Transverse Isotropic Material Research Articles

Comparative Study for the Design of Optimal Composite Pressure Vessels

Composite pressure vessels require special design attention to the dome region because of the varying wind angles generated using the filament winding process. Geometric variations in the dome region cause the fiber to change angels and thickness and hence offer difficulty to acquire a constant stress profile (isotensoid). Therefore a dome contour which allows an isotensoid behavior is the required structure. Two design methods to generate dome profiles for similar dome openings were investigated namely Netting Analysis and Optimal Design method. Both methods assume that loads are carried by the fiber alone (monotropic) ignoring the complete composite behavior. Former method produced a lower dome internal volume and a higher fiber thickness as compared to the later optimal design method when studied against different normalized dome opening radiuses. The optimal dome contour was studied in ANSYS with a trial design. The dome was considered to have transversely isotropic property with a dome contour based on monotropic model. While investigating the dome with non linear large displacement finite element analysis, the dome still exhibited isotensoid behavior with transverse isotropic material assignment. Elliptic integrals were used to generate the optimal dome contours and hence elliptic dome contours were formed which were isotensoid in nature with complete composite representation.

A Cyclic Life Prediction Approach for Directionally Solidified Nickel Superalloys

Abstract The performance of heavy duty gas turbines is closely related to the material capability of the components of the first turbine stage. In modern gas turbines single crystal (SX) and directionally solidified (DS) nickel superalloys are applied, which, compared with their conventionally cast version, hold a higher cyclic life and a significantly improved creep rupture strength. SX and DS nickel superalloys feature a significant directional dependence of the material properties. To fully exploit the material capability, the anisotropy needs to be accounted for in both the constitutive and lifing model. In this context, the paper addresses a cyclic life prediction procedure for DS materials with transverse isotropic material symmetry. Thereby, the well-known local approaches to fatigue life prediction of isotropic materials under uniaxial loading are extended toward materials with transverse isotropic properties under multiaxial load conditions. As part of the proposed methodology, a Hill type function is utilized for describing the anisotropic failure behavior. The coefficients of the Hill surface are determined from the actual multiaxial loading, material symmetry, and anisotropic fatigue strength of the material. In this paper we first characterize the anisotropy of DS superalloys. We then present the general mathematical framework of the proposed lifing procedure. Later we discuss a validation of the cyclic life model by comparing the measured and predicted fatigue lives of the test specimens. Finally, the proposed method is applied to the cyclic life prediction of a gas turbine blade.

New Interfacial Shear-Horizontal Waves in Piezoelectric Cubic Crystals

This theoretical study reports results on acoustic wave propagation along the interface of two half-spaces representing cubic crystals of both piezoelectric classes ?43m and 23 with strong piezoelectric effect. In similar configurations, the interfacial Maerfeld-Tournois waves can propagate along the interface of two transversely-isotropic materials of class 6 mm, in which the shear-horizontal surface acoustic waves (SH-SAWs) called the Bleustein-Gulyaev (BG) waves can also exist. Cubic piezoelectrics cannot support existence of the surface BG-waves, according to the recent report by Gulyaev and Hickernell. Hence, new interfacial SH-waves are studied in this paper concerning unique direction [101] of wave propagation in cubic crystals using different electrical boundary conditions (EBCs) of both metallized and non-metallized interfaces. The new interfacial SH-waves can always propagate along the interface of two identical piezoelectric crystals with opposite polarization. In this case, the calculated velocities for both EBCs coincide with the velocity of the ultrasonic surface Zakharenko wave (USZW) propagating in direction [101] on the metallized surface of a cubic piezoelectrics. It was also found that the new interfacial SH-waves can exist when wave propagation is along the interface of two dissimilar half-spaces, for instance, the piezoelectric cubic crystals Bi12SiO20 and Bi12GeO20. Several calculations are also carried out as examples. PACS: 51.40.+p, 62.65.+k, 68.35.Gy, 68.35.Iv, 68.60.Bs, 74.25.Ld.

An eigen theory of electro-magnetic acoustic waves in magnetoelectroelastic media

The Maxwell’s equations, coupled to the mechanical equations of equilibrium, and the mechanical equations of motion, coupled to the equations of static electric and magnetic field, are studied here based on the standard spaces of the physical presentation. The complete set of uncoupled electromagnetic wave equations and elastic wave equations in magnetoelectroelastic solids is deduced. The results show that the number of electromagnetic waves and elastic waves in magnetoelectroelastic solids is determined by both the subspaces of electromagnetically anisotropic media and ones of mechanically anisotropic media. Based on these laws, we discuss the propagation behavior of electromagnetic waves and elastic waves in the transverse isotropic magnetoelectroelastic material poled in x3.

Microstructural behaviour of transversal isotropic material

AbstractWe discuss and simulate transversal isotropic material under tension loading. The preferential direction of the material is inclined under 45 degrees to the direction of the tensile resultant. In this configuration the deformation of a rectangular test specimen differ from the behaviour of isotropic material in the way, that beside Poissons effect additional displacement appear perpendicular to the tension direction. In classical continuum theories, this transverse deformations describe a typical S–shape. By using a non–local continuum theory, the effect of microstructural orientation is incorporated into the numerical model. Then, it depends on a phenomenological parameter of inner structure whether the energetically favoured configuration is classical or contains microstructural behaviour. In the second case, the transverse deformation is not described by the typical S–shape, but with higher forms of it. A simple experimental model will show the connection between the inner structure of the material and the rotational parameters within the non–local continuum theory. It is evident, that these parameters are responsible for the non–classical behaviour and give the possibility to find energetically favoured solutions. The results of the finite–element–analyses can help to understand constitutive parameters for the non–local continuum theory and to apply it to other specimens. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On a Possible Approximation of Changes in Elastic Properties of a Transversely Isotropic Material due to an Arbitrarily Oriented Crack

The present paper addresses an approximate analytical model for contribution of an arbitrarily oriented circular crack into effective elastic compliance of a transversely isotropic material. We numerically examine the bounds of applicability of the hypothesis that change in elastic potential due to an arbitrarily oriented circular crack in a transversely-isotropic material can be approximated by the change calculated for a certain isotropic environment. In particular, we obtained that the error of such an approximation is less than 20% if the extent of anisotropy is moderate – the ratio of Young’s moduli in transverse and in-plane directions is less than 1.87. The obtained result can be used for development of a simple model for microcracked transversely-isotropic materials with mild-to-moderate extent of anisotropy.

Anisotropy effects on the acoustical properties of porous materials

Porous materials are now widely used in noise control for their acoustic properties in sound absorption and transmission. These properties are function of the internal porous medium structure. Generally, most of the models assume that the porous medium is isotropic. Mineral wools (as well as some foams) clearly present an anisotropic structure. This communication is concerned with the adaptation of recent works on isotropic materials to the case of anisotropic porous materials. The general theory will be exposed for sound absorbing materials with anisotropic acoustical and mechanical parameters. The case of transverse isotropic materials (with fibers organized in planes running parallels one to each other) will then be detailed in particular in the case when the plane of fibers is not the same than the normal plane of the sample. The influence on the acoustical properties anisotropic porous materials will then be presented. Illustrations are then provided with measurements performed on wools and it will b...

Analysis of the axisymmetric indentation of a semi-infinite piezoelectric material: The evaluation of the contact stiffness and the effective piezoelectric constant

A general solution of the axisymmetric indentation is obtained in the closed form for a semi-infinite, transverse isotropic piezoelectric material by a rigid-conducting indenter of arbitrary-axisymmetric profile. Explicit relationships are derived for dependences of the indentation depth and the indentation-induced charge on indentation force and applied electrical potential. Simple formulas are obtained for contact stiffness and effective piezoelectric constant, which can be used in indentation test and piezoresponse force microscopy to analyze the elastic and piezoelectric responses of piezoelectric materials. Depending on the direction of electric field (the potential difference), the electric field can either increase or suppress indentation deformation. The corresponding results are given for cylindrical, conical, and paraboloidal indenters.

On universal relations in orthotropic material subclasses

Universal relations that hold true for specific classes or subclasses of elastic materials form an integral part of the characterisation process for any material that can deform elastically. On the other hand, it has become understood that any class of hyper-elastic materials possessing anisotropic properties more complicated to those of transverse isotropy obeys no universal relations. However, there are met in practice special cases (subclasses) of anisotropic hyper-elastic materials that, under certain circumstances, may still obey a certain number of universal relations. Material characterisation purposes suggest therefore that there is a practical purpose in identifying and classifying different subclasses of anisotropic hyper-elastic materials that may obey any kind of universal relations and, hence, to derive and gradually build up catalogues or tables of different universal relations that such material subclasses obey when subjected to different deformation patterns. This paper heads towards this research direction by initially considering the orthotropic material class which is alternatively identified as the hyper-elastic crystal class of rhombic symmetry [A.E. Green, J.E. Adkins, Large Elastic Deformations, Clarendon Press, Oxford, 1960]. Then, for a certain set of appropriately chosen orthotropic and transverse isotropic hyper-elastic material subclasses, it develops and presents a considerable number of relevant universal relations, most of which are new in the literature.

On an Arbitrarily Oriented Crack in a Transversely-isotropic Medium

Transversely-isotropic material with an arbitrarily oriented penny-shaped crack is considered. We calculate fourth-rank compliance contribution tensor of the crack and second-rank crack opening displacement tensor and examine their dependence on crack orientation. It is shown that this dependence for the crack opening displacement tensor is negligible if transverse isotropy has elliptic character, i.e. if material symmetry can be described in terms of a certain second rank tensor.

압전재료 내의 균열에 대한 그린함수

A general form solution is considered for a piezoelectric material containing impermeable cracks subjected to a combined mechanical and in-plane electrical loading. The analysis is based upon the Hilbert problem formulation. Using this solution, typically for a central crack in transverse isotropic piezoelectric material, a closed form solution is obtained, where one concentrated mechanical and electrical load is subjected to the crack surface. This problem could be used as a Green's function to generate the solutions of other problems with the same geometry but of different loading conditions.

Green's function solution and displacement potentials for Transformed Transversely Isotropic materials

Abstract A totally non-degenerate expression for the Green's function of infinite Transversely Isotropic (TI) materials is first deduced from the solutions given by Pan and Chou [Pan, Y.-C., Chou, T.-W., 1976. Point force solution for an infinite transversely isotropic solid. Trans. ASME, J. Appl. Mech. 43 (4), 608–612]. Then this solution and also the displacement potentials for TI materials are extended by a linear transformation to a larger family of anisotropic materials (Transformed Transversely Isotropic or TraTI materials). This family depends on 12 independent parameters and contains non-orthotropic materials and in this way a first explicit analytical solution for the Green's function for a non-orthotropic material is obtained. The TraTI materials which have orthotropic Symmetry (StraTI materials) constitute a sub-family depending on 6 independent parameters in the symmetry basis of the material. These materials present a 3D anisotropy (different stiffnesses in three orthogonal directions). General displacement potentials and the Green's function solution for STraTI materials can be deduced by a simple change and introducing one additional parameter in the well-known TI solutions.

Book Review: Ding, Haojiang; Chen, Weiqiu; Zhang, L., Elasticity of Transversely Isotropic Materials, Series: Solid Mechanics and Its Applications (Ed. G.M.L. Gladwell)

Book Review: Ding, Haojiang; Chen, Weiqiu; Zhang, L., Elasticity of Transversely Isotropic Materials, Series: Solid Mechanics and Its Applications (Ed. G.M.L. Gladwell)

On the assessment of brittle–elastic cortical bone fracture in the distal radius

The primary objective of this work is to outline a simple methodology for the evaluation of the risk of cortical bone fracture in the distal radius in the event of a fall from standing height onto an outstretched hand. The approach involves conducting an elastic finite element (FE) analysis wherein the cortical bone is considered to be a transversely-isotropic material and, subsequently, verifying the admissibility of the stress field. The latter is based on a proposed macroscopic fracture criterion, which takes into account the anisotropic nature of the cortical tissue. The methodology is illustrated by a numerical example, which involves FE simulation of an experimental test designed to produce a Colles’ fracture of the radius.

An improved transverse isotropic hyperelastic material model for simulation of mitral valve response

An improved transverse isotropic hyperelastic material model for simulation of mitral valve response

Optimal orientation of anisotropic solids

Results are presented for finding the optimal orientation of an anisotropic elastic material. The problem is formulated as minimizing the strain energy subject to rotation of the material axes, under a state of uniform stress. It is shown that a stationary value of the strain energy requires the stress and strain tensors to have a common set of principal axes. The new derivation of this well known coaxiality condition uses the 6-dimensional expression of the rotation tensor for the elastic moduli. Using this representation it is shown that the stationary condition is a minimum or a maximum if an explicit set of conditions is satisfied. Specific results are given for materials of cubic, transversely isotropic (TI) and tetragonal symmetries. In each case the existence of a minimum or maximum depends on the sign of a single elastic constant. The stationary (minimum or maximum) value of energy can always be achieved for cubic materials. Typically, the optimal orientation of a solid with cubic material symmetry is not aligned with the symmetry directions. Expressions are given for the optimal orientation of TI and tetragonal materials, and are in agreement with results of Rovati and Taliercio \cite{Rovati03} obtained by a different procedure. A new concept is introduced, the strain deviation angle, which defines the degree to which a state of stress or strain is not optimal. The strain deviation angle is zero for coaxial stress and strain. An approximate formula is given for the strain deviation angle which is valid for materials that are weakly anisotropic.

Stationary random waves propagation in 3D viscoelastic stratified solid

Propagation of stationary random waves in viscoelastic stratified transverse isotropic materials is investigated. The solid was considered multi-layered and located above the bedrock, which was assumed to be much stiffer than the soil, and the power spectrum density of the stationary random excitation was given at the bedrock. The governing differential equations are derived in frequency and wave-number domains and only a set of ordinary differential equations (ODEs) must be solved. The precise integration algorithm of two-point boundary value problem was applied to solve the ODEs. Thereafter, the recently developed pseudo-excitation method for structural random vibration is extended to the solution of the stratified solid responses.

Transverse isotropic poroelastic osteon model under cyclic loading

The poroelastic problem associated with a hollow cylinder under cyclic loading is solved. This cylinder models an osteon, basic unit of cortical bone. Both fluid and solid phases are supposed compressible. Solid matrix is modeled as an elastic transverse isotropic material. An explicit close-form solution for the steady state is obtained. Fluid flow distribution as a function of poroelastic properties and cyclic loading is discussed as it could influence bone remodeling. Strain rate of loading is shown to play a significant role in mass flux in the porous material.

Cylindre transverse isotrope poroélastique chargé cycliquement : application à un ostéon

The poroelastic problem associated with a hollow cylinder under cyclic loading is solved. Both fluid and solid phases are supposed compressible. Solid matrix is modeled as an elastic transverse isotropic material. An explicit close-form solution for the steady state is obtained. This cylinder is considered as a model for an osteon, the basic unit of cortical bone. The fluid flow distribution as a function of poroelastic properties and cyclic loading is discussed, as this could influence bone remodeling. To cite this article: A. Rémond, S. Naili, C. R. Mecanique 332 (2004).

Transverse-Isotropic Elastic and Viscoelastic Solids

A set of invariants are presented for transverse-isotropic materials whose gradients produce strain fields, instead of deformation fields as is typically the case. Finite-strain theories for elastic and K-BKZ-type viscoelastic solids are derived. Shear-free and simple shearing deformations are employed to illustrate the constitutive theory.