Showing papers on "Orthotropic material published in 2011"

Computational modeling of passive myocardium

Abstract: This work deals with the computational modeling of passive myocardial tissue within the framework of mixed, non-linear finite element methods. We consider a recently proposed, convex, anisotropic hyperelastic model that accounts for the locally orthotropic micro-structure of cardiac muscle. A coordinate-free representation of anisotropy is incorporated through physically relevant invariants of the Cauchy–Green deformation tensors and structural tensors of the corresponding material symmetry group. This model, which has originally been designed for exactly incompressible deformations, is extended towards entirely three-dimensional inhomogeneous deformations by additively decoupling the strain energy function into volumetric and isochoric parts along with the multiplicative split of the deformation gradient. This decoupled constitutive structure is then embedded in a mixed finite element formulation through a three-field Hu–Washizu functional whose simultaneous variation with respect to the independent pressure, dilatation, and placement fields results in the associated Euler–Lagrange equations, thereby minimizing the potential energy. This weak form is then consistently linearized for uniform-pressure elements within the framework of an implicit finite element method. To demonstrate the performance of the proposed approach, we present a three-dimensional finite element analysis of a generic biventricular heart model, subjected to physiological ventricular pressure. The parameters employed in the numerical analysis are identified by solving an optimization problem based on six simple shear experiments on explanted cardiac tissue. Copyright © 2010 John Wiley & Sons, Ltd.

Delamination analysis of composites by new orthotropic bimaterial extended finite element method

Abstract: The extended finite element method (XFEM) is further improved for fracture analysis of composite laminates containing interlaminar delaminations New set of bimaterial orthotropic enrichment functions are developed and utilized in XFEM analysis of linear-elastic fracture mechanics of layered composites Interlaminar crack-tip enrichment functions are derived from analytical asymptotic displacement fields around a traction-free interfacial crack Also, heaviside and weak discontinuity enrichment functions are utilized in modeling discontinuous fields across interface cracks and bimaterial weak discontinuities, respectively In this procedure, elements containing a crack-tip or strong/weak discontinuities are not required to conform to those geometries In addition, the same mesh can be used to analyze different interlaminar cracks or delamination propagation The domain interaction integral approach is also adopted in order to numerically evaluate the mixed-mode stress intensity factors A number of benchmark tests are simulated to assess the performance of the proposed approach and the results are compared with available reference results Copyright © 2011 John Wiley & Sons, Ltd

Prestressed Morphing Bistable and Neutrally Stable Shells

Abstract: This study deals with prestressed shells, which are capable of “morphing” under large deflexions between very different load-free configurations. Prestressing involves plastically curving a flat, thin shell in orthogonal directions either in the opposite or same sense, resulting in two unique types of behavior for isotropic shells. Opposite-sense prestressing produces a bistable, cylindrically curved shell provided the prestress levels are large enough and similar in size: This effect forms the basis of a child’s “flick” bracelet and is well known. On the other hand, same-sense prestressing results in a novel, neutrally stable shell provided the levels are also sufficiently large but identical: The shell has to be made precisely, otherwise, it is monostable and is demonstrated here by means of a thin, helically curved strip. The equilibrium states associated with both effects are quantified theoretically and new expressions are determined for the requisite prestress levels. Furthermore, each stability response is revealed in closed form where it is shown that the neutrally stable case occurs only for isotropic materials, otherwise, bistability follows for orthotropic materials, specifically, those, which have a shear modulus different from the isotropic value. Finally, prestressing and initial shape are considered together and, promisingly, it is predicted that some shells can be neutrally stable and bistable simultaneously.

Propagation of waves in an incompressible transversely isotropic elastic solid with initial stress: Biot revisited

Abstract: In this paper, the general constitutive equation for a transversely isotropic hyperelastic solid in the presence of initial stress is derived, based on the theory of invariants. In the general finite deformation case for a compressible material this requires 18 invariants (17 for an incompressible material). The equations governing infinitesimal motions superimposed on a finite deformation are then used in conjunction with the constitutive law to examine the propagation of both homogeneous plane waves and, with the restriction to two dimensions, Rayleigh surface waves. For this purpose we consider incompressible materials and a restricted set of invariants that is sufficient to capture both the effects of initial stress and transverse isotropy. Moreover, the equations are specialized to the undeformed configuration in order to compare with the classical formulation of Biot. One feature of the general theory is that the speeds of homogeneous plane waves and surface waves depend nonlinearly on the initial stress, in contrast to the situation of the more specialized isotropic and orthotropic theories of Biot. The speeds of (homogeneous plane) shear waves and Rayleigh waves in an incompressible material are obtained and the significant differences from Biot's results for both isotropic and transversely isotropic materials are highlighted with calculations based on a specific form of strain-energy function.

A Discrete Element Model for Predicting Shear Strength and Degradation of Rock Joint by Using Compressive and Tensile Test Data

Abstract: A discrete element model is proposed to examine rock strength and failure. The model is implemented by UDEC, which is developed for this purpose. The material is represented as a collection of irregular-sized deformable particles interacting at their cohesive boundaries. The interface between two adjacent particles is viewed as a flexible contact whose constitutive law controls the material fracture and fragmentation properties. To reproduce rock anisotropy, an orthotropic cohesive law is developed for the contacts, which allows their shear and tensile behaviors to be different from each other. Using a combination of original closed-form expressions and statistical calibrations, a unique set of the contact microparameters are found based on the uniaxial/triaxial compression and Brazilian tension test data of a plaster. Applying the obtained microparameters, joint specimens, made of the same plaster, are simulated, where the comparison of the obtained results to laboratory data shows a reasonable agreement.

Analytical calculation of local buckling and post-buckling behavior of isotropic and orthotropic stiffened panels

Abstract: A methodology for the analytical assessment of local buckling and post-buckling behavior of isotropic and orthotropic stiffened plates is presented. The approach considers the stiffened panel segment located between two stiffeners, while the remaining panel is replaced by equivalent transverse and rotational springs of varying stiffness, which act as elastic edge supports. A two-dimensional Ritz displacement function (pb-2 Ritz) is utilized in the solution of the local buckling problem of isotropic and laminated symmetric composite panels with arbitrary edge boundary conditions. The buckling analysis of the segment provides an accurate and conservative prediction of the panel local buckling behavior. Consequently, the developed methodology is extended in the prediction of the post-buckling response of stiffened panels of which the skin has undergone local buckling. Of high importance for the calculation of the post-buckling behavior is the selection of appropriate boundary conditions for the structural members analyzed. A comparison of the present methodology results to respective finite element (FE) results has shown a satisfactory agreement.

Patient-Specific Finite-Element Analyses of the Proximal Femur with Orthotropic Material Properties Validated by Experiments

Abstract: Patient-specific high order finite-element (FE) models of human femurs based on quantitative computer tomography (QCT) with inhomogeneous orthotropic and isotropic material properties are addressed. The point-wise orthotropic properties are determined by a micromechanics (MM) based approach in conjunction with experimental observations at the osteon level, and two methods for determining the material trajectories are proposed (along organs outer surface, or along principal strains). QCT scans on four fresh-frozen human femurs were performed and high-order FE models were generated with either inhomogeneous MM-based orthotropic or empirically determined isotropic properties. In vitro experiments were conducted on the femurs by applying a simple stance position load on their head, recording strains on femurs' surface and head's displacements. After verifying the FE linear elastic analyses that mimic the experimental setting for numerical accuracy, we compared the FE results to the experimental observations to identify the influence of material properties on models' predictions. The strains and displacements computed by FE models having MM-based inhomogeneous orthotropic properties match the FE-results having empirically based isotropic properties well, and both are in close agreement with the experimental results. When only the strains in the femoral neck are being compared a more pronounced difference is noticed between the isotropic and orthotropic FE result. These results lay the foundation for applying more realistic inhomogeneous orthotropic material properties in FEA of femurs.

Characterization of Anisotropic Polymeric Foam Under Static and Dynamic Loading

Abstract: An orthotropic polymeric foam with transverse isotropy (Divinycell H250) used in composite sandwich structures was characterized at various strain rates. Uniaxial experiments were conducted along principal material axes as well as along off-axis directions under tension, compression, and shear to determine engineering constants, such as Young’s and shear moduli. Uniaxial strain experiments were conducted to determine mathematical stiffness constants, i. e., Cij. An optimum specimen aspect ratio for these tests was selected by means of finite element analysis. Quasi-static and intermediate strain rate tests were conducted in a servo-hydraulic testing machine. High strain rate tests were conducted using a split Hopkinson Pressure Bar system built for the purpose using polymeric (polycarbonate) bars. The polycarbonate material has an impedance that is closer to that of foam than metals and results in lower noise to signal ratios and longer loading pulses. It was determined by analysis and verified experimentally that the loading pulses applied, propagated along the polycarbonate rods at nearly constant phase velocity with very low attenuation and dispersion. Material properties of the foam were obtained at three strain rates, quasi-static (10−4 s−1), intermediate (1 s−1), and high (103 s−1) strain rates. A simple model proposed for the Young’s modulus of the foam was in very good agreement with the present and published experimental results.

Dynamic response of composite sandwich plates subjected to time-dependent pressure pulses

Abstract: The dynamic response of orthotropic sandwich composite plates impacted by time-dependent external blast pulses is studied by use of numerical techniques. The theory is based on classical sandwich plate theory including the large deformation effects, such as geometric non-linearities, in-plane stiffness and inertias, and shear deformation. The equations of motion for the plate are derived by the use of the virtual work principle. Approximate solutions are assumed for the space domain and substituted into the equations of motion. Then the Galerkin Method is used to obtain the non-linear differential equations in the time domain. The finite difference method is applied to solve the system of coupled non-linear equations. The results of theoretical analyses are obtained and compared with ANSYS results. Effects of the face sheet number, as well as those related to the ply-thickness, core thickness, geometrical non-linearities, and of the aspect ratio are investigated. Detailed analyses of the influence of different type of pressure pulses on dynamic response are carried out.

Graphene characterization: A fully non-linear spring-based finite element prediction

Abstract: In the present study, a spring-based finite element model is formulated and utilized to predict the stress–strain behavior of single-layer graphene. Generalized force–generalized displacement behavior of the developed nonlinear springs follows the relation between the first derivative of the potential energy and the corresponding bond deformation, describing interatomic interactions. A number of different loading cases are examined in order to predict mechanical properties and characterize the graphene sheet. Predicted Young's and shear moduli, tensile and shear strength, tensile and shear failure strain, etc., under tension, compression and pure shear, are compared to results found in the literature, which are based on numerical, analytical or experimental methodologies. In all the above loading cases the graphene sheet is examined as a virtually orthotropic material, exhibiting different material properties in the armchair and zigzag directions. Different behaviors in tension and compression, as suggested by the modified Morse atomic bond stretching potential, are illustrated by the predicted stress–strain curves.

The impact of bone and suture material properties on mandibular function in Alligator mississippiensis: testing theoretical phenotypes with finite element analysis

Abstract: The functional effects of bone and suture stiffness were considered here using finite element models representing three different theoretical phenotypes of an Alligator mississippiensis mandible. The models were loaded using force estimates derived from muscle architecture in dissected specimens, constrained at the 18th and 19th teeth in the upper jaw and 19th tooth of the lower jaw, as well as at the quadrate-articular joint. Stiffness was varied systematically in each theoretical phenotype. The three theoretical phenotypes included: (i) linear elastic isotropic bone of varying stiffness and no sutures; (ii) linear elastic orthotropic bone of varying stiffness with no sutures; and (iii) linear elastic isotropic bone of a constant stiffness with varying suture stiffness. Variation in the isotropic material properties of bone primarily resulted in changes in the magnitude of principal strain. By comparison, variation in the orthotropic material properties of bone and isotropic material properties of sutures resulted in: a greater number of bricks becoming either more compressive or more tensile, changing between being either dominantly compressive or tensile, and having larger changes in the orientation of maximum principal strain. These data indicate that variation in these model properties resulted in changes to the strain regime of the model, highlighting the importance of using biologically verified material properties when modeling vertebrate bones. When bones were compared within each set, the response of each to changing material properties varied. In two of the 12 bones in the mandible, varied material properties within sutures resulted in a decrease in the magnitude of principal strain in bricks adjacent to the bone/suture interface and decreases in stored elastic energy. The varied response of the mandibular bones to changes in suture stiffness highlights the importance of defining the appropriate functional unit when addressing relationships of performance and morphology.

A mesostructurally-based anisotropic continuum model for biological soft tissues—Decoupled invariant formulation

Abstract: Characterising and modelling the mechanical behaviour of biological soft tissues is an essential step in the development of predictive computational models to assist research for a wide range of applications in medicine, biology, tissue engineering, pharmaceutics, consumer goods, cosmetics, transport or military. It is therefore critical to develop constitutive models that can capture particular rheological mechanisms operating at specific length scales so that these models are adapted for their intended applications. Here, a novel mesoscopically-based decoupled invariant-based continuum constitutive framework for transversely isotropic and orthotropic biological soft tissues is developed. A notable feature of the formulation is the full decoupling of shear interactions. The constitutive model is based on a combination of the framework proposed by Lu and Zhang [Lu, J., Zhang, L., 2005. Physically motivated invariant formulation for transversely isotropic hyperelasticity. International Journal of Solids and Structures 42, 6015-6031] and the entropic mechanics of tropocollagen molecules and collagen assemblies. One of the key aspects of the formulation is to use physically-based nanoscopic quantities that could be extracted from experiments and/or atomistic/molecular dynamics simulations to inform the macroscopic constitutive behaviour. This effectively couples the material properties at different levels of the multi-scale hierarchical structure of collagenous tissues. The orthotropic hyperelastic model was shown to reproduce very well the experimental multi-axial properties of rabbit skin. A new insight into the shear response of a skin sample subjected to a simulated indentation test was obtained using numerical direct sensitivity analyses.

Three‐dimensional analysis of functionally graded plates

Abstract: Based on the state-space formalism, a three-dimensional analysis is presented for orthotropic functionally graded rectangular plates with simply supported edges under static and dynamic loads. The material properties are assumed to be variable through the thickness. The governing equations for the functionally graded material (FGM) are developed on the state-space approach in the Laplace transform domain. Assuming constant material properties, we derive the analytical solutions that can be used to validate any numerical methods. For FGM plates, the numerical solutions are obtained by the use of radial basis function method. Three examples are presented for the FGMs and laminated composite. The accuracy of the proposed numerical technique has been compared with the exact solutions. Copyright © 2011 John Wiley & Sons, Ltd.

Free vibration of circular cylindrical shell with constrained layer damping

Abstract: Free vibration characteristics of circular cylindrical shell with passive constrained layer damping (PCLD) are presented. Wave propagation approach rather than finite element method, transfer matrix method, and Rayleigh-Ritz method is used to solve the problem of vibration of PCLD circular cylindrical shell under a simply supported boundary condition at two ends. The governing equations of motion for the orthotropic cylindrical shell with PCLD are derived on the base of Sanders’ thin shell theory. Numerical results show that the present method is more effective in comparison with other methods. The effects of the thickness of viscoelastic core and constrained layer, the elastic modulus ratio of orthotropic constrained layer, the complex shear modulus of viscoelastic core on frequency parameter, and the loss factor are discussed.