly from the microstructural images. Four datasets of various shapes of BGs (9000 2D images) generated by a finite element analysis showed that the deep neural network (DNN) model could efficiently predict the mechanical properties of the composite hydrogel, including the Young's modulus and Poisson's ratio. ResNet and AlexNet architecture were tuned to ensure the excellent performance and high accuracy of the proposed methods with R-values greater than 0.99 and a mean absolute error of the prediction of less than 7%. The results for the full dataset revealed that AlexNet had a better performance than ResNet in predicting the elastic material properties of BGs-COL with R-values of 0.99 and 0.97 compared to 0.97 and 0.96 for the Young's modulus and Poisson's ratio, respectively. This work provided bridging methods to combine a finite element analysis and a DNN for applications in diverse fields such as tissue engineering, materials science, and medical engineering. [ABSTRACT FROM AUTHOR]

A two-stage micromechanics technique is used to predict the elastic modulus, as well as the major and minor Poisson's ratio of unidirectional natural fiber (NF) reinforced composites. The actual NF microstructure consists of cellulose, hemicellulose, lignin, lumen, etc., and these constituents and their contributions are neglected in classical models while quantifying their mechanical properties. The present paper addresses the effect of the real microstructure of the natural jute fiber (JF) by applying a micromechanics approach with the Finite Element Method. Six different hierarchically micro-structured JFs are considered to quantify the JF elastic properties in the first level of homogenization. Later, the JF reinforced polypropylene matrix properties are investigated in the second stage by adopting a homogenization approach. Taking into account the different hierarchical structures (HS), the fiber direction modulus (E1), transverse modulus (E2 and E3), in-plane and out-of-plane shear modulus (G12 and G23), and major (ν12, ν13) and minor (ν23, ν21) Poisson's ratios are estimated for JF and JF reinforced polypropylene composites. The predicted elastic modulus from micromechanics models is validated against the analytical results and experimental predictions. From the present work, it is observed that the HS of NF needs to be considered while addressing the elastic properties of the NF-reinforced composite for their effective design, particularly at a higher volume fraction of NF. [ABSTRACT FROM AUTHOR]

Combined hybrid element method is one kind of stable finite element discrete method in which the famous Babuska–Brezzi condition is satisfied automatically. So, the method is more widely used, compared with other kinds of mixed/hybrid element methods. In this paper, we develop a non-nested multigrid algorithm for combined hybrid quadrilateral or hexahedron elements of linear elasticity problem. The critical ingredient in the algorithm is a proper intergrid transfer operator. We establish such an operator on quadrilateral or hexahedron meshes and prove the mesh-independent convergence of the k t h level iteration and full multigrid algorithm in L 2 norm. Numerical experiments are reported to support our theoretical results and illustrate the efficiency of the developed methods. We also give the numerical experiments showing the convergence of the developed method as Poisson's ratio is close to 0.5. [ABSTRACT FROM AUTHOR]

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]

The purpose of this paper is to develop a reduced Crouzeix–Raviart immersed finite element method (RCRIFEM) for two-dimensional elasticity problems with interface, which is based on the Kouhia–Stenberg finite element method (Kouhia et al. 1995) and Crouzeix–Raviart IFEM (CRIFEM) (Kwak et al. 2017). We use a P 1 {P_{1}} -conforming like element for one of the components of the displacement vector, and a P 1 {P_{1}} -nonconforming like element for the other component. The number of degrees of freedom of our scheme is reduced to two thirds of CRIFEM. Furthermore, we can choose penalty parameters independent of the Poisson ratio. One of the penalty parameters depends on Lamé's second constant μ, and the other penalty parameter is independent of both μ and λ. We prove the optimal order error estimates in piecewise H 1 {H^{1}} -norm, which is independent of the Poisson ratio. Numerical experiments show optimal order of convergence both in L 2 {L^{2}} and piecewise H 1 {H^{1}} -norms for all problems including nearly incompressible cases. [ABSTRACT FROM AUTHOR]

• MSG is applied for the first time to the homogenization of masonry. • The results agree with numerical or theoretical methods, including a 3D FEA. • MSG considerably reduces the computational cost. • 3D properties are obtained from the solution of 2D problems. • Absence of necessity of applying boundary conditions. Masonry is a composite material formed by units and joints, highly anisotropic and difficult to characterize. This paper presents the application of Mechanics of Structure Gene (MSG) to the homogenization of masonry. Since it is a semi-analytical technique, MSG considerably reduces the computational cost and maintains the same precision of three-dimensional (3D) analyses, for example, by the Finite Element Method. Other interesting features are the possibility of obtaining 3D properties from the solution of 1D or 2D problems and the absence of necessity of applying boundary conditions. In the analyzed examples, the 3D elastic constants of the masonry, considered as an anisotropic material, are calculated from Young's modulus and Poisson's ratio of the blocks (or units) and the mortar joints, considered as isotropic. The results obtained are compared with numerical or theoretical methods by different authors, including a 3D finite element analysis, and present agreement, even for large ratios between Young's moduli of blocks and mortar. Thus, the results presented in the paper show that the MSG method can be successfully applied in the homogenization of masonry and presents advantages over other methods for the same purpose. [ABSTRACT FROM AUTHOR]

Dentin, the main tissue of the tooth, is made of tubules surrounded by peri-tubular dentin (PTD), embedded in a matrix of inter-tubular dentin (ITD). The PTD and the ITD have different relative fractions of collagen and hydroxyapatite crystals. The ITD is typically less rigid than the PTD, which can be seen as a set of parallel hollow cylindrical reinforcements in the ITD matrix. In this paper, we extend Hashin and Rozen's homogenization scheme to a nonuniform distribution of hollow PTD cylinders, determined from image analysis. We relate the transverse isotropic elastic coefficients of a Representative Elementary Volume (REV) of dentin to the elastic and topological properties of PTD and ITD. The model is calibrated against experimental data. Each sample tested is consistently characterized by Environmental Scanning Electron Microscopy (ESEM), nanoindentation and Resonant Ultrasound Spectroscopy (RUS), which ensures that macroscopic mechanical properties measured are correlated with microstructure observations. Despite the high variability of microstructure descriptors and mechanical properties, statistical analyses show that Hashin's bounds converge and that the proposed model can be used for back-calculating the microscopic Poisson's ratios of dentin constituents. Three-point bending tests conducted in the laboratory were simulated with the Finite Element Method (FEM). Elements were assigned transverse isotropic elastic parameters calculated by homogenization. The tubule orientation and the pdf of the ratio inner/outer tubule radius were determined in several zones of the beams before testing. The remainder of the micro-mechanical parameters were taken equal to those calibrated by RUS. The horizontal strains found experimentally by Digital Image Correlation (DIC) were compared to those found by FEM. The DIC and FEM horizontal strain fields showed a very good agreement in trend and order of magnitude, which verifies the calibration of the homogenization model. By contrast with previous studies of dentin, we fully calibrated a closed form mechanical model against experimental data and we explained the testing procedures. In elastic conditions, the proposed homogenization scheme gives a better account of microstructure variability than micro–macro dentin models with periodic microstructure. [ABSTRACT FROM AUTHOR]

In this paper, we present a family of new mixed finite element methods for linear elasticity for both spatial dimensions n=2,3, which yields a conforming and strongly symmetric approximation for stress. Applying Pk+1-Pk as the local approximation for the stress and displacement, the mixed methods achieve the optimal order of convergence for both the stress and displacement when k≥n. For the lower order case (n-2≤k

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]

Purpose The purpose of this paper is to deal with large deformation analysis of plane beams composed of functionally graded (FG) elastic material with a variable Poisson’s ratio.Design/methodology/approach The material is assumed to be linear elastic, with a Poisson’s ratio varying according to a power law along the thickness direction. The finite element used is a plane beam of any-order of approximation along the axis, and with four transverse enrichment schemes, which can describe constant, linear, quadratic and cubic variation of the strain along the thickness direction. Regarding the constitutive law, five materials are adopted: two homogeneous limiting cases, and three intermediate FG cases. The effect of both finite element kinematics and distribution of Poisson’s ratio on the mechanical response of a cantilever is investigated.Findings In accordance with the scientific literature, the second scheme, in which the transverse strain is linearly variable, is sufficient for homogeneous long (or thin) beams under bending. However, for FG short (or moderate thick) beams, the third scheme, in which the transverse strain variation is quadratic, is needed for a reliable strain or stress distribution.Originality/value In the scientific literature, there are several studies regarding nonlinear analysis of functionally graded materials (FGMs) via finite elements, analysis of FGMs with constant Poisson’s ratio, and geometrically linear problems with gradually variable Poisson’s ratio. However, very few deal with finite element analysis of flexible beams with gradually variable Poisson’s ratio. In the present study, a reliable formulation for such beams is presented. [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]

Mechanical metamaterials have tunable material properties, and the architecture of such materials can be tuned to impart Negative Poisson's Ratio (NPR). However, architected lattices typically have low stiffness. In the current study, the filler-based and infill-based strategies for creating auxetic lattices with enhanced stiffness are proposed and demonstrated. Analytic expressions for different in-plane elastic properties of the sinusoidal re-entrant honeycomb (SRH) lattice are developed. Finite element models are validated using data from published literature and analytic models. Using validated FE modelling, parametric studies involving infill patterns and filler materials in the SRH lattices are undertaken to find combinations leading to enhanced stiffness with minor loss in auxeticity. The possibility of attaining a massive increment in stiffness than that of the empty lattices, while retaining significant auxeticity (Poisson's ratio < −1), is demonstrated, which is a key outcome of this work. Using the proposed approach, high stiffness has been achieved in case of both non-auxetic infill-based (NAIB) and auxetic infill-based (AIB) while retaining NPR is established. Further studies have confirmed that the AIB lattices exhibit much higher stiffness compared to all the other lattices. Finally, the proposed approach is benchmarked against four published approaches towards generating stiff lattices with NPR. When compared with existing approaches, it is found that the strategies proposed in this paper perform better; for the same NPR, the proposed approaches lead to lattices with higher stiffness, and conversely, for the same normalised stiffness higher auxeticity is achieved. Implementation of the proposed approaches can be realized using in-built infill capabilities of prevalent additive manufacturing 3 D printing technologies. New opportunities to enhance the capabilities of the existing technology are also indicated. [Display omitted] • Three novel strategies proposed for increasing stiffness whilst retaining auxeticity. • Auxetic infill patterns leads to significant improvement in mechanical attributes. • Analytic expressions for sinusoidal reentrant honeycomb lattices are developed. • Lattice with 700–900% improvement in stiffness with Poisson's ratio ∼ −1 is achieved. • Novel strategies are compared with prevalent approaches confirming superior mechanical attributes. [ABSTRACT FROM AUTHOR]

Bi-modulus materials exhibit the different modulus in tension and compression. The value of elastic modulus and Poisson ratio of every point in the bi-modulus elastic body not only depend on the material itself, but also the stress state and the strain state of the point. The uncertainty and nonlinearity of the elastic constitutive relation result in that the bi-modulus elastic problem is the complicated nonlinear problem This paper aims at studying the bi-modulus elastic constitutive equation employed in the bi-modulus finite element numerical method (FEM). The new elastic matrix model is proposed based on Ye's principal strain criterion with the assumption that the Poisson ratio maintain constant whenever in tension or in compression, and the elastic matrix is symmetric by equivalent transmitting. The shear modulus expression of this elastic matrix model is derived to enable the elastic matrix completely and improve the convergence of the FEM calculation. The statically indeterminate bi-modulus beam is analyzed by means of FEM employing the proposed elastic matrix model. The effects of the tensile modulus to compressive modulus ratio and the boundary condition on the stress and deflection of the bi-modulus beam is studied. [ABSTRACT FROM AUTHOR]

The use of cellular elastomer substrates not only reduces its restriction on natural diffusion or convection of biofluids in the realm of stretchable electronics but also enhances the stretchability of the electronic systems. An analytical model of "zigzag" cellular substrates under finite deformation is established and validated in this paper. The deformed shape, nonlinear stress-strain curve, and Poisson's ratio-strain curve of the cellular elastomer substrate calculated using the reported analytical model agree well with those from finite element analysis (FEA). Results show that lower restriction on the natural motion of human skin could be achieved by the proposed zigzag cellular substrates compared with the previously reported hexagonal cellular substrates, manifesting another leap toward mechanically "invisible" wearable, stretchable electronic systems. [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]

Graphical abstract Highlights • Models of zero Poisson's ratio (ZPR) cellular structures were established. • Effects of cell wall relative thickness and corner radius on elastic properties were investigated. • Higher relative corner radius always increases the Poisson's ratio (PR) of ZPR honeycombs. • Effect of cell wall thickness depends on the corner radius and type of honeycomb. • Deviation of PR on ZPR honeycombs can be eliminated by altering the effective length. Abstract Cellular structures with zero Poisson's ratio (ZPR) have potential application in tissue engineering. Although the Poisson's ratio of a certain network is mainly determined by the internal cell wall arrangement, it is also influenced by the fine-scale geometry parameters. In this paper, the effects of cell wall relative thickness and the corner radius on the elastic properties of two types of ZPR cellular structures, including reversed semi-re-entrant (RSRE) and semi-re-entrant (SRE) honeycombs, were investigated by means of finite element method (FEM). The result shows that the cell wall relative thickness and the corner radius have a significant effect on the Poisson's ratios of RSRE and SRE honeycombs. This phenomenon is attributed to the deformation effect of the vertexes and it can be eliminated by altering the effective length of the inclined strut. This effect is also validated as documented later by our experiments. [ABSTRACT FROM AUTHOR]

The surface elasticity theory of Gurtin–Murdoch has proven to be remarkably successful in predicting the behavior of materials at the nano scale, which can be attributed to the fact that the surface-to-volume ratio increases as the problem dimension decreases. On the other hand, surface tension can deform soft elastic solids even at the macro scale resulting e.g. in elastocapillary instabilities in soft filaments reminiscent of Plateau–Rayleigh instabilities in fluids. Due to the increasing number of applications involving nanoscale structures and soft solids such as gels, the surface elasticity theory has experienced a prolific growth in the past two decades. Despite the large body of literature on the subject, the constitutive models of surface elasticity theory at large deformations are not suitable to capture the surface behavior from fully compressible to nearly incompressible elasticity, especially from a computational perspective. A physically meaningful and proper decomposition of the surface free energy density in terms of area-preserving and area-varying contributions remains yet to be established. We show that an immediate and intuitive generalization of the small-deformation surface constitutive models does not pass the simple extension test at large deformations and results in unphysical behavior at lower Poisson's ratios. Thus, the first contribution of the manuscript is to introduce a novel decomposed surface free energy density that recovers surface elasticity across the compressibility spectrum. The second objective of this paper is to formulate an axisymmetric counterpart of the elastocapillary theory methodically derived from its three-dimensional format based on meaningful measures relevant to the proposed surface elasticity model. Various aspects of the problem are elucidated and discussed through numerical examples using the finite element method enhanced with surface elasticity. • A novel additive split of the hyperelastic surface energy density is proposed. • The split into area-preserving and area-varying parts is non-intuitive. • The split is suitable for the entire compressibility spectrum. • The split is advantageous for numerical treatment of nearly incompressible surfaces. • Degenerate three-dimensional cases such as axisymmetric problems are elaborated on. • A systematic treatment of elastocapillary for axisymmetric problems is introduced. • The developed axisymmetric variational elastocapillary formulation is implemented. • Numerical examples show the significance of the proposed surface elasticity model. [ABSTRACT FROM AUTHOR]

For fixed dentures, new generations of zirconia with diverse characteristics and design choices are of significant interest. Although in vitro studies and finite element analysis (FEA) studies have been published, comprehension of various new methods of material testing and analysis remains insufficient. Young's modulus and Poisson's ratio of the desired materials must be available for investigators to validate FEA investigations that are accompanied by mechanical testing. The aim of this narrative review was to find recent FEA studies that report these values for newly developed commercial CAD/CAM zirconia restorative materials and compile them in a data list. A PubMed search was performed (English articles; 2018–2023; keywords: FEA, finite element, zirconia). Full-text articles (157) were examined, including studies (36) reporting the commercial materials' names, Young's modulus, and Poisson's ratio. Only 21 studies had the source of their values referenced. A list of the materials and values used in these studies was compiled. Researchers are highly recommended to trace back references to determine the origins of these values for commercial materials. New research is encouraged to test the ever expanding list of new commercial esthetic monolithic CAD/CAM zirconia materials, as well as their different translucencies, to report their Young's modulus and Poisson's ratio. [ABSTRACT FROM AUTHOR]

In this paper, a 3D augmented re-entrant cellular structure (ARCS) is proposed and its Poisson's ratios and elastic properties can be modulated in a wide range. Based on the classical beam theory, the elastic properties on the principle directions are obtained as functions of the structural parameters and then are verified by finite element method (FEM) simulations. Compared with the classical 3D re-entrant cellular structure (RCS), the Young's moduli of the new 3D structure on the principal directions show a significant increase, and the Poisson's ratio can be tunable with the control of the internal parameters of cellular structure. In addition, the elastic properties on off-axis directions are obtained by analytical solutions, which show that the Young's moduli on the off-axis directions are much lower than the principle ones. In addition, the shear moduli also show strong dependence on the loading directions. Moreover, by stretching in the principal directions, the ARCS expands in all vertical directions when the moduli ratio is below 0.5. However, stretching in the off-axis directions, the Poisson's ratios are no longer negative in its vertical directions. The results suggest a possible approach to design new auxetic materials with tunable Poisson's ratios for engineering applications. [ABSTRACT FROM AUTHOR]

Based on a 2D cross chiral structure, two novel 3D cross chiral structures (structure-1 and structure-2) with negative Poisson's ratios were proposed in this paper. Structure-1 could be evolved into structure-2 by adding a star structure. Analytical models of the two auxetic cellular structures were established based on the Timoshenko beam theory. The Young's modulus and Poisson's ratio of the cellular structures were obtained in all principal directions, which were verified by finite element method (FEM). Structure-1 exhibits anisotropic auxetic behavior while structure-2 shows uniform auxetic behavior in all three principal directions with all on-axis Poisson's ratios closer to the limit of -1. Additionally, the extra addition of star structure can enhance the Young's modulus of structure-2 significantly in the case of same relative density, compared to structure-1. Moreover, the effect of parameter variation on elastic properties of two structures and the comparison with other classical 3D auxetic structures were also thoroughly studied and discussed in detail. These results are expected to eventually contribute to the advance of research and the application of new 3D auxetic structures in the future. [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]

The negative Poisson's ratio (NPR) mechanical metamaterials exhibit excellent mechanical properties, whereas their low stiffness limits the development. In this paper, we investigated an NPR mechanical metamaterial: star-circle honeycomb (SCH), which possesses enhanced stiffness compared to the classical star-shaped honeycomb (SH). Based on the Castigliano's second theorem and the principle of virtual work, a theoretical model was built to calculate the effective elastic properties of the SCH, and validated by the finite element method (FEM). The comparison with the SH showed that the SCH possessed a significantly enhanced elastic modulus. Also, we find that the elastic properties can be adjusted broadly and tailored to meet the engineering needs by selecting parameters reasonably. Subsequently, the anisotropic quasi-static compression responses of the SCH were studied. The results showed that the plateau stress and energy absorption capacity in the y -direction load were both better than that in the x -direction load. The parameter study indicated that θ and ψ produced a greater impact on the quasi-static responses. A reasonable combination of parameters can give full play to the mechanical properties of the structure. This work provided a new design idea for improving the stiffness and choosing the optimal in-plane loading direction of metamaterials. • The theoretical enclosed formulas of effective elastic properties for the SCH are derived. • The coupling between thin-walled circle and corner point strongly enhances the effective Young's modulus. • The SCH exhibits two plateau stages in the y direction, while three plateau stages in the x direction. • The energy absorption of the SCH in the y direction is greatly better than that in the x direction. [ABSTRACT FROM AUTHOR]

Elastic properties of open-cell metallic foams are investigated in correlation with relative density and pore size variation. A variety of foam architectures, with open porosity above 70% (relative density below 0.30) and various pore size distributions, were modeled using Laguerre–Voronoi tessellations (LVT). The coefficient of pore volume variation, CV(V), was introduced to quantify the uniformity of designed structures and ranged between 0.5 to 2.1. Elastic behavior of the modeled foams to uniaxial compression along three orthogonal directions was analyzed using the finite element (FE) method. It is shown that Young's modulus and Poisson's ratio of open-cell metals is not solely a function of relative density (porosity) but the pore size variation as well. For similar porosity (approx. 74–98%), Young's modulus and Poisson's ratio may be reduced by approx. 25–30% and 10–25%, respectively, when CV(V) increases from 0.5 to 2.1. Furthermore, the incorporation of a relationship between Young's modulus and the coefficient of pore volume variation to the Gibson–Ashby model is proposed. [ABSTRACT FROM AUTHOR]

The Poisson effect, measured by the Poisson's ratio, plays an important role in the regulation of the elastic properties of composite materials, but it is not considered in the conventional Voigt (iso-strain) and Reuss (iso-stress) formulas, which explains why the formulas are inaccurate even if the iso-strain or the iso-stress conditions are satisfied. To consider the Poisson effect, we derived a set of new formulas based on the governing equations of elasticity. The obtained formulas show greater mathematical complexity. To further understand how the Poisson effect influences composite elastic properties, two types of finite element models (FEM) were constructed to simulate the situations where the Poisson effect does or does not have an influence. The results show that the conventional Voigt and Reuss formulas are special cases of the newly derived ones. The Poisson effect induces secondary strains and stresses into the phase materials, which demands more strain energy to achieve the same deformation in the primary (loading) direction, and thus increases composite stiffness; the magnitude of the increase is dependent on the contrast of phase properties. The findings may have significant impact on the study of the emerging nanocomposites and functionally graded materials, where the conventional Voigt and Reuss formulas have wide applications. [ABSTRACT FROM AUTHOR]

Micromechanics models of composite materials are preferred in the analysis and design of composites for their high computational efficiency. However, the accuracy of the micromechanics models varies widely, depending on the volume fraction of inclusions and the contrast of phase properties, which have not been thoroughly studied, primarily due to the lack of complete and representative experimental data. The recently developed microstructure-free finite element modeling (MF-FEM) is based on the fact that, for a particulate-reinforced composite, if the characteristic size of the inclusions is much smaller than the composite representative volume element (RVE), the elastic properties of the RVE are independent of inclusion shape and size. MF-FEM has a number of advantages over the conventional microstructure-based finite element modeling. MF-FEM predictions have good to excellent agreement with the reported experiment results. In this study, predictions produced by MF-FEM are used in replace of experimental data to compare the accuracy of selected micromechanics models of particulate composites. The results indicate that, only if both the contrasts in phase Young's moduli and phase Poisson's ratios are small, the micromechanics models are able to produce accurate predictions. In other cases, they are more or less inaccurate. This study may serve as a guide for the appropriate use of the micromechanics models. [ABSTRACT FROM AUTHOR]

Compression of elastic layers bonded between parallel plates often find applications in the mechanical characterization of soft materials or the transfer-printing of nanomembranes with polymeric stamps. In addition, annular rubbery gaskets and sealers are often under uniaxial compression during service. Analysis of elastic layers under compression has been focused on nearly incompressible materials such as rubbers, and empirical assumptions of displacements were adopted for simplicity. For compressible materials, solutions obtained by the method of averaged equilibrium are sufficient for effective compression modulus but inaccurate for the displacement or stress fields whereas solutions obtained by the method of series expansion are considerably complicated. In this paper, we report full field, closed-form solutions for bonded elastic layers (disks, annuli, annuli with rigid shafts, infinitely long strips) in compression using separation of variables without any pre-assumed deformation profile. These solutions can satisfy the exact forms of the equilibrium equations and all essential boundary conditions as well as the weak form of the natural boundary conditions. Therefore the predicted stress, displacement, and effective modulus have found excellent agreement with finite element modeling (FEM) results over a wide range of Poisson’s ratio and aspect ratio. The analytical and FEM results of the stress, displacement, and effective modulus are highly sensitive to Poisson’s ratio, especially near 0.5. Therefore we also propose a viable means to simultaneously measure the intrinsic Young’s modulus and Poisson’s ratio of elastically compressible layers without camera settings. When Poisson’s ratio approaches 0.5, our solutions can degenerate to classical solutions for incompressible elastic layers. [ABSTRACT FROM AUTHOR]

A finite element formulation for a non-local particle method is proposed in this paper for elasticity and fracture analysis of 2D solids. The model is based on a new particle method which incorporates a non-local multi-body particle interaction into the conventional pair-wise particle interactions. The non-local particle method is capable of modeling solids with arbitrary Poisson׳s ratio. Finite element formulation is proposed for the implicit solution of elasticity and fracture problems under static/quasi-static conditions, which is very efficient compared to the direct explicit solution in particle dynamics. Energy minimization principle is used to develop a new finite element with both local pair-wise and non-local multi-body particle interactions. The developed finite element formulation is verified with classical finite element simulation of some benchmark problems. Fracture simulation using the proposed particle-based finite element formulation is demonstrated. Some conclusions and future work is drawn based on the current investigation. [ABSTRACT FROM AUTHOR]

Honeycomb composites are now common materials in applications where high specific stiffness is required. Previous research has found that honeycombs with polymer infills in their cells, here referred to as honeycomb-polymer composites (HPCs), exhibit effective stiffnesses greater than the honeycomb or polymer alone. Currently, the state of analytic models for predicting the elastic properties of these composites is limited, and further research is needed to better characterize the behavior of these materials. In this research, a nonlinear finite element analysis was employed to perfor2m parametric studies of a filled honeycomb unit cell with isotropic wall and infill materials. A rigid wall model was created as an upper bound on the deformable wall model's performance, and an empty honeycomb model was employed to better understand the mechanisms of stiffness amplification. Parametric studies were completed for infill material properties and cell geometry, with the effective Young's modulus studied in two in-plane material directions. The mechanisms by which the stiffness amplification occurs are studied, and comparisons to existing analytic models are made. It has been observed that both the volume change within the honeycomb cell under deformation and the mismatch in Poisson's ratios between the honeycomb and infill influence the effective properties. Stiffness amplifications of over 4000 have been observed, with auxetic behavior achieved by tailoring of the HPC geometry. Additionally, the effect of large effective strains up to 10% is explored, where the cell geometry changes significantly. This research provides an important step toward understanding the design space and benefits of HPCs. [ABSTRACT FROM AUTHOR]

This paper proposes one-dimensional formulations based on hierarchical expansions of the unknown displacement variables for the analysis of multilayered structures made of anisotropic composite layers. The hierarchical technique shows variable kinematic properties and it is based on the Carrera unified formulation. Two different classes of refined theories are proposed: the first expands the unknown variables in terms of power polynomials of the cross-sectional coordinates (it consists of a Taylor-like expansion); the second class of one- dimensional theories uses Lagrange polynomials (Lagrange expansion) and subdomain discretizations of the cross section, and it leads to only pure displacements as the unknown variables. Taylor-like expansion is used to develop equivalent single-layer formulations, and Lagrange expansion is used to construct both equivalent single-layer and layerwise descriptions. The finite element method is employed to develop numerical applications. Using the Carrera unified formulation, finite element matrices are obtained in terms of a few fundamental nuclei that are formally independent of all the considered one-dimensional formulations. A number of numerical examples are given concerning on beams, plates, and more complex structures. Comparisons with results from plate and solid models are provided. The following has been concluded: 1) The proposed formulation represents a reliable, compact, and accurate method to develop refined one-dimensional models. 2) The present one-dimensional models are very effective at detecting both global and local responses of composite structures. 3) Shell- and solidlike results are obtained with a significant reduction in the computational costs. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the initial yield surface of a new type of hollow sphere structure (HSS). For this new type, the sphere shell is perforated by several holes in order to open the inner sphere volume and surface. Multi-axial tensile loading is applied to investigate the initial yield surface of perforated HSS with ideal plastic base material properties. The influence of the hole diameters and different geometries of linking elements on the initial yield surface are shown. The results are compared to classical configurations without perforation. It is shown that the initial yield surface can be represented as a cone in the principal stress coordinate system. Increasing of the hole diameter (decreasing of the average density) decreases the diameter of this cone. Compared to the changes for different hole diameters, the shape of the initial yield surface is less sensitive to the geometry of the link between two spheres. In addition, the elastic properties of PHSS, i.e. Young''s modulus and Poisson''s ratio, are investigated. To this end, three-dimensional finite element analysis is used to investigate primitive cubic unit cell models. [Copyright &y& Elsevier]

Abstract: This paper considers the problem of determining the nonlinear bimodular stiffness properties, i.e., the tensile and compressive Young’s moduli and Poisson’s ratios, and the shear modulus, of particulate composite materials with particle–matrix interfacial debonding. It treats the general case in which some of the particles are debonded while the others remain intact. The Mori–Tanaka approach is extended to formulate the method of solution for the present problem. The resulting auxiliary problem of a single debonded particle in an infinite matrix subjected to a remote stress equal to the average matrix stress, for which Eshelby’s solution does not exist, is solved by the finite element method accounting for the particle–matrix separation and contact at the debonded particle–matrix interface. Because of the nonlinear nature of the problem, an iterative process is employed in calculating the stiffness properties. The predicted stiffness properties are compared to the exact solutions of the stiffness properties of particulate composites with body-centered cubic packing arrangement. [Copyright &y& Elsevier]

Abstract: In this paper, the elastic stresses and strains in the circular cross-section bars with semicircular groove subjected to uniaxial tension are systematically examined using the finite element method. It is shown that the stress and strain concentration factors are different even if the material is in the elastic state. Poisson’s ratio can have a significant effect on the strain concentration factor. The relation of stress and strain concentration factors is also obtained for stress concentration region in cylindrical coordinates. This relation depends on Poisson’s ratio, the radial stress factor and the triaxial stress constraint factor. [Copyright &y& Elsevier]

Abstract: This paper derives an exact solution for the non-uniform stress and displacement fields within a finite, transversely isotropic, and linear elastic cylinder under compression with a kind of radial constraint induced by friction between the end surfaces of the cylinder and the loading platens. The main feature of the present work is the introduction of a general solution form for Lekhnitskii’s stress function such that the governing equation and all end and curved boundary conditions of the cylinder are satisfied exactly. Two different solutions were obtained corresponding to the real or complex characteristic roots of the governing equation, depending on the combination of the elastic material constants. The solution by Watanabe [Watanabe, S., 1996. Elastic analysis of axi-symmetric finite cylinder constrained radial displacement on the loading end. Structural Engineering/Earthquake Engineering JSCE 13, 175s–185s] for isotropic cylinders under compression test can be recovered as a special case. Our numerical results show that both the non-uniform stress distribution and the difference between the apparent and the true Young’s moduli of the cylinder are very sensitive to the anisotropy of Young’s moduli, Poisson’s ratios and shear moduli. A more distinct bulging shape of the cylinder is expected when anisotropy in shear modulus is strong, the cylinder is relatively short, and the end constraint is large. The bulging shape, however, does not depend strongly on anisotropy of either Poisson’s ratio or Young’s modulus. [Copyright &y& Elsevier]

The stresses and strains in a diamond anvil cell device were investigated using a finite-element code NIKE2D for the case of an ultra-hard composite gasket material. The pressure distribution in a diamond-coated rhenium gasket was measured by the energy dispersive diffraction technique to 213 GPa and compared with the finite-element modeling results. We examine various models for the mechanical properties of diamond-coated rhenium gasket as well as for diamond failure for shear stresses exceeding 100 GPa. The elastic and plastic properties of gasket were varied such that a good agreement between the experimentally measured pressure distribution and the computational pressure profiles were obtained. As a result, we obtained the effective Young's modulus, Poisson's ratio, yield stress for indented gasket, linear hardening modulus, and hardening parameter value for this layered ultra-hard composite gasket material. Future diamond design strategies for attainment of extreme high pressures using ultra-hard gasket materials are also discussed. [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]

The mechanical properties of soft tissues are strongly dependent on their microstructures which evolve with aging and diseases. In this paper, a micromechanical model is presented to investigate the mechanical properties of tendons and ligaments, which are treated as planar crimped fiber-reinforced composites. The interaction among the constituents in such a composite is accounted for by utilizing the Mori–Tanaka method. Explicit analytical solutions are derived for describing the effects of microstructures on its macroscopic elastic properties, which are in good agreement with both finite element analysis and relevant experimental results. It is found that fiber waviness has a significant influence on the elastic properties of tendon and ligament. Our findings also demonstrate that planar crimp is significant to achieve the large Poisson's ratio of ligament and tendon, thereby revealing a novel structure–function mechanism. Parametric analysis further elucidates that their Poisson's ratios are also dependent on the volume fractions of crimped fibers and the elastic properties of the matrix. This work not only provides a theoretical method to predict the constitutive relation of biocomposites containing wavy fibers, but also expands our knowledge on the microstructural origin of large Poisson's ratios of soft tissues. [ABSTRACT FROM AUTHOR]

Fish Cells as a new metamaterial with zero Poisson's ratio in two planar directions is introduced with application in morphing aircraft skin. In order to tailor the design of this metamaterial for arbitrary loadings, equivalent elastic properties of the Fish Cells metamaterial are derived and analyzed using analytical and numerical methods. The admissible range of geometric parameters is presented and variation of elastic properties with parameters is studied. The effective elastic modulus of the metamaterial is derived analytically and verified with finite element models. The in-plane and transverse shear modulus of the metamaterial are evaluated using finite element analysis where accurate periodic boundary conditions for in-plane shear loading are investigated. The lower and upper bounds of the transverse shear modulus are derived based on strain and complementary energy relations which are verified with finite element results. As zero Poisson's ratio behavior of the Fish Cells topology is proved, derivative geometries from this topology with zero Poisson's ratio behavior are also presented. [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]

In this work, differently shaped carbon nano-sized allotropes reinforced composite properties are estimated and interfacial stresses are calculated and compared to get the best carbon reinforcement. Carbon nanopowder, carbon nanotubes, nanographene and Buckminster fullerenes are selected as these materials have different shapes and reinforcement of these materials in the aluminium matrix will give different properties. The comparative studies are performed by using the Micromechanics and Finite element method. The longitudinal, transverse modulus, Poisson's ratio are estimated along with the interface stresses between the constituents of carbon power/Al matrix composite, fullerene/Al matrix composite, CNT/Al matrix composite and graphene/Al matrix composite. From this work, it is found that the longitudinal modulus of the composite will be higher by using CNT or Graphene reinforcement and carbon particle or Buckminster fullerene reinforcement will give high transverse modulus than CNT and graphene reinforcement. The interfacial stresses generated between the reinforcement and the Aluminum matrix will be less by using carbon nanopowder than the other allotropes consider for the studies. This work will give an idea of the selection of nanoreinforcement of composite material in the perspective of elastic properties and interfacial stresses. [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]

The initial vertical stiffness of the bonded spherical elastic layer with Poisson's ratio from 0 to 0.5 is formulated on the basis of two kinematic assumptions. The governing equations of the stiffness are solved by numerical method. The vertical stiffness is not only related to the load area and the thickness of the elastic layer, but also related to the shape factor and inner edge angle of the spherical elastic layer. The analytical method is verified by FE analysis with a 2D axisymmetric model with Poisson's ratio within (0.49, 0.499999). Poisson's ratio, radius-thickness ratio and edge angles will influence the stiffness error. The stiffness error increases as the radius-thickness ratio increases and tends to saturate when the radius-thickness ratio exceeds 50. When the inner edge angle is constant, the relative errors of the vertical stiffness will decrease as the outer edge angle increases. When the outer edge angle is constant, the errors will increase and reach a maximum value and then decrease as the inner edge angle increases. For a single elastic layer with the radius-thickness ratio of 20, the relative error of vertical stiffness is within (−10, 12%), which is acceptable in bearing design. [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]