Orthotropic Parameters Research Articles

Singular integral equation method for 2D fracture analysis of orthotropic solids containing doubly periodic strip-like cracks on rectangular lattice arrays under longitudinal shear loading

The doubly periodic arrays of cracks represent an important mesoscopic model for analysis of the damage and fracture mechanics behaviors of materials. Here, in the framework of a continuously distributed dislocation model and singular integral equation approach, a highly accurate solution is proposed to describe the fracture behavior of orthotropic solids weakened by doubly periodic strip-like cracks on rectangular lattice arrays under a far-field longitudinal shear load. By fully comparing the current numerical results with known analytical and boundary element solutions, the high precision of the proposed solution is verified. Furthermore, the effects of periodic parameters and orthotropic parameter ratio on the stress intensity factor, crack tearing displacement, and effective shear modulus are studied, and an analytically polynomial estimation for the equivalent shear modulus is proposed in a certain range. The interaction distances among the vertical and horizontal periodic cracks are quite different, and their effects vary with the orthotropic parameter ratio. In addition, the dynamic problem is discussed briefly in the case where the material is subjected to harmonic longitudinal shear stress waves. Further work will continue the in-depth study of the dynamics problem of the doubly periodic arrays of cracks.

Experimental study on mechanical properties of the ventral and the dorsal tissues of porcine descending aorta

The mechanical properties of the aorta tissue is not only important for maintaining the cardiovascular health, but also is closely related to the development of cardiovascular diseases. There are obvious differences between the ventral and dorsal tissues of the descending aorta. However, the cause of the difference is still unclear. In this study, a biaxial tensile approach was used to determine the parameters of porcine descending aorta by analyzing the stress-strain curves. The strain energy functions Gasser-Ogden-Holzapfel was adopted to characterize the orthotropic parameters of mechanical properties. Elastic Van Gieson (EVG) and Sirius red stain were used to observe the microarchitecture of elastic and collagen fibers, respectively. Our results showed that the tissue of descending aorta had more orthotropic and higher elastic modulus in the dorsal region compared to the ventral region in the circumferential direction. No significant difference was found in hyperelastic constitutive parameters between the dorsal and ventral regions, but the angle of collagen fiber was smaller than 0.785 rad (45°) in both dorsal and ventral regions. The arrangement of fiber was inclined to be circumferential. EVG and Sirius red stain showed that in outer-middle membrane of the descending aorta, the density of elastic fibrous layer of the ventral region was higher than that of the dorsal region; the amount of collagen fibers in dorsal region was more than that of the ventral region. The results suggested that the difference of mechanical properties between the dorsal and ventral tissues in the descending aorta was related to the microstructure of the outer membrane of the aorta. In the relatively small strain range, the difference in mechanical properties between the ventral and dorsal tissues of the descending aorta can be ignored; when the strain is higher, it needs to be treated differently. The results of this study provide data for the etiology of arterial disease (such as arterial dissection) and the design of artificial blood vessel.

Determination of the orthotropic parameters of a representative sample by computed tomography

The simulation of the stress-strain state of porous media is actual problem nowadays. The application of the mathematical apparatus of continuum mechanics to such media will make it possible to extend the scope of the problems to be solved. In this paper we study method of determination of mechanical properties in representative element bases on computer tomography data. To this task algorithm to create finite element grid connected with the data of the computed tomography was developed. Orthotopic properties can be determined by using target function. Unknown components of the target function are orthotropic directions. These directions can be determined by minimization of the target function. Rotating the matrix of anisotropic constants leads to components of the orthotopic tensor in orthotopic axes. These tensors are compared using of stress invariant.

Interfacial debonding of an orthotropic half-plane bonded to a rigid foundation

A partial debonding of the interface of an orthotropic elastic half-plane bonded to a rigid foundation is studied when shear and compressive loads are applied. A debonding/crack face smoothly contacts with a rigid base under applied compressive load, but relatively slides. The Fourier transform method is used to reduce a mixed boundary value problem to dual integral equations. Full elastic fields at any position are obtained in terms of preliminary functions with the aid of the well-known integrals of Bessel functions for odd and even shear loads. Asymptotic elastic stresses near the debonding tips together with stress intensity factors are determined explicitly. Only inverse square-root singularity near the debonding tips appears. The influence of material orthotropy parameters on energy release rate and stress distribution is discussed.

Folded orthotropic tape-springs

We consider the large-displacement, elastic folding of orthotropic tape-springs—thin-walled curved strips made from metal and from a woven laminated composite. Bending of the strips leads to a tight localised fold with a characteristic radius, connected on both sides to straight parts by doubly-curved transition, or ploy, regions. We calculate the shapes of these consistent features for a range of orthotropic parameters using geometrically non-linear, compact models. This study is our initial foray into the performance of tape-springs as safety latching mechanisms for aircraft landing gear.

Validation of Orthotropic Parameters of Timber by Means of Elastic Layer Theory

The known solution of isotropic elastic layer was modified for orthotropic elastic material behavior in this contribution. The solution was original derived for calculation of footing settlement. However it should be useful for estimation of orthotropic material parameters. Timber is classical orthotropic material. Timber board which is placed on the rigid basement it could be considered as the elastic layer. From the known load displacement curve we can, vice versa, estimate the material parameters. The present solution should be able to control loading by rigid strip footing acting perpendicular to the plane of orthotropy. The contribution summarize the first steps of the proposed back analysis.

Vibration-based identification of mechanical properties of orthotropic arbitrarily shaped plates: Numerical and experimental assessment

Abstract An innovative procedure is introduced for the identification of the mechanical parameters of orthotropic plates of arbitrary shape, under various boundary conditions, based on vibration data. The method employs a combination of a convenient Rayleigh-Ritz approach and Particle-Swarm Optimization to estimate elastic constants of the orthotropic material in a straightforward manner, without requiring computationally demanding iterative Finite Element analyses. Specifically, the pb-2 Rayleigh-Ritz procedure is extended and applied to deal with orthotropic plates, simplifying the approach to more easily treat generic plate shapes, taking advantage of the Green's theorem. The method is then appropriately combined with the Particle-Swarm Optimization procedure to expeditiously identify material parameters based on available vibration data. Several numerical applications are presented to show the reliability of the approach, and comparisons with pertinent results available in the literature demonstrate the efficiency and accuracy of the proposed procedure. The study is then supplemented by experimental tests developed in the Laboratory of Experimental Dynamics at the University of Palermo, Italy. In this context, because of the obvious relevance for modern additive manufacturing processes, vibration tests are performed on several 3D printed stiffened plates. Numerical vis-a-vis experimental data are examined, showing that the proposed procedure accurately capture equivalent orthotropic parameters of the stiffened plates.

The sliding contact problem for an orthotropic coating bonded to an isotropic substrate

We consider the sliding contact problem of an orthotropic coating/substrate system. The coating/substrate system is pressed by a rigid flat or cylindrical stamp. For the orthotropic coating, the principal material directions are assumed to be parallel and perpendicular to the contact surface. The governing integral equations corresponding to the mentioned contact problem are extracted by means of the Fourier transform technique. Later, the numerical solution of the singular integral equations is provided by applying the Gauss-Chebyshev integration method. The main goal of this study is to obtain analytical benchmark solutions in order to examine the effect of material orthotropy parameters, relative stiffness, the coefficient of friction and the coating thickness on the stress distribution at the surface of the orthotropic coating. The behavior of the surface in-plane stress intensity factor is analyzed as well. For a constant value of the applied load, the results indicate that the stiffness ratio and the shear parameter have a more pronounced effect on the surface stress components than the effective Poisson's ratio. Also, the stress intensity factor at sharp edges of the flat punch decreases as the coating softens with respect to the substrate and/or the coating thickness decreases.

Influence of the Variations of Orthotropy Parameters on the Stress State of Hollow Cylinders with Concave Corrugated Cross Sections

In the three-dimensional statement, by the method of approximation of functions by discrete Fourier series, we analyze the influence of orthotropy parameters on the stress state of hollow cylinders with cross sections in the form of connected concave semicorrugations subjected to the action of internal pressure under certain conditions on the ends. The results of investigations of the stress state are presented in the form of plots and a table.

Study of Stresses Induced in Axisymmetric Buried Thin Orthotropic Fluid Filled Clindrical Shell due to P-Wave Loading

Axisymmetric dynamic response and the stresses induced in a fluid –filled buried pipe due to an incident p-wave for different orthotropic parameters and different fluid is the subject of this investigation. In this work the shell is assumed perfectly bonded to the surrounding medium of infinite extent. The pipeline has been modelled as an infinitely long circular cylindrical shell buried in homogeneous, isotropic and elastic medium of infinite extent. For perfect bonding between soil and pipe, the stiffness and damping properties of soil are neglected. Results have been obtained for hard (rocky), medium hard and very soft (sandy) soil conditions surrounding the shell. The radial displacement at the shell and fluid interface (i.e., at the inner surface of the shell) is taken to be continuous while considering a fluid filled shell. The stress variations of pipe due to change in cylinder orthotropic parameters has been carefully studied. Different angles of wave incidence and different soil around shell conditions along with the different kind of fluids have been considered. The different kind of soils from soft (sandy) to hard and rocky condition has been taken into account. It is realised that the effect of fluid have a significant influence on the stresses (axial and hoop) depending on the soil conditions and the angle of incidence

On the fully coupled partial slip contact problems of orthotropic materials loaded by flat and cylindrical indenters

Fully coupled partial slip contact problems for orthotropic materials are considered in this paper. The problem is formulated by virtue of the Fourier transform method. The governing singular integral equations are solved numerically for both flat and cylindrical stamps under the plane strain conditions. An extensive parametric study is carried out to investigate the effect of material orthotropy parameter as well as the coefficient of friction on the contact stresses and the stress intensity factors. It is found that the coefficient of friction and the orthotropic material parameters have a great effect on the stress intensity and the in-plane contact stresses as well as stick and slip zones. Especially, the shearing ratio parameter has a pronounced effect on the stress distribution of cylindrical punches which is important from the crack initiation and fretting wear point of view. The results obtained from this study can be used as benchmark results in the design of contacting parts with orthotropic material properties.

Two‐dimensional analysis of the fully coupled rolling contact problem between a rigid cylinder and an orthotropic medium

AbstractIn this paper, the fully‐coupled rolling contact problem between a rigid cylinder and an orthotropic medium is investigated. The governing equations are developed analytically; then, a numerical method, the Gauss‐Chebyshev method, is used to solve the coupled integral equations. The rolling contact problem is solved by assuming a central stick zone accompanied with two slip regions. The main purpose of this study is to obtain the surface stresses in the contact area and investigate the effect of material orthotropic properties such as shear parameter and stiffness ratio and also the coefficient of friction on these contact stresses. In addition, the subsurface stresses in the orthotropic medium are determined and a parametric study, was subsequently executed. The current paper shows that the orthotropic parameters and the coefficient of friction significantly influence the contact surface stresses and the distribution of the interior field stresses. By appropriately choosing the values of these parameters, the stresses will decrease; thus, the failure behavior of the orthotropic medium improves.

Applicability of a Structurally Orthotropic Model in Problems on Tension, Bending, and Stability of Densely Perforated Plates and Shells

The applicability of a structurally orthotropic model to the calculation of perforated plates and cylindrical shells subjected to tension and bending is studied by the finite-element method. The parameters of the orthotropic material are used in the form of coefficients of stiffness reduction. They are determined from the solution to the problem on deformation of a cyclically repeating structural element, with a varying degree of perforation (porosity), in tension, shear, and bending. The structural element is investigated by the methods of continuum mechanics and the theory of Timoshenko-type shells, and the limit of applicability of the theory of shells to such problems is found. The numerical results obtained are compared with the analytical estimates given by E. I. Grigolyuk and L. A. Filshtinskii. Verification of the numerically obtained orthotropic parameters is carried out based on the solution to the problem of bending of one quarter of a cylindrical strip and a plate perforated with one row of holes. It is shown that the approach chosen is applicable to perforated plates and shells in bending problems with waves whose length exceeds the characteristic size of their structural element. The stability of a perforated elastic cylindrical shell under external pressure, with two variants of boundary conditions, is investigated. Values of the critical pressure and the corresponding buckling modes in relation to the length of the shell and the degree of perforation are obtained.

Nonlinear stability of sensor elastic element—corrugated shallow spherical shell in coupled multi-field

Nonlinear stability of sensor elastic element—corrugated shallow spherical shell in coupled multi-field is studied. With the equivalent orthotropic parameter obtained by the author, the corrugated shallow spherical shell is considered as an orthotropic shallow spherical shell, and geometrical nonlinearity and transverse shear deformation are taken into account. Nonlinear governing equations are obtained. The critical load is obtained using a modified iteration method. The effect of temperature variation and shear rigidity variation on stability is analyzed.

Retrieving the time-dependent thermal conductivity of an orthotropic rectangular conductor

The aim of this paper is to determine the thermal properties of an orthotropic planar structure characterized by the thermal conductivity tensor in the coordinate system of the main directions (Oxy) being diagonal. In particular, we consider retrieving the time-dependent thermal conductivity components of an orthotropic rectangular conductor from nonlocal overspecified heat flux conditions. Since only boundary measurements are considered, this inverse formulation belongs to the desirable approach of non-destructive testing of materials. The unique solvability of this inverse coefficient problem is proved based on the Schauder fixed point theorem and the theory of Volterra integral equations of the second kind. Furthermore, the numerical reconstruction based on a nonlinear least-squares minimization is performed using the MATLAB optimization toolbox routine lsqnonlin. Numerical results are presented and discussed in order to illustrate the performance of the inversion for orthotropic parameter identification.

A physics based approach to the pulse wave velocity prediction in compliant arterial segments

Pulse wave velocity (PWV) quantification commonly serves as a highly robust prognostic parameter being used in a preventative cardiovascular therapy. Being dependent on arterial elastance, it can serve as a marker of cardiovascular risk. Since it is influenced by a blood pressure (BP), the pertaining theory can lay the foundation in developing a technique for noninvasive blood pressure measurement. Previous studies have reported application of PWV, measured noninvasively, for both the estimation of arterial compliance and blood pressure, based on simplified physical or statistical models. A new theoretical model for pulse wave propagation in a compliant arterial segment is presented within the framework of pseudo-elastic deformation of biological tissue undergoing finite deformation. An essential ingredient is the dependence of results on nonlinear aspects of the model: convective fluid phenomena, hyperelastic constitutive relation, large deformation and a longitudinal pre-stress load. An exact analytical solution for PWV is presented as a function of pressure, flow and pseudo-elastic orthotropic parameters. Results from our model are compared with published in-vivo PWV measurements under diverse physiological conditions. Contributions of each of the nonlinearities are analyzed. It was found that the totally nonlinear model achieves the best match with the experimental data. To retrieve individual vascular information of a patient, the inverse problem of hemodynamics is presented, calculating local orthotropic hyperelastic properties of the arterial wall. The proposed technique can be used for non-invasive assessment of arterial elastance, and blood pressure using direct measurement of PWV, with account of hyperelastic orthotropic properties.

Interface crack between different orthotropic media under uniform heat flow.

In this paper, plane thermo-elastic solutions are presented for the problem of a crack in two bonded homogeneous orthotropic media with a graded interfacial zone. The graded interfacial zone is treated as a nonhomogeneous interlayer having spatially varying thermo-elastic moduli between dissimilar, homogeneous orthotropic half-planes, which is assumed to vary exponentially in the direction perpendicular to the crack surface. Using singular integral equation method, the mixed boundary value conditions with respect to the temperature field and those with respect to the stress field are reduced to a system of singular integral equations and solved numerically. Numerical results are obtained to show the influence of non-homogeneity parameters of the material thermo-elastic properties, the orthotropy parameters and the dimensionless thermal resistance on the temperature distribution and the thermal stress intensity factors.

Identification of Elastic Orthotropic Material Parameters by the Singular Boundary Method

AbstractThis article addresses the resolution of the inverse problem for the parameter identification in orthotropic materials with a number of measurements merely on the boundaries. The inverse problem is formulated as an optimization problem of a residual functional which evaluates the differences between the experimental and predicted displacements. The singular boundary method, an integration-free, mathematically simple and boundary-only meshless method, is employed to numerically determine the predicted displacements. The residual functional is minimized by the Levenberg-Marquardt method. Three numerical examples are carried out to illustrate the robustness, efficiency, and accuracy of the proposed scheme. In addition, different levels of noise are added into the boundary conditions to verify the stability of the present methodology.

Determination of orthotropic properties of glass fibre reinforced thermoplastics using X-ray tomography and multiscale finite element computation

We report a new approach to measure orthotropic properties of short glass fibre reinforced thermoplastics at the macroscopic scale taking into account all microstructural details. 3D imaging technique based on X-ray micro-tomography is used to assess fibrous architecture of an injected part at different positions characterised by different fibre flow histories. Finite element computation is used as a multiscale process, firstly by computing orthotropic parameters at a micro-scale for hundreds of bi-phasic 3D domains composing the macrostructure of the composite at all studied positions. Results are implemented in a second finite element computation as a collection of orthotropic material models composing the heterogeneous structure of the composite.

Interface crack between a thin film and an orthotropic substrate under uniform heat flow

An interface crack between a thin film and an orthotropic substrate under uniform heat flow is analyzed. Four thermal load parameters are proposed to describe the interface stress intensity factors based on the thermoelastic formalism with transformed function representation. The interface stress intensity factors are expressed in terms of the thermal load parameters and dimensionless coefficients. The dimensionless coefficients are shown to depend on seven material parameters and one geometric parameter. The dependence of the dimensionless coefficients on one orthotropic parameter of the film is explicitly found by means of the orthotropic rescaling technique. The effects of other material parameters on the dimensionless coefficients as the geometric parameter varies were numerically investigated using finite element analysis.