Mixed-mode K-calculations in anisotropic materials

The crack tip stress singularities for anisotropic materials are derived using the finite difference method and they are compared to other derivations. Subsequently, these asymptotic fields are implemented into a local stress method, enabling the determination of the mixed-mode stress intensity factor distribution along an arbitrary crack in an anisotropic material. Comparison with the interaction integral method shows that the local method yields excellent results and exhibits a better robustness with respect to irregular meshes.     

Non-linear analysis for anisotropic materials

An elasto-plastic analysis of anisotropic work-hardening materials, using the finite element method is presented. The analysis is based on the generalized Huber-Mises yield criterion extended by Hill for anisotropic materials. General expressions for the anisotropic parameters in the yield criterion have been derived both for initial yielding as well as subsequent yielding in the case of work-hardening materials. The isoparametric ‘quadratic’ quadrilateral elements have been used for the analysis and the ‘initial stress technique’ has been adopted for the iterative solution of the non-linear problems. The results of the various numerical examples have been compared with the available solutions.     

Constitutive relationships for anisotropic viscous materials

Constitutive relationships for anisotropic materials are considered to describe the viscous flow of fiber-reinforced, thermoplastic composites during forming. The fully anisotropic and the orthotropic cases are first presented. The special case of a transversely isotropic viscous material, which is of particular interest to the deformation of assemblies of oriented fibers suspended in a viscous fluid, is then investigated and the correspondence between two approaches found in the literature on the subject is established.     

Kinked cracks in anisotropic elastic materials

The problem of a kinked crack is analysed for the most general case of elastic anisotropy. The kinked crack is modelled by means of continuous distributions of dislocations which are assumed to be singular both at the crack tips and at the kink vertex. The resulting system of singular integral equations is solved numerically using Chebyshev polynomials and the reciprocal theorem. The stress intensity factors for modes I, II and III and the generalised stress intensity factor at the vertex are obtained directly from the dislocation densities. This revised version was published online in July 2006 with corrections to the Cover Date.     

Strain condition of plasticity of anisotropic materials

A condition for the plasticity of anisotropic materials is formulated in the deformation space on the basis of the hypothesis that uniform linear strain does not affect the development of plastic strain. This condition describes more adequately than the Hill condition certain experimental data on the strain of zirconium-alloy shells.Translated from Problemy Prochnosti, No. 1, pp. 35–40, January, 1993.     

Differential theory of gratings made of anisotropic materials

Arbitrary profiled gratings made with anisotropic materials are discussed; the anisotropic character concerns electric and/or magnetic properties. Our aim is to avoid the use of the staircase approximation of the profile, whose convergence is questionable. A coupled first-order differential-equation set is derived by taking into account Li's remarks about Fourier factorization [J. Opt. Soc. Am. A 13, 1870 (1996)], but the present formulation shows that, in return for a convenient form of the differential system, it is possible to use only the intuitive Laurent rule. Our method, when applied to the simpler case of isotropic gratings, is shown to be consistent with that of previous studies. Moreover, from the numerical point of view, the convergence of our formulation for an anisotropic grating is faster than that of the conventional differential method.     

Failure criteria for multiply flawed anisotropic materials

This study presents overall failure criteria for an infinite anisotropic solid containing multiple flaws subjected to a set of uniform applied loads. Based on the inclusion method, flaws are treated as elliptical inclusions where their elastic moduli are considered to be zero. The explicit expression of elastic fields is obtained for a cubic crystal multiply flawed solid through the use of the Mori-Tanaka mean field theory. The resulting expression is further utilized to find an interaction energy function between the applied loads and flaws. With this energy function, the energy release rates and critical stresses are acquired separately in a closed form for Mode I, II, and III. The closed forms for energy release rates and critical stresses reveal that they are a function of the aspect ratio and the volume fraction of flaws, the modes of the loading, and the material properties. As an illustrated numerical example, the energy release rates and the critical stresses that vary with both the aspect ratio and the volume fraction of the flaws in a cubic crystal material are discussed.     

Interfacial cracks between two dissimilar anisotropic materials

The two-dimensional problem of a crack opened in a dissimilar anisotropic composite under uniform normal loading is considered. In both the phases, the stresses and displacements have been formulated with the stress potentials of Muskhelishvili. The corresponding boundary value problem may be reduced to a pair of dual-homogeneous Hilbert equations. The order of signularity of the stresses at the crack tips has been considered.     

Indirect tensile test applied to anisotropic materials

The paper presents the general theory of stresses and displacements in a two-dimensional cross-anisotropic disc subjected to two diametrically opposite loads. Such an indirect tensile test is often used for paving materials and this theory provides the necessary background for the determination of the stiffness, Poisson's ratio, and the anisotropy ratio on a single sample. Two successive tests along two perpendicular diameters (directions of anisotropy) are sufficient for measuring the corresponding vertical displacements and one horizontal displacement.

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Resume Dans l'essai de compression diamétrale une éprouvette cylindrique est chargée selon deux génératrices opposées ce qui induit des contraintes de traction dans la direction perpendiculaire à la charge. Cet essai, de par sa simplicité et son applicabilité à des éprouvettes directement carottées dans la chaussée, est souvent utilisé pour évaluer les caractéristiques mécaniques des matériaux routiers enrobés aux liants hydrocarbonés. Jusqu'à présent, les calculs théoriques permettant l'exploitation de tels essais reposaient tous sur l'hypothèse d'un matériau parfaitement isotrope, ce qui n'est pas nécessairement le cas. Le compactage, par un effet d'orientation préférentielle des granulats, mais aussi les phénomènes de fissuration, induisent un certain degré d'anisotropie qu'il est intéressant de mesurer pour mieux caractériser le matériau et suivre son évolution dans le temps. Cet article développe la théorie générale permettant le calcul des contraintes, déformations et déplacements générés dans un disque bi-dimensionnel et anisotrope soumis à deux charges ponctuelles diamétralement opposées. Les équations pratiques permettant la détermination des modules de rigidité, coefficients de Poisson et d'un ratio d'anisotropie sont ensuites explicitées. Il suffit pour cela de tester l'éprouvette selon les deux directions perpendiculaires d'anisotropie et de mesurer les déplacements verticaux correspondants ainsi qu'au moins un déplacement horizontal.

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Fundamental concepts of photoelasticity for anisotropic composite materials

A unidirectionally reinforced glass fibre composite has been shown to Behave photoelastically, in the sense of effective medium theory, like hexagonal crystal classes 6 m₂, 6 mm and 6/mmm, and Pockels' phenomenologlcal theory of photoelastlcity for crystals has been extended to study birefringent behaviour of the composite. Important differences between photo-isotrople-elasticity and photo-anisotropic-elasticity have been brought out by examining critically the analogous behaviour of composites and maintaining clear distinction between elastic and optical aniaotropy. This has led to better understanding of fundamental concepts involved in photoelastlcity of composites which either have been overlooked or misunderstood in the literature. It has been shown that the composite exhibits a lower degree of orthotropy with respect to strain-optic behaviour than with respect to stress-optic behaviour, and isocllnlcs, ingeneral, represent neither the directions of principal stresses nor of principal strains.     

Analysis of sharp angular notches in anisotropic materials

The singular stresses at the tip of a sharp angular notch are analysed for the most general case of elastic anisotropy. The problem is stated in relation with the kinked crack and is modelled by means of continuous distributions of dislocations which are assumed to be singular at the notch vertex, the kind of the main singularity λ being unknown and weaker than at the crack tip. The Mellin transform is applied to obtain a system of simultaneous functional equations that enables one to find the parameter λ. The reciprocal theorem is used to compute the generalised stress intensity factor which characterises the singular stresses in a neighbourhood of the notch tip. This revised version was published online in July 2006 with corrections to the Cover Date.     

Failure of fibrous anisotropic materials under combined loading

A failure criterion for anisotropic materials under combined stress is developed and demonstrated. The generality and accuracy of the present theory are illustrated by examination through the use of material systems under various loading conditions. Calculated results are compared with the experimental data throughout four quadrants. It agrees with observation quite well at high values of shear stress, where the Tsai–Hill theory becomes too conservative. The present criterion is also compared with other criteria. The comparison shows that this criterion has a good agreement with the experimental data even when the shear stress component is greater than the shear strength.     

Stochastic identification of elastic constants for anisotropic materials

This paper presents an energy‐based characterization technique that stochastically identifies the elastic constants of anisotropic materials by modeling the measurement noise and removing its effect unlike conventional deterministic techniques, which deterministically identify the elastic constants directly from noisy measurements. The technique recursively estimates the elastic constants at every acquisition of measurements using Kalman Filter. Owing to the non‐linear expression of the measurement model, a Kalman gain has been newly derived and achieves optimal estimation. Since the variances in addition to the means are computed, the proposed technique can not only identify the elastic constants but also describe their certainty as an additional advantage. The validity of the proposed technique and its superiority to the conventional technique were first demonstrated via parametric studies of low‐dimensional problems. The proposed technique was then successfully applied to the identification of elastic constants of an anisotropic material. Copyright © 2009 John Wiley & Sons, Ltd.