Journal articles: 'Orthotropic Elastic Moduli'

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SOFIYEV, A. H., E. SCHNACK, V. C. HACIYEV, and N. KURUOGLU. "EFFECT OF THE TWO-PARAMETER ELASTIC FOUNDATION ON THE CRITICAL PARAMETERS OF NONHOMOGENEOUS ORTHOTROPIC SHELLS." International Journal of Structural Stability and Dynamics 12, no. 05 (October 2012): 1250041. http://dx.doi.org/10.1142/s0219455412500411.

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A theoretical analysis is presented for determining the free vibrational and buckling characteristics of the nonhomogeneous, orthotropic, thin-walled, circular cylindrical and conical shells under a hydrostatic pressure and resting on a two-parameter elastic foundation. The basic relations have been obtained for the orthotropic truncated conical shell, the Young's moduli and density of which vary continuously in the thickness direction. By applying the Galerkin method, the buckling hydrostatic pressure and dimensionless frequency parameter of the homogeneous and nonhomogeneous orthotropic truncated conical shells with or without elastic foundations are obtained. Finally, the effects of the Winkler and Pasternak-type elastic foundations, the variations of shell characteristics, the effects of the nonhomogeneity and orthotropy on the critical parameters have been studied. The results are presented in tables, figures and compared with other works.

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Diaco, Marina. "On Torsion of Functionally Graded Elastic Beams." Modelling and Simulation in Engineering 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/8464205.

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The evaluation of tangential stress fields in linearly elastic orthotropic Saint-Venant beams under torsion is based on the solution of Neumann and Dirichlet boundary value problems for the cross-sectional warping and for Prandtl stress function, respectively. A skillful solution method has been recently proposed by Ecsedi for a class of inhomogeneous beams with shear moduli defined in terms of Prandtl stress function of corresponding homogeneous beams. An alternative reasoning is followed in the present paper for orthotropic functionally graded beams with shear moduli tensors defined in terms of the stress function and of the elasticity of reference inhomogeneous beams. An innovative result of invariance on twist centre is also contributed. Examples of functionally graded elliptic cross sections of orthotropic beams are developed, detecting thus new benchmarks for computational mechanics.

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Turner, C. H., and S. C. Cowin. "Errors Induced by Off-Axis Measurement of the Elastic Properties of Bone." Journal of Biomechanical Engineering 110, no. 3 (August 1, 1988): 213–15. http://dx.doi.org/10.1115/1.3108433.

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Misalignment between the axes of measurement and the material symmetry axes of bone causes error in anisotropic elastic property measurements. Measurements of Poisson’s ratio were strongly affected by misalignment errors. The mean errors in the measured Young’s moduli were 9.5 and 1.3 percent for cancellous and cortical bone, respectively, at a misalignment angle of 10 degrees. Mean errors of 1.1 and 5.0 percent in the measured shear moduli for cancellous and cortical bone, respectively, were found at a misalignment angle of 10 degrees. Although, cancellous bone tissue was assumed to have orthotropic elastic symmetry, the possibility of the greater symmetry of transverse isotropy was investigated. When the nine orthotropic elastic constants were forced to approximate the five transverse isotropic elastic constants, errors of over 60 percent were introduced. Therefore, it was concluded that cancellous bone is truly orthotropic and not transversely isotropic. A similar but less strong result for cortical bone tissue was obtained.

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Ozyhar, Tomasz, Stefan Hering, and Peter Niemz. "Moisture-dependent orthotropic tension-compression asymmetry of wood." Holzforschung 67, no. 4 (May 1, 2013): 395–404. http://dx.doi.org/10.1515/hf-2012-0089.

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Abstract The influence of moisture content (MC) on the tension-compression (Te-Co) asymmetry of beech wood has been examined. The elastic and strength parameters, including Te and Co Young’s moduli, Poisson’s ratios, and ultimate and yield stress values, were determined and compared in terms of different MCs for all orthotropic directions. The results reveal a distinctive Te-Co strength asymmetry with a moisture dependency that is visualized clearly by the Te to Co yield stress ratio. The Te-Co asymmetry is further shown by the inequality of the elastic properties, known as the “bimodular behavior”. The latter is proven for the Young’s moduli values in the radial and tangential directions and for individual Poisson’s ratios. Although the bimodularity of the Young’s moduli is significant at low MC levels, there is no evidence of moisture dependency on the Te-Co asymmetry of the Poisson’s ratios.

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Vorobyev, Alexey, Olivier Arnould, Didier Laux, Roberto Longo, Nico P. van Dijk, and E. Kristofer Gamstedt. "Characterisation of cubic oak specimens from the Vasa ship and recent wood by means of quasi-static loading and resonance ultrasound spectroscopy (RUS)." Holzforschung 70, no. 5 (May 1, 2016): 457–65. http://dx.doi.org/10.1515/hf-2015-0073.

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Abstract The cylindrical orthotropy, inherent time-dependency response, and variation between and within samples make the stiffness characterisation of wood more challenging than most other structural materials. The purpose of the present study is to compare static loading with resonant ultrasound spectroscopy (RUS) and to investigate how to combine the advantages of each of these two methods to improve the estimation of the full set of elastic parameters of a unique sample. The behavior of wood as an orthotropic mechanical material was quantified by elastic engineering parameters, i.e. Poisson’s ratios and Young’s and shear moduli. Recent and waterlogged archaeological oak impregnated with polyethylene glycol (PEG) from the Vasa warship built in 1628 was in focus. The experimental results were compared, and the difference between RUS and static loading was studied. This study contributes additional information on the influence of PEG and degradation on the elastic engineering parameters of wood. Finally, the shear moduli and Poisson’s ratios were experimentally determined for Vasa archaeological oak for the first time.

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Subhani, Mahbube, Jian Chun Li, Hauke Gravenkamp, and Bijan Samali. "Effect of Elastic Modulus and Poisson's Ratio on Guided Wave Dispersion Using Transversely Isotropic Material Modelling." Advanced Materials Research 778 (September 2013): 303–11. http://dx.doi.org/10.4028/www.scientific.net/amr.778.303.

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Timber poles are commonly used for telecommunication and power distribution networks, wharves or jetties, piling or as a substructure of short span bridges. Most of the available techniques currently used for non-destructive testing (NDT) of timber structures are based on one-dimensional wave theory. If it is essential to detect small sized damage, it becomes necessary to consider guided wave (GW) propagation as the behaviour of different propagating modes cannot be represented by one-dimensional approximations. However, due to the orthotropic material properties of timber, the modelling of guided waves can be complex. No analytical solution can be found for plotting dispersion curves for orthotropic thick cylindrical waveguides even though very few literatures can be found on the theory of GW for anisotropic cylindrical waveguide. In addition, purely numerical approaches are available for solving these curves. In this paper, dispersion curves for orthotropic cylinders are computed using the scaled boundary finite element method (SBFEM) and compared with an isotropic material model to indicate the importance of considering timber as an anisotropic material. Moreover, some simplification is made on orthotropic behaviour of timber to make it transversely isotropic due to the fact that, analytical approaches for transversely isotropic cylinder are widely available in the literature. Also, the applicability of considering timber as a transversely isotropic material is discussed. As an orthotropic material, most material testing results of timber found in the literature include 9 elastic constants (three elastic moduli and six Poisson's ratios), hence it is essential to select the appropriate material properties for transversely isotropic material which includes only 5 elastic constants. Therefore, comparison between orthotropic and transversely isotropic material model is also presented in this article to reveal the effect of elastic moduli and Poisson's ratios on dispersion curves. Based on this study, some suggestions are proposed on selecting the parameters from an orthotropic model to transversely isotropic condition.

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Adibaskoro, Tito, Michalina Makowska, Aleksi Rinta-Paavola, Stefania Fortino, and Simo Hostikka. "Elastic Modulus, Thermal Expansion, and Pyrolysis Shrinkage of Norway Spruce Under High Temperature." Fire Technology 57, no. 5 (April 30, 2021): 2451–90. http://dx.doi.org/10.1007/s10694-021-01123-z.

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AbstractThe orthotropic and temperature-dependent nature of the mechanical properties of wood is well recognized. However, past studies of mechanical properties at elevated temperatures are either limited to temperatures below 200 °C or focus only on the direction parallel to grain. The effect of time-dependent pyrolysis during measurement is often neglected. This paper presents a novel method for determining elastic modulus at high temperatures and thermal expansion coefficient in different orthotropic directions via Dynamic Mechanical-Thermal Analyser (DMTA). The method allows for drying, drying verification, and measurement in one chamber, eliminating the possibility of moisture reabsorption from ambient air. The repeatable measurements can be carried out in temperatures up to 325°C, adequate for observing time-dependent pyrolysis during measurement. Results of the measurements of Norway Spruce provide data of its mechanical response at temperature range previously not explored widely, as well as in the orthotropic direction. Time-dependent behaviour was observed in the thermal expansion and shrinkage experiment, where above 250°C the amount of shrinkage depends on heating rate. At such temperature, elastic moduli measurement also shows time dependence, where longer heating at certain temperature slightly increases the measured elastic modulus. Additionally, bilinear regression of the relationship between elastic moduli and temperature shows quantitatively good fit. Numerical simulation of the DMTA temperature history and wood chemical components mass losses show the onset of shrinkage and onset of hemicellulose mass loss occurring at around the same time, while decomposition of cellulose correlate with the sudden loss of elastic moduli.

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Tokovyy, Yuriy V., Anatoliy V. Yasinskyy, Sebastian Lubowicki, and Dariusz M. Perkowski. "Elastic and Thermoelastic Responses of Orthotropic Half-Planes." Materials 15, no. 1 (December 31, 2021): 297. http://dx.doi.org/10.3390/ma15010297.

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A unified approach is presented for constructing explicit solutions to the plane elasticity and thermoelasticity problems for orthotropic half-planes. The solutions are constructed in forms which decrease the distance from the loaded segments of the boundary for any feasible relationship between the elastic moduli of orthotropic materials. For the construction, the direct integration method was employed to reduce the formulated problems to a governing equation for a key function. In turn, the governing equation was reduced to an integral equation of the second kind, whose explicit analytical solution was constructed by using the resolvent-kernel algorithm.

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Zhao, Aihong, and Jilin Yu. "The overall elastic moduli of orthotropic composite and description of orthotropic damage of materials." International Journal of Solids and Structures 37, no. 45 (November 2000): 6755–71. http://dx.doi.org/10.1016/s0020-7683(99)00226-7.

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Gotkhindi, Tejas P., and K. R. Y. Simha. "Transverse orthotropic elastic moduli of bundled coated thin elliptical tubes." Composite Structures 118 (December 2014): 178–99. http://dx.doi.org/10.1016/j.compstruct.2014.07.030.

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Zhao, Y. H., and G. J. Weng. "Effective Elastic Moduli of Ribbon-Reinforced Composites." Journal of Applied Mechanics 57, no. 1 (March 1, 1990): 158–67. http://dx.doi.org/10.1115/1.2888297.

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Based on the Eshelby-Mori-Tanaka theory the nine effective elastic constants of an orthotropic composite reinforced with monotonically aligned elliptic cylinders, and the five elastic moduli of a transversely isotropic composite reinforced with two-dimensional randomly-oriented elliptic cylinders, are derived. These moduli are given in terms of the cross-sectional aspect ratio and the volume fraction of the elliptic cylinders. When the aspect ratio approaches zero, the elliptic cylinders exist as thin ribbons, and these moduli are given in very simple, explicit forms as a function of volume fraction. It turns out that, in the transversely isotropic case, the effective elastic moduli of the composite coincide with Hill’s and Hashin’s upper bounds if ribbons are harder than the matrix, and coincide with their lower bounds if ribbons are softer. These results are in direct contrast to those of circular fibers. Since the width of the Hill-Hashin bounds can be very wide when the constituents have high modular ratios, this analysis suggests that the ribbon reinforcement is far more effective than the traditional fiber reinforcement.

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Chen, Tungyang, George J. Dvorak, and Yakov Benveniste. "Mori-Tanaka Estimates of the Overall Elastic Moduli of Certain Composite Materials." Journal of Applied Mechanics 59, no. 3 (September 1, 1992): 539–46. http://dx.doi.org/10.1115/1.2893757.

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Simple, explicit formulae are derived for estimates of the effective elastic moduli of several multiphase composite materials with the Mori-Tanaka method. Specific results are given for composites reinforced by aligned or randomly oriented, transversely isotropic fibers or platelets, and for fibrous systems reinforced by aligned, cylindrically orthotropic fibers.

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Saito, Akira, Yasunari Nishikawa, Shintaro Yamasaki, Kikuo Fujita, Atsushi Kawamoto, Masakatsu Kuroishi, and Hideo Nakai. "Equivalent orthotropic elastic moduli identification method for laminated electrical steel sheets." Mechanical Systems and Signal Processing 72-73 (May 2016): 607–28. http://dx.doi.org/10.1016/j.ymssp.2015.10.027.

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14

Ashman, R. B., J. Y. Rho, and C. H. Turner. "Anatomical variation of orthotropic elastic moduli of the proximal human tibia." Journal of Biomechanics 22, no. 8-9 (January 1989): 895–900. http://dx.doi.org/10.1016/0021-9290(89)90073-0.

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15

Pao, Yih-Hsing, Tsung-Tsong Wu, and Udo Gamer. "Acoustoelastic Birefringences in Plastically Deformed Solids: Part I—Theory." Journal of Applied Mechanics 58, no. 1 (March 1, 1991): 11–17. http://dx.doi.org/10.1115/1.2897137.

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A modified theory of acoustoelasticity is proposed to include the effect of small plastic deformation on propagational speeds of elastic waves in orthotropic media. In the constitutive equation for the incremental stresses of a predeformed body, the elastic moduli are modified by elastic deformation and plastic strains. The latter is related to the texture of the material. Several formulae for the acoustoelastic birefringences (differences of two shear wave speeds polarized at perpendicular directions) are derived. They can be applied to measure residual stresses and plastic strains by ultrasonic techniques.

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Clauß, Sebastian, Corina Pescatore, and Peter Niemz. "Anisotropic elastic properties of common ash (Fraxinus excelsior L.)." Holzforschung 68, no. 8 (December 1, 2014): 941–49. http://dx.doi.org/10.1515/hf-2013-0189.

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Abstract Hardwoods in principle show a similar orthotropic behavior as softwoods; however, the ratios of the mechanical parameters between the three anatomical directions and their magnitudes are different and depend strongly on the individual microstructure of the species. The aim of the current study was to characterize the 3-D elastic behavior of common ash (Fraxinus excelsior L.) by tensile, compression, and shear tests in the three anatomical directions and stepwise in between, by means of a universal testing machine in combination with a digital image correlation technique. Young’s moduli, shear moduli, and Poisson’s ratios have been determined for the different load directions. From studies on the radial-tangential plane of other wood species, it is known that the elastic moduli in the principal directions and the off-axis elastic moduli vary in a nonlinear correlation, depending on density gradients between earlywood and latewood. This angular dependency has been experimentally and theoretically proven for ash. Furthermore, the dependency of mechanical parameters on the fiber-load angle has been experimentally determined. The measurements for principal and off-axis load directions provide a sound basis for modeling of hardwood structures.

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Saito, Akira, Atsushi Kawamoto, Masakatsu Kuroishi, Hideo Nakai, and Shintaro Yamasaki. "Estimation of measurement errors in orthotropic elastic moduli determined from natural frequencies." Structural and Multidisciplinary Optimization 55, no. 3 (August 10, 2016): 987–99. http://dx.doi.org/10.1007/s00158-016-1552-9.

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Mazumder, Dibbyan, Gurudas Kar, Ram Mohan Vasu, Debasish Roy, and Rajan Kanhirodan. "Orthotropic elastic moduli of biological tissues from ultrasound-assisted diffusing-wave spectroscopy." Journal of the Optical Society of America A 34, no. 11 (October 4, 2017): 1945. http://dx.doi.org/10.1364/josaa.34.001945.

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Lipton, Rob, and Jim Northrup. "Optimal Bounds on the in-Plane Shear Moduli for Orthotropic Elastic Composites." SIAM Journal on Applied Mathematics 54, no. 2 (April 1994): 428–42. http://dx.doi.org/10.1137/s0036139992235986.

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Lubarda, Vlado, and Michelle Chen. "On the elastic moduli and compliances of transversely isotropic and orthotropic materials." Journal of Mechanics of Materials and Structures 3, no. 1 (March 1, 2008): 153–71. http://dx.doi.org/10.2140/jomms.2008.3.153.

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Bacigalupo, Andrea, and Luigi Gambarotta. "Micro-Polar and Second Order Homogenization of Periodic Masonry." Materials Science Forum 638-642 (January 2010): 2561–66. http://dx.doi.org/10.4028/www.scientific.net/msf.638-642.2561.

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Micro-polar and second order homogenization procedures for periodic elastic masonry are implemented to include geometric and material length scales in the constitutive equation. By the solution of the RVE equilibrium problems with properly prescribed boundary conditions the orthotropic elastic moduli of the higher order continua are obtained on the basis of an enhanced Hill–Mandel condition. A shear layer problem is analysed and the results from the heterogeneous models are compared with those ones obtained by the homogenization procedures; the second-order homogenization appears to provide better results in comparison to the micro-polar homogenization.

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Sofiyev, A. H., S. N. Keskin, and Ali H. Sofiyev. "Effects of Elastic Foundation on the Vibration of Laminated Non-Homogeneous Orthotropic Circular Cylindrical Shells." Shock and Vibration 11, no. 2 (2004): 89–101. http://dx.doi.org/10.1155/2004/424926.

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In this paper an analytical procedure is given to study the free vibration characteristics of laminated non-homogeneous orthotropic thin circular cylindrical shells resting on elastic foundation, accounting for Karman type geometric non-linearity. At first, the basic relations and modified Donnell type stability equations, considering finite deformations, have been obtained for laminated thin orthotropic circular cylindrical shells, the Young's moduli of which varies piecewise continuously in the thickness direction. Applying Galerkin method to the latter equations, a non-linear time dependent differential equation is obtained for the displacement amplitude. The frequency is obtained from this equation as a function of the shell displacement amplitude. Finally, the effect of elastic foundation, non-linearity, non-homogeneity, the number and ordering of layers on the frequency is found for different mode numbers. These results are given in the form of tables and figures. The present analysis is validated by comparing results with those in the literature.

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Ayorinde, E. O., and R. F. Gibson. "Improved Method for In-situ Elastic Constants of Isotropic and Orthotropic Composite Materials Using Plate Modal Data With Trimodal and Hexamodal Rayleigh Formulations." Journal of Vibration and Acoustics 117, no. 2 (April 1, 1995): 180–86. http://dx.doi.org/10.1115/1.2873882.

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This paper relates a further development of an earlier work by the authors, in which they presented a method for deriving the four independent elastic constants (longitudinal and transverse Young’s moduli, in-plane shear modulus and major Poisson’s ratio) of an orthotropic material from resonance data obtained in a modal analysis of a freely-supported plate made out of the material. In the present work, simple averaging, as opposed to the weighted averaging employed in the earlier version, is utilized. The use of three modes and six modes is compared on the basis of results of both the forward and the inverse problems. Results are obtained for materials spanning orthotropy ratios from unity (i.e., isotropic) to about 13. The results suggest that, in comparison with our earlier method, the improved method is easier to use and is just as accurate. The adaptability of the basic method developed by the authors to various levels and types of refinement is also demonstrated, as is the potential of the method for fast characterization of elastic properties of advanced composites.

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Zhu, Xuefeng, Longkun Xu, Xiaochen Liu, Jinting Xu, Ping Hu, and Zheng-Dong Ma. "Theoretical prediction of mechanical properties of 3D printed Kagome honeycombs and its experimental evaluation." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 18 (July 16, 2019): 6559–76. http://dx.doi.org/10.1177/0954406219860538.

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Kagome honeycomb structure is proved to incorporate excellent mechanical and actuation performances due to its special configuration. However, until now, the mechanical properties of 3D printed Kagome honeycomb have not been investigated. Hence, the objective of this work is to explore some mechanical properties of 3D-printed Kagome honeycomb structures such as elastic properties, buckling, and so on. In this paper, the analytical formulas of some mechanical properties of Kagome honeycombs made of 3D-printed materials are given. Effective elastic moduli such as Young's modulus, shear modulus, and Poisson's ratio of orthotropic Kagome honeycombs under in-plane compression and shear are derived in analytical forms. By these formulas, we investigate the relationship of the elastic moduli, the relative density, and the shape anisotropy–ratio of 3D-printed Kagome honeycomb. By the uniaxial tensile testing, the effective Young's moduli of 3D printed materials in the lateral and longitudinal directions are obtained. Then, by the analytical formulas and the experimental results, we can predict the maximum Young's moduli and the maximum shear modulus of 3D-printed Kagome honeycombs. The isotropic behavior of 3D-printed Kagome honeycombs is investigated. We also derived the equations of the initial yield strength surfaces and the buckling surfaces. We found that the sizes of the buckling surfaces of 3D printed material are smaller than that of isotropic material. The efficiency of the presented analytical formulas is verified through the tensile testing of 3D printed Kagome honeycomb specimens.

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Allam, M. N. M., R. Tantawy, A. Yousof, and A. M. Zenkour. "Elastic and Viscoelastic Stresses of Nonlinear Rotating Functionally Graded Solid and Annular Disks with Gradually Varying Thickness." Archive of Mechanical Engineering 64, no. 4 (December 20, 2017): 423–40. http://dx.doi.org/10.1515/meceng-2017-0025.

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Abstract Analytical and numerical nonlinear solutions for rotating variable-thickness functionally graded solid and annular disks with viscoelastic orthotropic material properties are presented by using the method of successive approximations.Variable material properties such as Young’s moduli, density and thickness of the disk, are first introduced to obtain the governing equation. As a second step, the method of successive approximations is proposed to get the nonlinear solution of the problem. In the third step, the method of effective moduli is deduced to reduce the problem to the corresponding one of a homogeneous but anisotropic material. The results of viscoelastic stresses and radial displacement are obtained for annular and solid disks of different profiles and graphically illustrated. The calculated results are compared and the effects due to many parameters are discussed.

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Elad, D., A. Foux, and Y. Kivity. "A Model for the Nonlinear Elastic Response of Large Arteries." Journal of Biomechanical Engineering 110, no. 3 (August 1, 1988): 185–89. http://dx.doi.org/10.1115/1.3108429.

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The nonlinear elastic response of large arteries subjected to finite deformations due to action of biaxial principal stresses, is described by simple constitutive equations. Generalized measures of strain and stress are introduced to account for material nonlinearity. This also ensures the existence of a strain energy density function. The orthotropic elastic response is described via quasi-linear relations between strains and stresses. One nonlinear parameter which defines the measures of strain and stress, and three elastic moduli are assumed to be constants. The lateral strain parameters (equivalent to Poisson’s ratios in infinitesimal deformations) are deformation dependent. This dependence is defined by empirical relations developed via the incompressibility condition, and by the introduction of a fifth material parameter. The resulting constitutive model compares well with biaxial experimental data of canine carotid arteries.

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Selivanov, M. F., Y. R. Kulbachnyy, and D. R. Onishchenko. "Determining the stress concentration change with time in a viscoelastic orthotropic solid." Reports of the National Academy of Sciences of Ukraine, no. 10 (October 2020): 28–34. http://dx.doi.org/10.15407/dopovidi2020.10.028.

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The procedure for solving the plane problem of the linear theory of viscoelasticity by the finite element method is described. Based on the virtual work principle and the assumption of the constancy of the strain rate at small intervals of time, the matrix form of the equilibrium equations of the finite-element approximation of a body is written. The solution procedure is described for the constitutive relations in the Boltzmann—Volterra integral form. This integral is transformed into an incremental form on a time mesh, at each interval of which the problem is solved by the finite element method with unknown increments of displacements. The numerical procedure is constructed by ununiformly dividing the time interval, at which the study is conducted. In this case, the stiffness matrix requires recalculation at each time step. The relaxation functions of the moduli of a viscoelastic orthotropic material are described in the form of the Proni—Dirichlet series. The solution to the problem of determining the change over time of the stress concentration in a body with a round hole in a viscoelastic orthotropic plate is presented. To construct a numerical solution, the three moduli of orthotropic material were written using one exponent with the same relaxation time. For these initial data, an analytic expression for the viscoelastic components of the stiffness matrix of an orthotropic plate under plain stress conditions is constructed. Numerical examples are presented for several ratios of the hole radius to the size of the plate. These results are compared with the solution obtained for an infinite plate by inverse transformation by a numerical method of the well-known analytic elastic solution.

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Mate̤milo̤la, S. A., W. J. Stronge, and D. Durban. "Diffusion Rate for Stress in Orthotropic Materials." Journal of Applied Mechanics 62, no. 3 (September 1, 1995): 654–61. http://dx.doi.org/10.1115/1.2895996.

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Axial rates of diffusion of the symmetrical state of stress caused by equal but opposed normal forces acting on opposite sides of an indefinitely long strip or plate, are examined in the context of orthotropic elastic materials. To obtain the stress components for this boundary value problem, the imposed surface tractions are represented by a Fourier integral. At distances larger than one quarter of the thickness, the normal stress on the middle surface is closely represented by the sum of eigenfunctions for this problem, up to, and including the first complex eigenfunction as well as its conjugate. Each eigenfunction is a product of exponentially decreasing and oscillatory terms. The exponential term is more significant for determining the rate of diffusion of stress in materials with a large ratio of axial to transverse Young’s moduli Ex/Ey ⩾ 3; this term shows a strong dependence on the ratio of transverse Young’s modulus to shear modulus Ey/G.

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Haciyev, Vaqif C., Gulnar R. Mirzoeva, and Matlab G. Agayarov. "Free vibrations of anisotropic rectangular plate laying on a heterogeneous viscouselastic basis." Structural Mechanics of Engineering Constructions and Buildings 15, no. 6 (December 15, 2019): 470–76. http://dx.doi.org/10.22363/1815-5235-2019-15-6-470-476.

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The aim of the work. Free, transverse vibrations are considered heterogeneous along the three spatial coordinates of rectangular plates lying on an inhomogeneous viscoelastic base. It is assumed that the boundary conditions are homogeneous. A closed solution for the problem of free vibration of an inhomogeneous rectangular orthotropic plate based on an inhomogeneous viscoelastic foundation is developed in the article. Young's moduli and the density of the orthotropic plate continuously change with respect to three spatial coordinates, while the characteristics of a viscoelastic base change depending on the coordinates in the plane. Methods. The corresponding equation of motion is obtained using the classical theory of plates. The solution to the problem was constructed using the method of separation of variables and the Bubnov - Galerkin method. Results. Explicit formulas of the fundamental tone of the frequency of the transverse vibration of an anisotropic plate lying on an inhomogeneous viscoelastic base are determined. The influence of heterogeneity of orthotropic materials, viscosity inhomogeneities, inelastic and elastic substrates at dimensionless plate frequencies have been studied in detail.

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Formato, Andrea, Domenico Ianniello, Arcangelo Pellegrino, and Francesco Villecco. "Vibration-Based Experimental Identification of the Elastic Moduli Using Plate Specimens of the Olive Tree." Machines 7, no. 2 (June 20, 2019): 46. http://dx.doi.org/10.3390/machines7020046.

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Mechanical parameters of the olive wood plate have been computed by data inversion of vibrational experimental tests. A numerical-experimental method has allowed the evaluation of the two transverse shear moduli and the four in-plane moduli of a thick orthotropic olive tree plate. Therefore, the natural flexural vibration frequencies of olive trees plates have been evaluated by the impulse technique. For our purposes, we define the objective function as the difference between the numerical computation data and the experimental ones. The Levenberg–Marquardt algorithm was chosen as optimization strategy in order to minimize the matching error: the evaluation of the objective function has required a complete finite element simulation by using the ANSYS code. As input, we have used the uniaxial test data results obtained from the olive plates. The converged elastic moduli with n = 10 natural modes were E1 = 14.8 GPa, E2 = 1.04 GPa, G12 = 4.45 GPa, G23 = 4.02 GPa, G13 = 4.75 GPa, ν12 = 0.42, and ν13 = 0.42. The relative root mean square (RMS) errors between the experimental frequencies and the computed one is 9.40%. Then, it has been possible to obtain a good agreement between the measured and calculated frequencies. Therefore, it has been found that for plates of moderate thickness the reliability of the estimated values of the transverse shear moduli is good.

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Tadmor, E. B., and D. Durban. "Plastic Deformation and Burst of Pressurized Multilayered Cylinders." Journal of Pressure Vessel Technology 117, no. 1 (February 1, 1995): 85–91. http://dx.doi.org/10.1115/1.2842096.

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A large strain analysis is presented for internally pressurized multilayered tubes, in generalized plane strain. Material behavior is modeled by an elastoplastic deformation theory with an orthotropic yield function, introduced by Hill, and arbitrary hardening. Elastic compressibility is neglected. An exact solution is given, in terms of quadratures, along with a general condition for burst. Simple yet useful relations are derived for thin-walled cylinders with the neglect of elastic strains. For rigid/nonlinear-hardening response, we obtain an expression for the onset of burst in terms of overall effective moduli. A few numerical examples are given and the possibility of locating an optimal two-layer configuration is discussed. It appears that optimization with respect to weight is attainable provided that appropriate materials are selected.

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Paipetis, A., Y. Z. Pappas, D. E. Vlachos, and V. Kostopoulos. "Damage Modelling and Simulation of Composite Materials using Ultrasonic Measurements." Advanced Composites Letters 14, no. 3 (May 2005): 096369350501400. http://dx.doi.org/10.1177/096369350501400301.

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The monitoring of the elastic properties of Al2O3/Al2O3 composites during the exposure at high temperature environment that simulates the working conditions of a gas turbine has been performed non-destructively using ultrasonics. The applied methodology is based on velocity measurements of the elastic waves that propagate in an orthotropic medium. These were estimated experimentally using a custom pulser-receiver setup which allows control of the angle of the incident pulse on the sample, while the latter is immersed in a water bath. The derivation of the elastic constants in order to reproduce the stiffness matrix of the composite is an inverse wave propagation problem described by the Christoffel equation. The damage initiation and propagation as depicted by the deterioration of the moduli of the material was described using deterministic and stochastic approaches. Finally, the damage accumulation process was simulated as a Markov process.

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Moshki, Alireza, Akbar Ghazavizadeh, Ali Asghar Atai, Mostafa Baghani, and Majid Baniassadi. "3D-Printable Unit Cell Design for Cubic and Orthotropic Porous Microstructures Using Topology Optimization Based on Optimality Criteria Algorithm." International Journal of Applied Mechanics 10, no. 06 (July 2018): 1850060. http://dx.doi.org/10.1142/s1758825118500606.

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Optimal design of porous and periodic microstructures through topology identification of the associated periodic unit cell (PUC) constitutes the topic of this work. Here, the attention is confined to two-phase heterogeneous materials in which the topology identification of manufacturable 3D-PUC is conducted by means of a topology optimization technique. The associated objective function is coupled with 3D numerical homogenization approach that connects the elastic properties of the 3D-PUC to the target product. The topology optimization methodology that is adopted in this study is the combination of solid isotropic material with penalization (SIMP) method and optimality criteria algorithm (OCA), referred to as SIMP-OCA methodology. The fairly simple SIMP-OCA is then generalized to handle the topology design of 3D manufacturable microstructures of cubic and orthotropic symmetry. The performance of the presented methodology is experimentally validated by fabricating real prototypes of extremal elastic constants using additive manufacturing. Experimental evaluation is performed on two designed microstructures: an orthotropic sample with Young’s moduli ratios [Formula: see text], [Formula: see text] and a cubic sample with negative Poisson’s ratio of [Formula: see text]. In all practical examples studied, laboratory measurements are in reasonable agreement with the prescribed values; thus, corroborating the applicability of the proposed methodology.

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Smardzewski, Jerzy, Adam Gajęcki, and Marlena Wojnowska. "Investigation of elastic properties of paper honeycomb panels with rectangular cells." BioResources 14, no. 1 (January 8, 2019): 1435–51. http://dx.doi.org/10.15376/biores.14.1.1435-1451.

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Multilayer panels that have paper cores with hexagonal cells continue to have a limited application in furniture production. In contrast, there are no sandwich honeycomb panels with cores containing rectangular cells employed in this industry. Such cores should distinguish themselves by strong orthotropic advantages, in particular, for designing shelves and partitions of cabinet furniture. Hence, the objective of this study was to determine the effect of core rectangular paper cells on the mechanical properties of three-layer furniture panels. The authors decided to ascertain relative density and elasticity constants of the designed cells. The results of empirical experiments of cell elasticity moduli were compared with the results of the analytical calculations. The impact of sample width on their mechanical properties was determined. It was demonstrated that cores with hexagonal cells in furniture panels could be replaced by cores with rectangular cells.

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Leonetti, Lorenzo, Nicholas Fantuzzi, Patrizia Trovalusci, and Francesco Tornabene. "Scale Effects in Orthotropic Composite Assemblies as Micropolar Continua: A Comparison between Weak- and Strong-Form Finite Element Solutions." Materials 12, no. 5 (March 5, 2019): 758. http://dx.doi.org/10.3390/ma12050758.

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The aim of the present work was to investigate the mechanical behavior of orthotropic composites, such as masonry assemblies, subjected to localized loads described as micropolar materials. Micropolar models are known to be effective in modeling the actual behavior of microstructured solids in the presence of localized loads or geometrical discontinuities. This is due to the introduction of an additional degree of freedom (the micro-rotation) in the kinematic model, if compared to the classical continuum and the related strain and stress measures. In particular, it was shown in the literature that brick/block masonry can be satisfactorily modeled as a micropolar continuum, and here it is assumed as a reference orthotropic composite material. The in-plane elastic response of panels made of orthotropic arrangements of bricks of different sizes is analyzed herein. Numerical simulations are provided by comparing weak and strong finite element formulations. The scale effect is investigated, as well as the significant role played by the relative rotation, which is a peculiar strain measure of micropolar continua related to the non-symmetry of strain and work-conjugated stress. In particular, the anisotropic effects accounting for the micropolar moduli, related to the variation of microstructure internal sizes, are highlighted.

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Dasgupta, A., and S. M. Bhandarkar. "Effective Thermomechanical Behavior of Plain-Weave Fabric-Reinforced Composites Using Homogenization Theory." Journal of Engineering Materials and Technology 116, no. 1 (January 1, 1994): 99–105. http://dx.doi.org/10.1115/1.2904262.

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A micromechanical analysis is presented to obtain the effective macroscale orthotropic thermomechanical behavior of plain-weave fabric reinforced laminated composites based on a two-scale asymptotic homogenization theory. The model is based on the properties of the constituents and an accurate, three-dimensional simulation of the weave microarchitecture, and is used for predicting the thermomechanical behavior of glass-epoxy (FR-4) woven-fabric laminates typically used by the electronics industry in Multilayered Printed Wiring Boards (MLBs). Parametric studies are conducted to examine the effect of varying fiber volume fractions on constitutive properties. Nonlinear constitutive behavior due to matrix nonlinearity and post-damage behavior due to transverse yarn failure under in-plane uniaxial loads is then investigated. Numerical results obtained from the model show good agreement with experimental values and with data from the literature. This model may be utilized by material designers to design and manufacture fabric reinforced composites with tailored effective properties such as elastic moduli, shear moduli, Poisson’s ratio, and coefficients of thermal expansion.

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Krüger, Robert, and André Wagenführ. "Comparison of methods for determining shear modulus of wood." European Journal of Wood and Wood Products 78, no. 6 (July 7, 2020): 1087–94. http://dx.doi.org/10.1007/s00107-020-01565-2.

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Abstract In this study, the relatively new picture frame method applied to wood is compared with three established shear test methods, namely the experimental modal analysis, the square plate twist method and the torsion test. For the investigations, the wood species European beech (Fagus sylvatica L.) and spruce (Picea abies L. Karst.) were used and the shear tests were conducted in LR and RL direction. The results show comparable shear moduli for beech and spruce in the range of 931–1289 Nmm−2 and 495–842 Nmm−2, respectively. In contrast to the theory of linear elastic orthotropic materials, significant differences in the results of the picture frame method between LR and RL direction were observed for spruce.

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Srivastava, P. K., P. Mahajan, P. K. Satyawali, and V. Kumar. "Observation of temperature gradient metamorphism in snow by X-ray computed microtomography: measurement of microstructure parameters and simulation of linear elastic properties." Annals of Glaciology 51, no. 54 (2010): 73–82. http://dx.doi.org/10.3189/172756410791386571.

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AbstractThe process of temperature gradient metamorphism in snow strongly affects the microstructure and associated mechanical properties of the snow. The purpose of this study was to: (1) examine the temporal variations in three-dimensional snow microstructure under the influence of a strong temperature gradient for 6 days using X-ray computed microtomography (μCT); and (2) numerically simulate the linear elastic properties of snow from microtomographic data using a voxel-based finite-element technique. The temporal changes in the snow structure were analyzed in terms of density, specific surface area (SSA), thickness distribution of ice matrix and pores, structure model index and mean intercept length (MIL) fabric tensor. The structural indices and orthotropic elastic compliance matrix were computed over several sub-volumes within the reconstructed volume to account for statistical uncertainties. The mean density increased by about 14% on day 1 and no significant trend was observed thereafter. The SSA decreased by 22%, whereas both the ice and pore thickness distributions widened with time. The computed Young’s moduli were 1.5–4 times larger than previously published dynamic measurements and found to be significantly correlated with ice volume fraction and MIL fabric measures. The increasing trend in computed moduli during the experiment is consistent with the observed development of thicker vertical ice structures. Multiple linear regression models of elastic compliances using fabric tensor formulation and ice volume fraction could explain 89.9–93.0% of the variance. Our results suggest a strong dependence of elastic properties on both density and microstructural fabric.

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Savchenko, V. G. "Nonaxisymmetric Deformation of Solids of Revolution Made of Elastic Orthotropic Materials with Different Tensile and Compressive Moduli." International Applied Mechanics 41, no. 7 (July 2005): 748–56. http://dx.doi.org/10.1007/s10778-005-0141-1.

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Kohles, Sean S., and Julie B. Roberts. "Linear Poroelastic Cancellous Bone Anisotropy: Trabecular Solid Elastic and Fluid Transport Properties." Journal of Biomechanical Engineering 124, no. 5 (September 30, 2002): 521–26. http://dx.doi.org/10.1115/1.1503374.

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The mechanical performance of cancellous bone is characterized using experiments which apply linear poroelasticity theory. It is hypothesized that the anisotropic organization of the solid and pore volumes of cancellous bone can be physically characterized separately (no deformable boundary interactive effects) within the same bone sample. Due to its spongy construction, the in vivo mechanical function of cancellous or trabecular bone is dependent upon fluid and solid materials which may interact in a hydraulic, convective fashion during functional loading. This project provides insight into the organization of the tissue, i.e., the trabecular connectivity, by defining the separate nature of this biphasic performance. Previous fluid flow experiments [Kohles et al., 2001, Journal of Biomechanics, 34(11), pp. 1197–1202] describe the pore space via orthotropic permeability. Ultrasonic wave propagation through the trabecular network is used to describe the solid component via orthotropic elastic moduli and material stiffness coefficients. The linear poroelastic nature of the tissue is further described by relating transport (fluid flow) and elasticity (trabecular load transmission) during regression analysis. In addition, an empirical relationship between permeability and porosity is applied to the collected data. Mean parameters in the superior-inferior (SI) orientation of cubic samples n=20 harvested from a single bovine distal femur were the largest p<0.05 in comparison to medial-lateral (ML) and anterior-posterior (AP) orientations: Apparent elastic modulus (2,139 MPa), permeability (4.65×10−10 m2), and material stiffness coefficient (13.6 GPa). A negative correlation between permeability as a predictor of structural elastic modulus supported a parametric relationship in the ML R2=0.4793, AP R2=0.3018, and SI R2=0.6445 directions p<0.05.

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Bonora, N., M. Marchetti, and P. P. Milella. "Theoretical Forecasting and Experimental Validation of Damage Tolerance and Accumulation in Glass/Epoxy Laminates." Journal of Reinforced Plastics and Composites 11, no. 1 (January 1992): 56–81. http://dx.doi.org/10.1177/073168449201100104.

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Damage and damage accumulation mechanisms under cyclic loads were studied in orthotropic cross-ply composite laminates realized in S-glass fibers with epoxy resin. Five different basic mechanisms of damage were observed and evaluated making use of x-ray and dye-penetrant nondestructive techniques. They are: transverse matrix cracks, fiber failure, fiber debonding, intralaminar delamination and random disperse longitudinal cracks. The effects of these different damage mechanisms are revealed through the reduction of the mechanical properties of the composite material. A comprehensive experimental analysis of GFRP and CFRP, with two different lay-ups for each one, was made. Variations of the elastic moduli in two different directions and Poisson's ratio were measured as a function of the number of cycles, for different stress levels, under alternate loads. The basic relations, developed by Talreja et al., which permit the prediction of the reduction of the elastic moduli for a given damage state, were directly related to the number of cycles N and to the stress levels employed in the fatigue tests. Tests to evaluate an eventual frequency effect on damage accumulation processes in composite material were made. Cumulative damage tests were also conducted to analyse material response under different and alternate load spectra. A damage index based on residual normalized strain energy ratio, which can describe a global damage state, is also proposed.

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Shahsavar, Vahid Lal, and Samira Tofighi. "Uncertainties Concerning the Free Vibration of Inhomogeneous Orthotropic Reinforced Concrete Plates." Slovak Journal of Civil Engineering 22, no. 3 (September 1, 2014): 21–30. http://dx.doi.org/10.2478/sjce-2014-0014.

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Abstract Analyzing nearly collapsed and broken structures gives good insights into possible architectural and engineering design mistakes and faults in the detailing and mismanagement of a construction by building contractors. Harmful vibration effects of construction operations occur frequently. The background reviews have demonstrated that the problem of the vibration serviceability of long-span concrete floors in buildings is complex and interdisciplinary in nature. In public buildings, floor vibration control is required in order to meet Serviceability Limit States that ensure the comfort of the users of a building. In industrial buildings, machines are often placed on floors. Machines generate vibrations of various frequencies, which are transferred to supporting constructions. Precision machines require a stable floor with defined and known dynamic characteristics. In recent years there has been increasing interest in the motion of elastic bodies whose material properties (density, elastic moduli, etc.) are not constant, but vary with their position, perhaps in a random manner. Concrete is a non-homogeneous and anisotropic material. Modeling the mechanical behavior of reinforced concrete (RC) is still one of the most difficult challenges in the field of structural engineering. One of several methods for determining the dynamic modulus of the elasticity of engineering materials is the vibration frequency procedure. In this method, the required variables except for the modulus of elasticity are accurately and certainly determined. In this research, the uncertainly analysis of the free vibration of inhomogeneous orthotropic reinforced concrete plates has been investigated. Due to the numerous outputs obtained, the software package has been written in Matlab, and an analysis of the data and drawing related charts has been done.

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Derevianko, I., K. Avramov, B. Uspensky, and A. Salenko. "Experimental analysis of the mechanical characteristics of launch vehicle parts manufactured by FDM additive technologies." Technical mechanics 2021, no. 1 (April 30, 2021): 92–100. http://dx.doi.org/10.15407/itm2021.01.092.

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Additive manufacturing is very promising for aerospace engineering and aircraft construction. Using these technologies, light structures with preset strength properties can be made. For lack of tables of the mechanical properties of materials made by additive technologies, any calculation must be accompanied by the experimental determination of their mechanical properties. This paper presents an experimental approach to the determination of the mechanical characteristics of parts printed by FDM technologies. Parts manufactured from polymers by FDM technologies are shown to be orthotropic. Therefore, their elastic properties are described by nine constants: three Young’s moduli, three shear moduli, and three Poisson ratios. A cube is printed for the experimental determination of these constants. Six specimens are cut out from the cube. Three specimens are cut parallel to the cube edges, and the other three are cut at an angle of 45° to them. Each such specimen is manufactured in five pieces. This makes it possible to average the tensile stress–strain diagrams obtained for all the components of the stress tensor. The mechanical properties of the material are determined from these diagrams. The three Young’s moduli and the three Poisson ratios are determined from the three specimen types parallel to the cube edges. The three shear moduli are determined from the specimens cut at an angle of 45° to the cube edges. To determine these constants, tensile stress–strain diagrams are obtained experimentally. A technology is presented for manufacturing specimens on a Stratasys FORTUS 900 MC 3D printer. The mechanical properties of two polymer materials (ULTEM 9085 and PLA) are determined and compared. PLA has higher Young’s moduli and shear moduli and lower Poisson ratios than ULTEM 9085.

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Abdulhamid, Hakim, Paul Deconinck, Pierre-Louis Héreil, and Jérôme Mespoulet. "Study of the ballistic behaviour of UHMWPE composite material: experimental characterization and numerical simulation." EPJ Web of Conferences 183 (2018): 01051. http://dx.doi.org/10.1051/epjconf/201818301051.

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This paper presents a comprehensive mechanical study of UHMWPE (Ultra High Molecular Weight Polyethylene) composite material under dynamic loadings. The aim of the study is to provide reliable experimental data for building and validate the composite material model under impact. Four types of characterization tests have been conducted: dynamic in-plane tension, out-of-plane compression, shear tests and plate impact tests. Then, several impacts of spherical projectiles have been performed. Regarding the numerical simulation, an intermediate scale multi-layered model (between meso and macro scale levels) is proposed. The material response is modelled with a 3d elastic orthotropic law coupled with fibre damage model. The modelling choice is governed by a balance between reliability and computing cost. Material dynamic response is unconventional [1, 2]: it shows large deformation before failure, very low shear modulus and peeling strength. Numerical simulation has been used both in the design and the analysis of tests. Many mechanical properties have been measured: elastic moduli, failure strength and EOS of the material. The numerical model is able to reproduce the main behaviours observed in the experiment. The study has highlighted the influence of temperature and fibre slipping in the impact response of the material.

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Shevtsov, Sergey, Valery Chebanenko, Maria Shevtsova, Shun-Hsyung Chang, Evgenia Kirillova, and Evgeny Rozhkov. "On the Directivity of Lamb Waves Generated by Wedge PZT Actuator in Thin CFRP Panel." Materials 13, no. 4 (February 18, 2020): 907. http://dx.doi.org/10.3390/ma13040907.

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This paper addresses investigation of guided-wave excitation by angle-beam wedge piezoelectric (PZT) transducers in multilayered composite plate structure with orthotropic symmetry of the material. The aim of the present study is to determine the capability of such actuators to provide the controlled generation of an acoustic wave of a desirable type with the necessary wavelength, propagation distance and directivity. The studied CFRP (Carbon Fiber Reinforced Plastic) panel is considered to be homogenous, with effective elastic moduli and anisotropic structural damping, whose parameters were determined experimentally. According to the results of dispersion analysis and taking into account the data of wave attenuation in a highly damping CFRP composite, the two types of propagating waves A0 and S0 were considered theoretically and experimentally in the frequency range of 10–100 kHz. Using the results of a previous study, we reconstructed the structure of the wedge actuator, to develop its finite-element (FE) model, and a modal analysis was carried out that revealed the most intense natural vibration modes and their eigenfrequencies within the frequency range used. Both experimental and numerical studies of the generation, propagation, directivity and attenuation of waves in the orthotropic composite panel under study revealed the influence of the angular orientation of the actuator on the formation of wave patterns and allowed to determine the capabilities of the wave’s directivity control.

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Bazˇant, Z. P. "Shear Buckling of Sandwich, Fiber Composite and Lattice Columns, Bearings, and Helical Springs: Paradox Resolved." Journal of Applied Mechanics 70, no. 1 (January 1, 2003): 75–83. http://dx.doi.org/10.1115/1.1509486.

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As shown three decades ago, in situations where the initial stresses before buckling are not negligible compared to the elastic moduli, the geometrical dependence of the tangential moduli on the initial stresses must be taken into account in stability analysis, and the stability or bifurcation criteria have different forms for tangential moduli associated with different choices of the finite strain measure. So it has appeared paradoxical that, for sandwich columns, different but equally plausible assumptions yield different formulas, Engesser’s and Haringx’ formulas, even though the axial stress in the skins is negligible compared to the axial elastic modulus of the skins and the axial stress in the core is negligible compared to the shear modulus of the core. This apparent paradox is explained by variational energy analysis. It is shown that the shear stiffness of a sandwich column, provided by the core, generally depends on the axial force carried by the skins if that force is not negligible compared to the shear stiffness of the column (if the column is short). The Engesser-type, Haringx-type, and other possible formulas associated with different finite strain measures are all, in principle, equivalent, although a different shear stiffness of the core, depending linearly on the applied axial load, must be used for each. The Haringx-type formula, however, is most convenient because it represents the only case in which the shear modulus of the core can be considered to be independent of the axial force in the skins and to be equal to the shear modulus measured in simple shear tests (e.g., torsional test). Extensions of the analysis further show that Haringx’s formula is preferable for a highly orthotropic composite because a constant shear modulus of the soft matrix can be used for calculating the shear stiffness of the column, and further confirm that Haringx’s buckling formula with a constant shear stiffness is appropriate for helical springs and built-up columns (laced or battened).

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Tevet, Ofer, David Svetlizky, David Harel, Zahava Barkay, Dolev Geva, and Noam Eliaz. "Measurement of the Anisotropic Dynamic Elastic Constants of Additive Manufactured and Wrought Ti6Al4V Alloys." Materials 15, no. 2 (January 15, 2022): 638. http://dx.doi.org/10.3390/ma15020638.

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Additively manufactured (AM) materials and hot rolled materials are typically orthotropic, and exhibit anisotropic elastic properties. This paper elucidates the anisotropic elastic properties (Young’s modulus, shear modulus, and Poisson’s ratio) of Ti6Al4V alloy in four different conditions: three AM (by selective laser melting, SLM, electron beam melting, EBM, and directed energy deposition, DED, processes) and one wrought alloy (for comparison). A specially designed polygon sample allowed measurement of 12 sound wave velocities (SWVs), employing the dynamic pulse-echo ultrasonic technique. In conjunction with the measured density values, these SWVs enabled deriving of the tensor of elastic constants (Cij) and the three-dimensional (3D) Young’s moduli maps. Electron backscatter diffraction (EBSD) and micro-computed tomography (μCT) were employed to characterize the grain size and orientation as well as porosity and other defects which could explain the difference in the measured elastic constants of the four materials. All three types of AM materials showed only minor anisotropy. The wrought (hot rolled) alloy exhibited the highest density, virtually pore-free μCT images, and the highest ultrasonic anisotropy and polarity behavior. EBSD analysis revealed that a thin β-phase layer that formed along the elongated grain boundaries caused the ultrasonic polarity behavior. The finding that the elastic properties depend on the manufacturing process and on the angle relative to either the rolling direction or the AM build direction should be taken into account in the design of products. The data reported herein is valuable for materials selection and finite element analyses in mechanical design. The pulse-echo measurement procedure employed in this study may be further adapted and used for quality control of AM materials and parts.

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Vishnuvardhan, J., C. V. Krishnamurthy, and Krishnan Balasubramaniam. "Genetic algorithm based reconstruction of the elastic moduli of orthotropic plates using an ultrasonic guided wave single-transmitter-multiple-receiver SHM array." Smart Materials and Structures 16, no. 5 (August 8, 2007): 1639–50. http://dx.doi.org/10.1088/0964-1726/16/5/017.

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Lysenko, A., L. Parshina, and B. Yartsev. "Effective mechanical characteristics of symmetric layered composite in different loading conditions." Transactions of the Krylov State Research Centre 1, no. 399 (March 15, 2022): 75–88. http://dx.doi.org/10.24937/2542-2324-2022-1-399-75-88.

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Object and purpose of research. This paper discusses balanced and quasi-isotropic (in the reinforcement plane) symmetric layered composite structures made up by the layers of cloth-reinforced GRP. The purpose of this work was to demonstrate the necessity to justify the applicability of experimental results for effective mechanical parameters determined in the conditions of uniaxial tension/compression to the calculation of thin-walled layered composite structures that work in bending/twisting conditions. Materials and methods. The straining of layered composite structures is simulated as per the updated theory of first-order plates, the model of complex moduli and the principle of elastic-viscoelastic correspondence in linear viscoelasticity theory. Limit state predictions are based on Tsai-Wu tensor-polynomial strength criterion. Main results. This paper suggests the expressions that predict effective elastic constants, dissipation properties and strength limits for symmetric layered structures under investigation. The study shows that balanced symmetric structure made up by four layers of composite may be regarded, with the accuracy sufficient for engineering calculations, as an ortho-tropic material for all loading conditions. At the same time, symmetric quasi-isotropic (in the reinforcement plane) structure made up by thirty two composite layers must be regarded as orthotropic in case of tension/compression and monoclinic in case of bending/twisting. Conclusion. The study has shown the necessity to justify the application of experimental effective mechanical properties for uniaxial tension/compression to calculation of thin-walled layered composite structures exposed to bending/twisting.

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Ju, J. W., and K. Yanase. "Elastoplastic damage micromechanics for elliptical fiber composites with progressive partial fiber debonding and thermal residual stresses." Theoretical and Applied Mechanics 35, no. 1-3 (2008): 137–70. http://dx.doi.org/10.2298/tam0803137j.

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Incorporating the interfacial damage and thermal residual stresses, an elasto-plastic damage formulation is proposed to predict the overall transverse mechanical behavior of continuous elliptical-fiber reinforced ductile matrix composites within the framework of micromechanics and homogenization. Based on the concept of equivalent inclusion and taking the progressive interfacial debonding angle into consideration, partially debonded fibers are replaced by equivalent orthotropic, perfectly bonded fibers. Three interfacial damage modes are considered. The Weibull's probabilistic function is adopted to describe the varying probability of progressive partial fiber debonding. The effective elastic moduli of four-phase composites, composed of a ductile matrix and randomly located yet unidirectionally aligned fibers are derived by a micromechanical formulation. Thermal residual stresses are taken into account through the concept of thermal eigenstrain to investigate the effects of the manufacturing processinduced residual stresses. Employing the micromechanical approximation, the overall stress-strain responses and the effective yield function are formulated with the thermal eigenstrain. When comparing with the available experimental data, significant effects of thermal residual stresses are discussed. Moreover, the effects of the interfacial strengths and the cross- sectional shapes of fibers on the mechanical behaviors of composites are systematically investigated.

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Journal articles on the topic 'Orthotropic Elastic Moduli'

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