Showing papers on "Orthotropic material published in 2009"
TL;DR: In this article, a structural model for the left ventricular myocardium is proposed, based on the invariants associated with the three mutually orthogonal directions of the myocardia.
Abstract: In this paper, we first of all review the morphology and structure of the myocardium and discuss the main features of the mechanical response of passive myocardium tissue, which is an orthotropic material. Locally within the architecture of the myocardium three mutually orthogonal directions can be identified, forming planes with distinct material responses. We treat the left ventricular myocardium as a non-homogeneous, thick-walled, nonlinearly elastic and incompressible material and develop a general theoretical framework based on invariants associated with the three directions. Within this framework we review existing constitutive models and then develop a structurally based model that accounts for the muscle fibre direction and the myocyte sheet structure. The model is applied to simple shear and biaxial deformations and a specific form fitted to the existing (and somewhat limited) experimental data, emphasizing the orthotropy and the limitations of biaxial tests. The need for additional data is highlighted. A brief discussion of issues of convexity of the model and related matters concludes the paper.
617 citations
TL;DR: In this paper, it is shown that it is theoretically impossible to fully characterize the properties of anisotropic elastic materials using such tests unless some assumption is made that enables a suitable subclass of models to be preselected.
Abstract: The mechanical testing of anisotropic nonlinearly elastic solids is a topic of considerable and increasing interest. The results of such testing are important, in particular, for the characterization of the material properties and the development of constitutive laws that can be used for predictive purposes. However, the literature on this topic in the context of soft tissue biomechanics, in particular, includes some papers that are misleading since they contain errors and false statements. Claims that planar biaxial testing can fully characterize the three-dimensional anisotropic elastic properties of soft tissues are incorrect. There is therefore a need to clarify the extent to which biaxial testing can be used for determining the elastic properties of these materials. In this paper this is explained on the basis of the equations of finite deformation transversely isotropic elasticity, and general planar anisotropic elasticity. It is shown that it is theoretically impossible to fully characterize the properties of anisotropic elastic materials using such tests unless some assumption is made that enables a suitable subclass of models to be preselected. Moreover, it is shown that certain assumptions underlying the analysis of planar biaxial tests are inconsistent with the classical linear theory of orthotropic elasticity. Possible sets of independent tests required for full material characterization are then enumerated.
180 citations
TL;DR: In this article, a cylindrical cloak is proposed to control bending waves propagating in thin plates, which is achieved through radially dependent isotropic mass density and orthotropic flexural rigidity deduced from a coordinate transformation for the biharmonic propagation equation.
Abstract: We introduce a cylindrical cloak to control the bending waves propagating in thin plates. This is achieved through radially dependent isotropic mass density and radially dependent and orthotropic flexural rigidity deduced from a coordinate transformation for the biharmonic propagation equation in the spirit of the paper of Pendry et al. [Science 312, 1780 (2006)]. We analyze the response of the cloak surrounding a clamped obstacle in the presence of a cylindrical excitation. We note that whereas the studied bending waves are of different physical and mathematical nature, they are cloaked in many ways as their electromagnetic and acoustic counterparts; e.g., when the source lies inside the coating, it seems to radiate from a shifted location (mirage effect).
154 citations
TL;DR: In this article, a novel separation of variables is presented for solving the exact solutions for the free vibrations of thin orthotropic rectangular plates with all combinations of simply supported (S) and clamped (C) boundary conditions, and the correctness of the exact solution is proved mathematically.
136 citations
TL;DR: In this paper, a yarn-parallel biaxial extension of PVC-coated polyester fabric cruciform specimens is proposed, where the material behaviour is assumed to be plane stress orthotropic for a particular load ratio, while the elastic properties can vary with the load ratio to represent the complex interaction between warp and fill yarns.
136 citations
TL;DR: In this paper, an analytical homogenization model for corrugated cardboard and its numerical implementation in a shell element are presented, which leads to an elastic stiffness matrix relative to the generalized strains and internal efforts for an equivalent orthotropic plate.
117 citations
TL;DR: In this article, the elastic buckling behavior of orthotropic small scale plates under biaxial compression is studied and the effects of small scale on the buckling loads of plates considering various material and geometrical parameters are examined.
113 citations
TL;DR: In this article, the authors presented a buckling analysis of isotropic and orthotropic plates using the two variable refined plate theory, which takes account of transverse shear effects and parabolic distribution of the transversal shear strains through the thickness of the plate.
Abstract: Buckling analysis of isotropic and orthotropic plates using the two variable refined plate theory is presented in this paper. The theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to in-plane loading has been obtained by using the Navier method. Numerical results obtained by the present theory are compared with classical plate theory solutions, first-order shear deformable theory solutions, and available exact solutions in the literature. It can be concluded that the present theory, which does not require shear correction factor, is not only simple but also comparable to the first-order shear deformable theory.
111 citations
TL;DR: Semi-analytical 3D elasticity solutions for orthotropic multi-directional functionally graded plates using the differential quadrature method (DQM) based on the state-space formalism are presented in this paper.
Abstract: Semi-analytical 3-D elasticity solutions are presented for orthotropic multi-directional functionally graded plates using the differential quadrature method (DQM) based on the state-space formalism. Material properties are assumed to vary not only through the thickness but also in the in-plane directions following an exponential law. The graded in-plane domain is solved numerically via the DQM, while exact solutions are sought for the thickness domain using the state-space method. Convergence studies are performed, and the present hybrid semi-analytical method is validated by comparing numerical results with the exact solutions for a conventional unidirectional functionally graded plate. Finally, effects of material gradient indices on the displacement and stress fields of the plates are investigated and discussed. Copyright © 2009 John Wiley & Sons, Ltd.
108 citations
Metz1
TL;DR: Molar position was revealed to be the most critical one, from a stress and strain level point of view, for implants and framework and consequently for peri-implant bone, and showed that the anisotropic behaviour of bone cannot be neglected in the numerical simulations.
101 citations
TL;DR: In this paper, a constitutive law describing the wood behavior, as elasto-plastic orthotropic material with 3D finite element model, is presented for compressive behavior.
TL;DR: The application of the method is seen to be straightforward even in the complicated case of laminated sandwich panels, and accurate predictions of the dispersion curves are found at negligible computational cost.
Abstract: This paper describes a wave finite element method for the numerical prediction of wave characteristics of cylindrical and curved panels. The method combines conventional finite elements and the theory of wave propagation in periodic structures. The mass and stiffness matrices of a small segment of the structure, which is typically modeled using either a single shell element or, especially for laminated structures, a stack of solid elements meshed through the cross-section, are postprocessed using periodicity conditions. The matrices are typically found using a commercial FE package. The solutions of the resulting eigenproblem provide the frequency evolution of the wavenumber and the wave modes. For cylindrical geometries, the circumferential order of the wave can be specified in order to define the phase change that a wave experiences as it propagates across the element in the circumferential direction. The method is described and illustrated by application to cylinders and curved panels of different constructions. These include isotropic, orthotropic, and laminated sandwich constructions. The application of the method is seen to be straightforward even in the complicated case of laminated sandwich panels. Accurate predictions of the dispersion curves are found at negligible computational cost.
TL;DR: In this article, the Laplace transformation has been applied to the problem of determining the thermo-elastic interaction due to step input of temperature on the boundaries of a functionally graded orthotropic hollow sphere in the context of linear theories of generalized thermoelasticity.
Abstract: This problem deals with the determination of thermo-elastic interaction due to step input of temperature on the boundaries of a functionally graded orthotropic hollow sphere in the context of linear theories of generalized thermo-elasticity. Using the Laplace transformation the fundamental equations have been expressed in the form of vector–matrix differential equation which is then solved by eigenvalue approach. The inverse of the transformed solution is carried out by applying a method of Bellman et al. Stresses, displacement and temperature distributions have been computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (TEWOED(GN-II), TEWED(GN-III) and three-phase-lag model) is presented. When the material is homogeneous, isotropic and outer radius of the hollow sphere tends to infinity, the corresponding results agree with that of existing literature for GN-III model.
TL;DR: In this paper, the authors solved free vibration problems of isotropic and orthotropic rectangular plates with linearly varying thickness along one direction using discrete singular convolution (DSC).
TL;DR: Hu et al. as discussed by the authors developed an accurate and computationally efficient homogenization-based continuum plasticity-damage (HCPD) model for macroscopic analysis of ductile failure in porous ductile materials containing brittle inclusions.
Abstract: This paper develops an accurate and computationally efficient homogenization-based continuum plasticity-damage (HCPD) model for macroscopic analysis of ductile failure in porous ductile materials containing brittle inclusions. Example of these materials are cast alloys such as aluminum and metal matrix composites. The overall framework of the HCPD model follows the structure of the anisotropic Gurson–Tvergaard–Needleman (GTN) type elasto-plasticity model for porous ductile materials. The HCPD model is assumed to be orthotropic in an evolving material principal coordinate system throughout the deformation history. The GTN model parameters are calibrated from homogenization of evolving variables in representative volume elements (RVE) of the microstructure containing inclusions and voids. Micromechanical analyses for this purpose are conducted by the locally enriched Voronoi cell finite element model (LE-VCFEM) [Hu, C., Ghosh, S., 2008. Locally enhanced Voronoi cell finite element model (LE-VCFEM) for simulating evolving fracture in ductile microstructures containing inclusions. Int. J. Numer. Methods Eng. 76(12), 1955–1992]. The model also introduces a novel void nucleation criterion from micromechanical damage evolution due to combined inclusion and matrix cracking. The paper discusses methods for estimating RVE length scales in microstructures with non-uniform dispersions, as well as macroscopic characteristic length scales for non-local constitutive models. Comparison of results from the anisotropic HCPD model with homogenized micromechanics shows excellent agreement. The HCPD model has a huge efficiency advantage over micromechanics models. Hence, it is a very effective tool in predicting macroscopic damage in structures with direct reference to microstructural composition.
TL;DR: The proposed method is suitable for identification of elastic constants from nanoindentation experiments and could be adapted to other (bio)materials, for which it is possible to describe elastic properties using a fabric-based model.
Abstract: The identification of anisotropic elastic properties of lamellar bone based on nanoindentation data is an open problem. Therefore, the purpose of this study was to develop a method to estimate the orthotropic elastic constants of human cortical bone secondary osteons using nanoindentation in two orthogonal directions. Since the indentation modulus depends on all elastic constants and, for anisotropic materials, also on the indentation direction, a theoretical model quantifying the indentation modulus from the stiffness tensor of a given material was implemented numerically (Swadener and Pharr, 2001, "Indentation of Elastically Anisotropic Half-Spaces by Cones and Parabolae of Revolution," Philos. Mag. A, 81(2), pp. 447-466). Nanoindentation was performed on 22 osteons of the distal femoral shaft: A new holding system was designed in order to indent the same osteon in two orthogonal directions. To interpret the experimental results and identify orthotropic elastic constants, an inverse procedure was developed by using a fabric-based elastic model for lamellar bone. The experimental indentation moduli were found to vary with the indentation direction and showed a marked anisotropy. The estimated elastic constants showed different degrees of anisotropy among secondary osteons of the same bone and these degrees of anisotropy were also found to be different than the one of cortical bone at the macroscopic level. Using the log-Euclidean norm, the relative distance between the compliance tensors of the estimated mean osteon and of cortical bone at the macroscopic level was 9.69%: Secondary osteons appeared stiffer in their axial and circumferential material directions, and with a greater bulk modulus than cortical bone, which is attributed to the absence of vascular porosity in osteonal properties. The proposed method is suitable for identification of elastic constants from nanoindentation experiments and could be adapted to other (bio)materials, for which it is possible to describe elastic properties using a fabric-based model.
TL;DR: In this paper, the authors compared the results of a simple, gradually damaging three-dimensional material model with full-scale tests and found that the damage caused by low velocity impact is often hidden and for thicker plates the transverse stresses are significant in promoting delamination.
TL;DR: In this article, a new analytic isotropic plastic potential for a random distribution of spherical voids is derived, which is sensitive to the third invariant of the stress deviator and displays tension-compression asymmetry.
Abstract: This paper is devoted to modeling the effects of the tension–compression asymmetry of the matrix on yielding of the void–matrix aggregate. The matrix plastic behavior is described by the Cazacu et al. [2006. Orthotropic yield criterion for hexagonal closed packed metals. Int. J. Plasticity 22, 1171–1194] isotropic yield criterion, which captures strength differential effects. Using an upper-bound approach, a new analytic isotropic plastic potential for a random distribution of spherical voids is obtained. The derived analytic potential is sensitive to the third invariant of the stress deviator and displays tension–compression asymmetry. In the case when the matrix material has the same yield in tension and compression, it reduces to Gurson's [1977. Continuum theory of ductile rupture by void nucleation and growth: Part I: Yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol. Trans. ASME Ser. H 99, 2–15.] criterion. Furthermore, the proposed criterion predicts the exact solution of a hollow sphere loaded in hydrostatic tension or compression. The accuracy of the proposed analytical criterion is assessed through comparisons with finite-element cell calculations.
TL;DR: In this article, constitutive equations to model anisotropic elasto-plastic timber composite beams with openings were formulated and implemented into the finite element (FE) package ABAQUS, via a user-defined subroutine.
TL;DR: Li et al. as mentioned in this paper presented an exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports, which is expressed as a 2-D Fourier cosine series supplemented with several terms in the form of 1-D series.
TL;DR: In this paper, a finite element model was developed to predict shear force versus shear angle for woven fabrics, based on the TexGen geometric modelling schema, developed at the University of Nottingham and orthotropic constitutive models for yarn behaviour, coupled with a unified displacement-difference periodic boundary condition.
Abstract: In this study, a finite element model to predict shear force versus shear angle for woven fabrics is developed. The model is based on the TexGen geometric modelling schema, developed at the University of Nottingham and orthotropic constitutive models for yarn behaviour, coupled with a unified displacement-difference periodic boundary condition. A major distinction from prior modelling of fabric shear is that the details of picture frame kinematics are included in the model, which allows the mechanisms of fabric shear to be represented more accurately. Meso- and micro-mechanisms of deformation are modelled to determine their contributions to energy dissipation during shear. The model is evaluated using results obtained for a glass fibre plain woven fabric, and the importance of boundary conditions in the analysis of deformation mechanisms is highlighted. The simulation results show that the simple rotation boundary condition is adequate for predicting shear force at large deformations, with most of the energy being dissipated at higher shear angles due to yarn compaction. For small deformations, a detailed kinematic analysis is needed, enabling the yarn shear and rotation deformation mechanisms to be modelled accurately.
TL;DR: A mesh-free Galerkin method for the free vibration analysis of unstiffened and stiffened corrugated plates is introduced in this article, in which the corrugation plates are simulated with an equivalent orthotropic plate model, and the stiffness matrix of the whole structure is then derived.
TL;DR: The proposed mathematical method serves as a completely rational and accurate model in plate bending analysis and can handle plates with different loadings in a uniform procedure, which is simpler than previous methods.
TL;DR: In this article, a 3D homogenization-based continuum damage mechanics (HCDM) model for fiber reinforced composites undergoing micro- mechanical damage is developed, which uses the evolving principal damage coordinate system as its reference in order to represent the anisotropic coefficients.
Abstract: This paper develops a 3D homogenization-based continuum damage mechanics (HCDM) model for fiber reinforced composites undergoing micro- mechanical damage. Micromechanical damage in the representative volume element (RVE) is explicitly incorporated in the form of fiber-matrix interfacial debonding. The model uses the evolving principal damage coordinate system as its reference in order to represent the anisotropic coefficients. This is necessary for retaining accuracy with nonproportional loading. The material constitutive law involves a fourth order orthotropic tensor with stiffness characterized as macroscopic internal variable. Damage in 3D composites is accounted for through functional forms of the fourth order damage tensor in terms of macroscopic strain components. The HCDM model parameters are calibrated by using homogenized micromechanical (HMM) solutions for the RVE for a few strain histories. The proposed model is validated by comparing the CDM results with HMM response of single and multiple fiber RVEs subjected to arbitrary loading history. Finally the HCDM model is incorporated in a macroscopic finite element code to conduct damage analysis in a structure. The effect of different microstructures on the macroscopic damage progression is examined through this study.
TL;DR: In this paper, a refined nonlinear finite element modeling approach for the analysis of corrugated fiberboard material and structural systems is presented for the performance of Tappi-type edge crush test (ECT) using a clamping fixture.
TL;DR: In this paper, an elastic orthotropic material containing a crack in Mode I is considered to formulate a new analytical model and the boundary conditions for the crack existence in the material lead to the solution of the homogeneous Riemann-Hilbert problems.
TL;DR: In this article, the sintering stress tensor is determined numerically for an open pore structure with orthotropic symmetry in three dimensions, and the deviatoric component is approximately proportional to the logarithm of the aspect ratio of the orthorhombic volume element.
TL;DR: In this paper, a homogeneous, orthotropic couple-stress continuum model is developed to take the place of the periodic heterogeneous cellular solids, and four characteristic lengths are introduced as material engineering constants for such kind of continuum.
Dissertation•
01 Jan 2009
TL;DR: In this paper, the authors report the mechanical properties of clear wood from Norway spruce, comprising each orthotropic material direction and plane over the complete loading range till failure, and the material prope...
Abstract: This thesis reports mechanical properties of clear wood from Norway spruce, comprising each orthotropic material direction and plane over the complete loading range till failure. The material prope ...
TL;DR: In this paper, the Haar wavelet discretization technique for solving the elastic bending problems of orthotropic plates and shells is proposed, and the results obtained are found to be in good agreement with those available in the literature.
Abstract: The Haar wavelet discretization technique for solving the elastic bending problems of orthotropic plates and shells is proposed. Free transverse vibrations of orthotropic rectangular plates with a variable thickness in one direction are considered as a model problem. In the case of constant plate thickness, the numerical results are validated by comparing them with an exact solution. The results obtained are found to be in good agreement with those available in the literature.