Artykuły w czasopismach: „Anisotropic elastic materials”

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Shen, Xianda, Giuseppe Buscarnera i Fengshou Zhang. "Anisotropic Breakage Mechanics for cemented granular materials". IOP Conference Series: Earth and Environmental Science 1330, nr 1 (1.05.2024): 012049. http://dx.doi.org/10.1088/1755-1315/1330/1/012049.

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Abstract The anisotropy of granular geomaterials is sensitive to their fabric, which exhibits anisotropic mechanical properties as a function of deposition history, microscopic fabric, and loading paths. Here, a new fabric-enriched continuum breakage model is proposed to examine the relation between elastic and inelastic anisotropy in granular materials and cemented granular materials. A microstructure model is first implemented in the framework of fabric-enriched continuum breakage mechanics (F-CBM), where the anisotropic behaviour prior to yielding is introduced through a symmetric second-order fabric tensor embedded in the expression of the elastic energy potential. The anisotropic strain energy storage prior to grain crushing leads to the rotation and distortion of the yield surface of cemented granular materials. Parametric analyses are performed to assess the overall capability of the model to characterize the anisotropic inelastic processes in cemented granular. It is shown that the proposed model can accurately predict the strong correlation between anisotropic elasticity and breakage-damage processes in cemented granular materials. When damage involving the skeleton is the dominant inelastic process, the size of the elastic domain contracts and the material exhibits augmented brittleness with the disintegration of cement. While breakage processes are predicted to dominate the response of lightly cemented granular materials resulting in hardening behaviour. This work can be further extended to dynamically capture the anisotropic response of cemented granular materials with water-sensitive mineral constituents by accounting for the evolution of microstructural anisotropy.

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Kaldar-ool, A. K. B., R. N. Sandan i A. Kh H. Mongush. "Elastic con- stants of cylindrically anisotropic material". Vestnik Tomskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta. JOURNAL of Construction and Architecture 26, nr 3 (13.06.2024): 158–69. http://dx.doi.org/10.31675/1607-1859-2024-26-3-158-169.

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This article examines new cylindrically anisotropic materials, including winding composite materials reinforced with various fiber, and a mathematical solution of the fourth-order partial differential equation with two variables in polar coordinates.Purpose: Ther aim of this work is to study anisotropy properties of composite materials with cylindrical anisotropy.Methodology/approach: Foe a solution, equations are translated into Cartesian coordinates, and stress functions are used as a sum of polynomials. As a result of the solution, two relations are obtained between the elastic constants in the main direction of anisotropy, i.e., elasticity parameters. These parameters are important to determine the mechanical properties of anisotropic material.Research findings: New high-strength composite materials are improved to apply in new technologies for building design and construction, high-strength structures are obtained using synthetic composite materials.Originality/value: Elastic constants for cylindrically anisotropic materials represent an innovative approach to determine the properties of composite materials with a flat anisotropy scheme, which make it easier and more efficient to determine elasticity parameters and strength in an arbitrary direction of coordinate axes.

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Krivosheina, Marina N. "Simulation of the stress state in barriers made of anisotropic materials". Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, nr 79 (2022): 89–99. http://dx.doi.org/10.17223/19988621/79/8.

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To study the properties of anisotropic materials, a mathematical model is proposed that accounts for the anisotropy of elastic and plastic properties, as well as the anisotropy of “thermal” and “cold” components of pressure. The model is applied in a threedimensional simulation of the deformation of an HCP-single-crystal barrier under impact loading by an aluminum impactor. The numerical simulation results are obtained using the dynamic finite element method with a difference scheme modified to account for the anisotropy of “cold” and “thermal” pressure components. To simulate the anisotropy of the stress deviator in the region of elastic deformations, generalized Hooke's law is used, while in the region of plastic deformations, the Mises-Hill plasticity function (Hill48) is used with account for the anisotropy of elastic properties and anisotropy of the Gruneisen coefficient. The experimentally and numerically obtained velocity profiles of the back surfaces of single-crystal zinc barriers during the spall fracture are compared with each other. When the impact loading direction coincides with [0001] axis, the elastic precursor is not observed on the velocity profile calculated numerically, which is the same for the one derived experimentally. This effect may be explained only with the use of anisotropic pressur.

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Ding, Chao, Jian Wang, Tianhan Liu, Hongbo Qin, Daoguo Yang i Guoqi Zhang. "The Mechanical Properties and Elastic Anisotropy of η′-Cu6Sn5 and Cu3Sn Intermetallic Compounds". Crystals 11, nr 12 (14.12.2021): 1562. http://dx.doi.org/10.3390/cryst11121562.

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Full intermetallic compound (IMC) solder joints present fascinating advantages in high-temperature applications. In this study, the mechanical properties and elastic anisotropy of η′-Cu6Sn5 and Cu3Sn intermetallic compounds were investigated using first-principles calculations. The values of single-crystal elastic constants, the elastic (E), shear (G), and bulk (B) moduli, and Poisson’s ratio (ν) were identified. In addition, the two values of G/B and ν indicated that the two IMCs were ductile materials. The elastic anisotropy of η′-Cu6Sn5 was found to be higher than Cu3Sn by calculating the universal anisotropic index. Furthermore, an interesting discovery was that the above two types of monocrystalline IMC exhibited mechanical anisotropic behavior. Specifically, the anisotropic degree of E and B complied with the following relationship: η′-Cu6Sn5 > Cu3Sn; however, the relationship was Cu3Sn > η′-Cu6Sn5 for the G. It is noted that the anisotropic degree of E and G was similar for the two IMCs. In addition, the anisotropy of the B was higher than the G and E, respectively, for η′-Cu6Sn5; however, in the case of Cu3Sn, the anisotropic degree of B, G, and E was similar.

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Gurvich, Mark R. "On Characterization of Anisotropic Elastomeric Materials for Structural Analysis". Rubber Chemistry and Technology 77, nr 1 (1.03.2004): 115–30. http://dx.doi.org/10.5254/1.3547805.

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Abstract Existing efforts in constitutive modeling of elastomers are primarily focused on isotropic materials. On the other hand, anisotropic elastic models were successfully developed for traditional composites with relatively small strains, where geometrical non-linearity of deformation may be ignored. There are, however, certain materials where neither large deformation and incompressibility nor anisotropy of material stiffness may be neglected. This study proposes a general constitutive approach to model both hyperelasticity (including incompressibility) and full anisotropy of material deformation in structural analysis. According to the proposed approach, an original hyperelastic anisotropic body is modeled as a combination of two hypothetical components (hyperelastic isotropic and elastic anisotropic ones). The proposed approach shows simplicity and convenience of practical application along with high accuracy of analysis. It may be easily implemented in computational analysis of 2- and 3-D problems using commercially available FEA codes without additional programming efforts. Analytical and computational implementation of the approach is considered on representative examples of elastomeric structures and rubber-based composites. Analytical solutions are shown for examples of biaxial tension of composites and inflation of a toroidal anisotropic tube. FEA solutions are discussed on examples of an inflated anisotropic sphere and non-uniform deformation of a composite layer. Obtained results are discussed to emphasize benefits of the proposed approach. Finally, a methodology to evaluate material parameters using corresponding test results is considered according to the proposed approach.

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CLEMENTS, DAVID L. "ON AN ANTIPLANE CRACK PROBLEM FOR FUNCTIONALLY GRADED ELASTIC MATERIALS". ANZIAM Journal 52, nr 1 (lipiec 2010): 69–86. http://dx.doi.org/10.1017/s1446181111000551.

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AbstractThis paper examines an antiplane crack problem for a functionally graded anisotropic elastic material in which the elastic moduli vary quadratically with the spatial coordinates. A solution to the crack problem is obtained in terms of a pair of integral equations. An iterative solution to the integral equations is used to examine the effect of the anisotropy and varying elastic moduli on the crack tip stress intensity factors and the crack displacement.

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Sokolova, Marina Yu, i Dmitriy V. Khristich. "On the inversion of nonlinear constitutive relations for hyperelastic anisotropic materials". Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, nr 85 (2023): 157–67. https://doi.org/10.17223/19988621/85/12.

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The polynomial elastic potentials represented by the power functions of their arguments are considered for hyperelastic anisotropic materials. The conditions for the elastic free energy W(e) and Gibbs potential V(T) in isothermal processes are assigned so that the nonlinear constitutive relations can be inverted. For polynomial elastic potentials, whose coefficients are dependent on elastic constants of the second and third orders, a dependence between the coefficients of the potential W(e) (elasticity constants) and the coefficients of the potential V(T) (elastic compliances) is obtained. The relationships between the elastic constants and the coefficients of elastic compliance of the second and third orders for an isotropic material and for an anisotropic material corresponding to a cubic crystallographic system are found. For a copper crystal belonging to the cubic system, uniaxial loading along one of the anisotropy axes is considered. The stress-strain dependence obtained from direct and inverted relations coincides in the vicinity of zero. The stress-strain dependence calculated using direct and inverted relations for copper crystals has made it possible to determine the strain range in which the results of calculations using direct and inverted relations differ by less than 5%.

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Felippa, Carlos A., i Eugenio On˜ate. "Volumetric Constraint Models for Anisotropic Elastic Solids". Journal of Applied Mechanics 71, nr 5 (1.09.2004): 731–34. http://dx.doi.org/10.1115/1.1748318.

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We study three “incompressibility flavors” of linearly elastic anisotropic solids that exhibit volumetric constraints: isochoric, hydroisochoric, and rigidtropic. An isochoric material deforms without volume change under any stress system. An hydroisochoric material does so under hydrostatic stress. A rigidtropic material undergoes zero deformations under a certain stress pattern. Whereas the three models coalesce for isotropic materials, important differences appear for anisotropic behavior. We find that isochoric and hydroisochoric models under certain conditions may be hampered by unstable physical behavior. Rigidtropic models can represent semistable physical materials of arbitrary anisotropy while including isochoric and hydroisochoric behavior as special cases.

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Yu, Jing, Yongmei Zhang, Yuhong Zhao i Yue Ma. "Anisotropies in Elasticity, Sound Velocity, and Minimum Thermal Conductivity of Low Borides VxBy Compounds". Metals 11, nr 4 (1.04.2021): 577. http://dx.doi.org/10.3390/met11040577.

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Anisotropies in the elasticity, sound velocity, and minimum thermal conductivity of low borides VB, V5B6, V3B4, and V2B3 are discussed using the first-principles calculations. The various elastic anisotropic indexes (AU, Acomp, and Ashear), three-dimensional (3D) surface contours, and their planar projections among different crystallographic planes of bulk modulus, shear modulus, and Young’s modulus are used to characterize elastic anisotropy. The bulk, shear, and Young’s moduli all show relatively strong degrees of anisotropy. With increased B content, the degree of anisotropy of the bulk modulus increases while those of the shear modulus and Young’s modulus decrease. The anisotropies of the sound velocity in the different planes show obvious differences. Meanwhile, the minimum thermal conductivity shows little dependence on crystallographic direction.

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Vladimirov, Ivaylo N., i Stefanie Reese. "Prediction of Springback in Unconstrained Bending by a Model for Evolving Elastic and Plastic Anisotropy". Key Engineering Materials 554-557 (czerwiec 2013): 2330–37. http://dx.doi.org/10.4028/www.scientific.net/kem.554-557.2330.

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Sheet metals exhibit anisotropic plastic behavior due to the large plastic deformations that occur during the rolling of the sheet and which induce texture and are responsible for the initial anisotropy. There exist various possibilities to introduce plastic anisotropy into the finite element modelling of sheet metal forming. The initial yield anisotropy can be incorporated either through an anisotropic yield surface or directly by means of a crystallographic texture model. Here, one basically differentiates between empirical and phenomenological anisotropic yield function equations, where the anisotropy coefficients can be obtained from mechanical tests, and texture-based models the coefficients of which are directly determined based on experimentally obtained orientation distributions. Another type of anisotropy that can be usually found in anisotropic materials is the elastic anisotropy. In metal plasticity one often considers the effect of elastic anisotropy significantly smaller than the effect of plastic anisotropy. Consequently, elastic isotropic expressions are often used for elastic stored energy functions with anisotropic yield criteria. However, the influence of elastic anisotropy in the elastoplastic behavior can be very important especially during elastic recovery processes during unloading after forming and springback. This research focuses, therefore, on the study of the influence of elastic anisotropy on the amount of springback in bending processes such as e.g. unconstrained bending. We discuss a finite strain material model for evolving elastic and plastic anisotropy combining nonlinear isotropic and kinematic hardening. The evolution of elastic anisotropy is described by representing the Helmholtz free energy as a function of a family of evolving structure tensors. In addition, plastic anisotropy is modelled via the dependence of the yield surface on the same family of structure tensors. Exploiting the dissipation inequality leads to the interesting result that all tensor-valued internal variables are symmetric. Thus, the integration of the evolution equations can be efficiently performed by means of an algorithm that automatically retains the symmetry of the internal variables in every time step. The material model has been implemented as a user material subroutine UMAT into the commercial finite element software ABAQUS/Standard and has been applied to the simulation of springback of unconstrained bending.

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Okoye, Patrick N., Ping Zhao i Norm F. Uren. "Inversion technique for recovering the elastic constants of transversely isotropic materials". GEOPHYSICS 61, nr 5 (wrzesień 1996): 1247–57. http://dx.doi.org/10.1190/1.1444049.

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A least‐squares iterative inversion technique has been developed for the determination of the elastic parameter δ* of any transversely isotropic modeling material in the laboratory. For most applications in petroleum geophysics, the elastic parameter δ* is very important and is the crucial anisotropic parameter for near‐vertical P‐wave propagation. Despite the potential importance of δ* in seismic exploration and for resolution in an anisotropic medium, the conventional procedures adopted in estimating its value unfortunately are faced with many ambiguities and the reliability of its measurement is doubtful prior to the development of this technique. The anisotropic inverse modeling technique finds the best fitting solution. To optimize the accuracy of the results presented in this paper, analytical rather than numerical differentiations were implemented and the modeling procedures allow for controlled iterative adjustments in resolving the parameter δ*. Inversion of the first‐arrival traveltimes obtained for vertical P‐waves through an anisotropic material known as phenolite yield estimates of the elastic parameter δ* as well as the vertical P‐wave velocity [Formula: see text] of the material. Accurate picking of the first‐arrival traveltimes is essential since δ* is found to be very sensitive to small differences between vertical and oblique traveltime picks. The inversion results have been found to be stable and convergent, and they also highlight the need for good angular coverage to determine the anisotropy parameters in materials suspected of being anisotropic.

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Alshits, V. I., i H. O. K. Kirchner. "Cylindrically anisotropic, radially inhomogeneous elastic materials". Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 457, nr 2007 (8.03.2001): 671–93. http://dx.doi.org/10.1098/rspa.2000.0687.

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MEHRABADI, MORTEZA M., i STEPHEN C. COWIN. "EIGENTENSORS OF LINEAR ANISOTROPIC ELASTIC MATERIALS". Quarterly Journal of Mechanics and Applied Mathematics 43, nr 1 (1990): 15–41. http://dx.doi.org/10.1093/qjmam/43.1.15.

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MEHRABADI, MORTEZA M., i STEPHEN C. COWIN. "EIGENTENSORS OF LINEAR ANISOTROPIC ELASTIC MATERIALS". Quarterly Journal of Mechanics and Applied Mathematics 44, nr 2 (1991): 331. http://dx.doi.org/10.1093/qjmam/44.2.331.

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Ting, T. C. T. "Transverse waves in anisotropic elastic materials". Wave Motion 44, nr 2 (grudzień 2006): 107–19. http://dx.doi.org/10.1016/j.wavemoti.2006.08.003.

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Li, Aimin, Tengfei Zhao, Zhiwen Lan i Mojia Huang. "Constitutive Relations of Anisotropic Polycrystals: Self-Consistent Estimates". Materials 15, nr 14 (17.07.2022): 4974. http://dx.doi.org/10.3390/ma15144974.

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In this paper, the elastic constitutive relation of polycrystals contains the effect of the mesostucture coefficients. We consider a general case and derive the average elastic constitutive relation pertaining to polycrystals of cubic crystals with any symmetry of crystalline orientation in their statistical distribution. Following Budiansky and Wu, we used self-consistent estimates of eigenstrain to obtain the effective elastic constitutive relation of polycrystals in an explicit form. For the Voigt assumption and the Reuss assumption, the effective elastic constitutive relation of polycrystals on cubic crystals contains the the mesostructure coefficients up to linear terms. In general, the linear term expression works well for materials such as aluminum, the single crystal of which has weak anisotropy. However the same expression (which allows the anisotropic part of the effective elastic constitutive relation to depend only linearly on the mesostructure coefficients) does not suffice for materials such as copper, in which the single crystal is strongly anisotropic. Per the Taylor theorem, we expand the expression based on the self-consistent estimates with respect to the mesostructure coefficients up to quadratic terms for anisotropic polycrystals of cubic crystals. While our numerical data are very close to those of Morris, our expression is much simpler.

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Daghash, Shaden, Phillip Servio i Alejandro Rey. "First-Principles Elastic and Anisotropic Characteristics of Structure-H Gas Hydrate under Pressure". Crystals 11, nr 5 (24.04.2021): 477. http://dx.doi.org/10.3390/cryst11050477.

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Evaluating gas hydrates properties contributes valuably to their large-scale management and utilization in fundamental science and applications. Noteworthy, structure-H (sH) gas hydrate lacks a comprehensive characterization of its structural, mechanical, and anisotropic properties. Anisotropic and pressure dependent properties are crucial for gas hydrates’ detection and recovery studies. The objective of this work is the determination of pressure-dependent elastic constants and mechanical properties and the direction-dependent moduli of sH gas hydrates as a function of guest composition. First-principles DFT computations are used to evaluate the mechanical properties, anisotropy, and angular moduli of different sH gas hydrates under pressure. Some elastic constants and moduli increase more significantly with pressure than others. This introduces variations in sH gas hydrate’s incompressibility, elastic and shear resistance, and moduli anisotropy. Young’s modulus of sH gas hydrate is more anisotropic than its shear modulus. The anisotropy of sH gas hydrates is characterized using the unit cell elastic constants, anisotropy factors, and the angular dependent moduli. Structure-properties composition correlations are established as a function of pressure. It is found that compressing filled sH gas hydrates increases their moduli anisotropy. Differences in atomic bonding across a crystal’s planes can be expected in anisotropic structures. Taken together the DFT-based structure–properties–composition relations for sH gas hydrates provide novel and significant material physics results for technological applications.

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Li, Bo, Yonghua Duan, Mingjun Peng, Li Shen i Huarong Qi. "Anisotropic Elastic and Thermal Properties of M2InX (M = Ti, Zr and X = C, N) Phases: A First-Principles Calculation". Metals 12, nr 7 (28.06.2022): 1111. http://dx.doi.org/10.3390/met12071111.

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First-principles calculations were used to estimate the anisotropic elastic and thermal properties of Ti2lnX (X = C, N) and Zr2lnX (X = C, N) M2AX phases. The crystals’ elastic properties were computed using the Voigt-Reuss-Hill approximation. Firstly, the material’s elastic anisotropy was explored, and its mechanical stability was assessed. According to the findings, Ti2lnC, Ti2lnN, Zr2lnC, and Zr2lnN are all brittle materials. Secondly, the elasticity of Ti2lnX (X = C, N) and Zr2lnX (X = C, N) M2AX phase are anisotropic, and the elasticity of Ti2lnX (X = C, N) and Zr2lnX (X = C, N) systems are different; the order of anisotropy is Ti2lnN > Ti2lnC, Zr2lnN > Zr2lnC. Finally, the elastic constants and moduli were used to determine the Debye temperature and sound velocity. Ti2lnC has the maximum Debye temperature and sound velocity, and Zr2lnN had the lowest Debye temperature and sound velocity. At the same time, Ti2lnC had the highest thermal conductivity.

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Gueddouh, A., B. Bentria, Y. Bourourou i S. Maabed. "Anisotropic elastic properties of FexB (x = 1, 2, 3) under pressure. First-principles study". Materials Science-Poland 34, nr 3 (1.09.2016): 503–16. http://dx.doi.org/10.1515/msp-2016-0078.

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AbstractSpin-polarization (SP) and pressure effects have been used to better clarify and understand anisotropic elastic properties of Fe-B intermetallic compounds using the first-principles calculation with generalized gradient approximation (GGA) within the plane-wave pseudopotential density functional theory. Elastic properties, including bulk, shear and Young’s moduli as well as Poisson ratio were obtained by Voigt-Reuss-Hill approximation. All studied Fe-B compounds were mechanically stable. The brittle and ductile properties were discussed using bulk to shear moduli ratio (B/G) of the studied structures in the pressure range of 0 GPa to 90 GPa in order to predict the critical pressure of phase transition from ferromagnetic (FM) to nonmagnetic (NM) state. Mechanical anisotropy in both cases was discussed by calculating different anisotropic indexes and factors. We have plotted three-dimensional (3D) surfaces and planar contours of the bulk and Young’s moduli of FexB (x = 1, 2, 3) compounds for some crystallographic planes, (1 0 0), (0 1 0) and (0 0 1), to reveal their elastic anisotropy. On the basis of anisotropic elastic properties the easy and hard axes of magnetization for the three studied compounds were predicted.

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Reimers, W., i R. Dupke. "Procedures for Residual Stress Analysis in Textured and in Coarse Grained Materials". Textures and Microstructures 23, nr 3 (1.01.1995): 173–83. http://dx.doi.org/10.1155/tsm.23.173.

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For the investigation of residual stresses by means of X-ray diffraction, special procedures for the registration and evaluation of the experimental strain data are necessary for textured and coarse grained materials. In both cases inhomogeneous diffraction intensity patterns are present which lead to the formation of intensity poles or even to Bragg reflections. Such experimental findings indicate also that the material properties within the investigated gauge volume are anisotropic so that the evaluation of the experimental strain up to stress values requires the introduction of anisotropic elastic constants. For the residual stress investigation of textured and fine grained materials averaging procedures using short wavelength radiation are discussed. A more detailed insight also in the microstress states may be obtained from the measurement of several different reflections whereby the effects of the elastic anisotropy may be corrected for by including the orientation distribution function as calculated from different poles figures. For coarse grained materials it is experimentally possible to determine the strain state of the individual crystallites so that their anisotropy is directly included in the evaluation of the stress data by using the single crystal elastic constants. The macroscopic residual stress values may then be obtained from the averaging over stress values of several crystallites.

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Sokolova, M. Yu, i D. V. Khristich. "FINITE STRAINS OF NONLINEAR ELASTIC ANISOTROPIC MATERIALS". Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, nr 70 (2021): 103–16. http://dx.doi.org/10.17223/19988621/70/9.

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Anisotropic materials with the symmetry of elastic properties inherent in crystals of cubic syngony are considered. Cubic materials are close to isotropic ones by their mechanical properties. For a cubic material, the elasticity tensor written in an arbitrary (laboratory) coordinate system, in the general case, has 21 non-zero components that are not independent. An experimental method is proposed for determining such a coordinate system, called canonical, in which a tensor of elastic properties includes only three nonzero independent constants. The nonlinear model of the mechanical behavior of cubic materials is developed, taking into account geometric and physical nonlinearities. The specific potential strain energy for a hyperelastic cubic material is written as a function of the tensor invariants, which are projections of the Cauchy-Green strain tensor into eigensubspaces of the cubic material. Expansions of elasticity tensors of the fourth and sixth ranks in tensor bases in eigensubspaces are determined for the cubic material. Relations between stresses and finite strains containing the second degree of deformations are obtained. The expressions for the stress tensor reflect the mutual influence of the processes occurring in various eigensubspaces of the material under consideration.

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Norris, A. N., i G. R. Wickham. "Elastic waves in inhomogeneously oriented anisotropic materials". Wave Motion 33, nr 1 (styczeń 2001): 97–107. http://dx.doi.org/10.1016/s0165-2125(00)00066-4.

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Ren, Jiu-Sheng, i Chang-Jun Cheng. "Cavitation for incompressible anisotropic hyper-elastic materials". Journal of Shanghai University (English Edition) 6, nr 3 (wrzesień 2002): 185–90. http://dx.doi.org/10.1007/s11741-002-0031-2.

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Sokolova, Marina, i Dmitrii Khristich. "Nonlinear constitutive relations for anisotropic elastic materials". Journal of Physics: Conference Series 973 (marzec 2018): 012018. http://dx.doi.org/10.1088/1742-6596/973/1/012018.

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Hicher, P. Y., i C. S. Chang. "Anisotropic Nonlinear Elastic Model for Particulate Materials". Journal of Geotechnical and Geoenvironmental Engineering 132, nr 8 (sierpień 2006): 1052–61. http://dx.doi.org/10.1061/(asce)1090-0241(2006)132:8(1052).

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Yalameha, Shahram, Zahra Nourbakhsh, Ali Ramazani i Daryoosh Vashaee. "Promising Bialkali Bismuthides Cs(Na, K)2Bi for High-Performance Nanoscale Electromechanical Devices: Prediction of Mechanical and Anisotropic Elastic Properties under Hydrostatic Tension and Compression and Tunable Auxetic Properties". Nanomaterials 11, nr 10 (16.10.2021): 2739. http://dx.doi.org/10.3390/nano11102739.

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Using first-principles calculations, we predict highly stable cubic bialkali bismuthides Cs(Na, K)2Bi with several technologically important mechanical and anisotropic elastic properties. We investigate the mechanical and anisotropic elastic properties under hydrostatic tension and compression. At zero pressure, CsK2Bi is characterized by elastic anisotropy with maximum and minimum stiffness along the directions of [111] and [100], respectively. Unlike CsK2Bi, CsNa2Bi exhibits almost isotropic elastic behavior at zero pressure. We found that hydrostatic tension and compression change the isotropic and anisotropic mechanical responses of these compounds. Moreover, the auxetic nature of the CsK2Bi compound is tunable under pressure. This compound transforms into a material with a positive Poisson’s ratio under hydrostatic compression, while it holds a large negative Poisson’s ratio of about −0.45 along the [111] direction under hydrostatic tension. An auxetic nature is not observed in CsNa2Bi, and Poisson’s ratio shows completely isotropic behavior under hydrostatic compression. A directional elastic wave velocity analysis shows that hydrostatic pressure effectively changes the propagation pattern of the elastic waves of both compounds and switches the directions of propagation. Cohesive energy, phonon dispersion, and Born–Huang conditions show that these compounds are thermodynamically, mechanically, and dynamically stable, confirming the practical feasibility of their synthesis. The identified mechanisms for controlling the auxetic and anisotropic elastic behavior of these compounds offer a vital feature for designing and developing high-performance nanoscale electromechanical devices.

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Ta, Na, Muhammad Umer Bilal, Ines Häusler, Alaukik Saxena, Yueh-Yu Lin, Felix Schleifer, Michael Fleck, Uwe Glatzel, Birgit Skrotzki i Reza Darvishi Kamachali. "Simulation of the θ′ Precipitation Process with Interfacial Anisotropy Effects in Al-Cu Alloys". Materials 14, nr 5 (8.03.2021): 1280. http://dx.doi.org/10.3390/ma14051280.

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The effects of anisotropic interfacial properties and heterogeneous elasticity on the growth and ripening of plate-like θ′-phase (Al2Cu) in Al-1.69 at.% Cu alloy are studied. Multi-phase-field simulations are conducted and discussed in comparison with aging experiments. The precipitate/matrix interface is considered to be anisotropic in terms of its energy and mobility. We find that the additional incorporation of an anisotropic interfacial mobility in conjunction with the elastic anisotropy result in substantially larger aspect ratios of the precipitates closer to the experimental observations. The anisotropy of the interfacial energy shows comparably small effect on the precipitate’s aspect ratio but changes the interface’s shape at the rim. The effect of the chemo-mechanical coupling, i.e., the composition dependence of the elastic constants, is studied as well. We show that the inverse ripening phenomenon, recently evidenced for δ’ precipitates in Al-Li alloys (Park et al. Sci. Rep. 2019, 9, 3981), does not establish for the θ′ precipitates. This is because of the anisotropic stress fields built around the θ′ precipitates, stemming from the precipitate’s shape and the interaction among different variants of the θ′ precipitate, that disturb the chemo-mechanical effects. These results show that the chemo-mechanical effects on the precipitation ripening strongly depend on the degree of sphericity and elastic isotropy of the precipitate and matrix phases.

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Zeng, Xianshi, Rufang Peng, Yanlin Yu, Zuofu Hu, Yufeng Wen i Lin Song. "First-Principles Calculations on Structural Property and Anisotropic Elasticity of γ1-Ti4Nb3Al9 under Pressure". Materials 11, nr 10 (18.10.2018): 2025. http://dx.doi.org/10.3390/ma11102025.

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The effect of pressure on the structural property and anisotropic elasticity of γ 1 -Ti 4 Nb 3 Al 9 phase has been investigated in this paper by using first-principles calculations. The obtained bulk properties at zero pressure are in good agreement with the previous data. The structural property and elastic constants under pressures up to 40 GPa have been obtained. According to the elastic stability conditions under isotropic pressure, the phase is found to be mechanically stable under pressures up to 37.3 GPa. From the obtained elastic constants, the elastic moduli, anisotropic factors and acoustic velocities under different pressures have also been obtained successfully together with minimum thermal conductivities and Debye temperature. It is shown that the ductility of the phase is improved and its anisotropy and Debye temperature are enhanced with increasing the pressure.

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29

IVANOVA, Yonka. "Application of Ultrasonic Methods for Evaluation the Anisotropy of Materials". Eurasia Proceedings of Science Technology Engineering and Mathematics 22 (30.08.2023): 258–67. http://dx.doi.org/10.55549/epstem.1350957.

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The reason for anisotropy in material properties is the thermo mechanical effect in the process of plastic deformation, which creates a texture along the direction of deformation. One of the established nondestructive methods for evaluating the elastic constants in anisotropic materials is by measuring the velocities of ultrasonic waves propagating in different directions in the material. For studying the elastic anisotropy of textured media, the established measurement methods are hardly applicable because the materials are inaccessible for volumetric measurements. Moreover, the differences in the velocities of the ultrasonic waves are very small and the changes are localized in the surface and subsurface layers. The purpose of the study is to test a methodology and carry out the experimental studies to determine the anisotropy parameters of metallic materials based on the data from changes in the velocity of ultrasonic waves.

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30

Tevet, Ofer, David Svetlizky, David Harel, Zahava Barkay, Dolev Geva i Noam Eliaz. "Measurement of the Anisotropic Dynamic Elastic Constants of Additive Manufactured and Wrought Ti6Al4V Alloys". Materials 15, nr 2 (15.01.2022): 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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31

Ashour, Hamdy A. "A compressive strength criterion for anisotropic rock materials". Canadian Geotechnical Journal 25, nr 2 (1.05.1988): 233–37. http://dx.doi.org/10.1139/t88-027.

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This paper proposes a general compressive strength criterion for anisotropic rock materials under multiaxial states of stress. The proposed criterion is a generalization of the Von Mises' criterion for yielding of ductile metals, which has also been used previously as a strength criterion for brittle fracture in the spirit of both being limits of linear elastic behavior. The presently proposed criterion takes into consideration the effects of the confining pressure, the various stress components, and the material anisotropy on rock material failure in a multiaxial stress state. To verify the applicability of the proposed criterion, it has been used to construct the failure envelopes for several types of rock materials. Consequently, the constructed failure envelopes and the corresponding experimental results have been compared. In all cases, a close agreement with the experimental results has been achieved. This result demonstrates the versatility and applicability of the proposed strength criterion in representing the compressive strength behavior of anisotropic rock materials under complex multiaxial states of stress. Key words: strength, rock materials, anisotropy.

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32

Evans, Jordan A., Blake T. Sturtevant, Bjørn Clausen, Sven C. Vogel, Fedor F. Balakirev, Jonathan B. Betts, Laurent Capolungo, Ricardo A. Lebensohn i Boris Maiorov. "Determining elastic anisotropy of textured polycrystals using resonant ultrasound spectroscopy". Journal of Materials Science 56, nr 16 (24.02.2021): 10053–73. http://dx.doi.org/10.1007/s10853-021-05827-z.

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AbstractPolycrystalline materials can have complex anisotropic properties depending on their crystallographic texture and crystal structure. In this study, we use resonant ultrasound spectroscopy (RUS) to nondestructively quantify the elastic anisotropy in extruded aluminum alloy 1100-O, an inherently low-anisotropy material. Further, we show that RUS can be used to indirectly provide a description of the material’s texture, which in the present case is found to be transversely isotropic. By determining the entire elastic tensor, we can identify the level and orientation of the anisotropy originated during extrusion. The relative anisotropy of the compressive (c11/c33) and shear (c44/c66) elastic constants is 1.5% ± 0.5% and 5.7% ± 0.5%, respectively, where the elastic constants (five independent elastic constants for transversely isotropic) are those associated with the extrusion axis that defines the symmetry of the texture. These results indicate that the texture is expected to have transversely isotropic symmetry. This finding is confirmed by two additional approaches. First, we confirm elastic constants and the degree of elastic anisotropy by direct sound velocity measurements using ultrasonic pulse echo. Second, neutron diffraction (ND) data confirm the symmetry of the bulk texture consistent with extrusion-induced anisotropy, and polycrystal elasticity simulations using the elastic self-consistent model with input from ND textures and aluminum single-crystal elastic constants render similar levels of polycrystal elastic anisotropy to those measured by RUS. We demonstrate the ability of RUS to detect texture-induced anisotropy in inherently low-anisotropy materials. Therefore, as many other common materials have intrinsically higher elastic anisotropy, this technique should be applicable for similar levels of texture, providing an efficient general diagnostic and characterization tool.

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33

Kušnír, Jakub, Tomáš Grabec, Kristýna Zoubková, Pavla Stoklasová, Petr Sedlák i Hanuš Seiner. "Apparent anisotropic thermal diffusivity measured in cubic single crystals by transient grating spectroscopy". Journal of Applied Physics 133, nr 12 (28.03.2023): 125108. http://dx.doi.org/10.1063/5.0136850.

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The effect of elastic anisotropy on thermal diffusivity determination by transient grating spectroscopy (TGS) was studied. In experiments performed on a set of cubic single crystals, it was observed that TGS measurements may indicate anisotropy of thermal diffusivity in otherwise thermally isotropic materials, and that the strength of this apparent anisotropy is correlated with the strength of the elastic anisotropy. To find a source of the observed phenomenon, finite-element simulations of the TGS measurements were carried out. Time-domain TGS signals were generated from the simulations and processed identically to the experimental data. The simulation results revealed that the elastic anisotropy affects the detected time-domain signals. Consequently, the thermal diffusivity coefficients determined from them showed the artificial directional dependence. For the chosen set of cubic crystals, ranging from nearly isotropic to strongly anisotropic in terms of elastic constants, this simulated directional dependence was in full agreement with the one observed in the experiments.

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34

Li, Lin, Jin Yang, Xiu Qing Qian, Hai Xia Zhang i Zhi Cheng Liu. "The Numerical Study on Errors of Stress in Anisotropic Linear Elastic Material when Simplified as Orthogonal one". Applied Mechanics and Materials 275-277 (styczeń 2013): 3–6. http://dx.doi.org/10.4028/www.scientific.net/amm.275-277.3.

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Keywords: strain, stress, material constants, constitutive equation, anisotropy. Abstract. If the material is anisotropic, there are differences in stress distribution under the same boundary conditions when it was simplified as an orthotropic material. We established a simple finite element model for rectangular perforated planar material, in which one side was fixed, the opposite side was loaded with uniform force, and the other sides were set free. Based on this model we studied the difference of distribution of stress between anisotropic material and its simplified form, orthotropic material. The results showed differences in some cases quite large, the maximum relative error of extreme stress can reach 341%. In conclusions, this study does not support that the complex anisotropic materials are simplified to orthotropic materials. If researchers only concern the location of extreme stress, this study does not deny that the complex anisotropic materials can be simplified to orthotropic one.

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35

Glukhikh, Vladimir. "PROBLEM OF THE ANISOTROPY OF ELASTICITY AND STRENGTH IN ANISOTROPIC FIBER MATERIALS". Architecture and Engineering 6, nr 2 (2021): 31–36. http://dx.doi.org/10.23968/2500-0055-2021-6-2-31-36.

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Introduction: The paper presents new results of studies on the anisotropy of fiber materials with cylindrical anisotropy, which include filament-wound composite materials reinforced with various fibers. Methods: We suggest a mathematical solution to a fourth-order partial differential equation in polar coordinates with two variables for an orthotropic anisotropic body. To solve this equation, we converted it into Cartesian coordinates and presented the stress function as a sum of polynomials. Results and Discussion: As a result of the solution, we obtained two relationships between the elastic constants in the principal directions of anisotropy (so-called elasticity parameters). One of them was obtained for the first time, and the other results from the solution of the anisotropy problem for an orthotropic curved body, suggested by S. G. Lekhnitsky. The obtained solution does not contradict Lekhnitsky’s solution. Thus, in our opinion, orthotropic materials can be divided into two groups. In one group, when shifting from the radial to the tangential direction, the elastic constants take on extreme values when the layers are at angles of 0, 60, and 90°. In the other group, there is no intermediate extreme value and the elastic constants take on extreme values when the layers are at angles of 0 and 90°. The obtained results can be applied in the development of new high-strength composite materials and new technologies for the design and manufacture of building structures, as well as in the design of high-strength structures from synthetic composite materials.

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36

Steuwer, Axel, Javier Roberto Santisteban, Philip J. Withers, Lyndon Edwards i Mike E. Fitzpatrick. "In situdetermination of stresses from time-of-flight neutron transmission spectra". Journal of Applied Crystallography 36, nr 5 (8.09.2003): 1159–68. http://dx.doi.org/10.1107/s0021889803013748.

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The pulsed neutron transmission diffraction technique exploits the sharp steps in intensity (Bragg edges) appearing in the transmitted spectra of thermal neutrons through polycrystalline materials. In this paper the positions of these edges acquired by the time-of-flight (TOF) technique are used to measure accurately the interplanar lattice distances to a resolution of Δd/d≃ 10−4of specimens subjected toin situuniaxial tensile loading. The sensitivity of the method is assessed for elastically isotropic (b.c.c. ferritic) and anisotropic (f.c.c. austenitic) polycrystalline specimens of negligible and moderately textured steels. For the more anisotropic austenitic steel, the elastic anisotropy is studied with regard to a Pawley refinement, and compared with previous results from conventional neutron diffraction experiments on the same material. It is shown that the method can be used to determine anisotropic strains, diffraction elastic constants, the residual and applied stress state as well as the unstrained lattice parameter by recording transmission spectra at different specimen inclinations, by complete analogy with the sin2ψ technique frequently used in X-ray diffraction. The technique is shown to deliver reliable measures of strain even in the case of moderate texture and elastic anisotropy.

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37

Duc, Nguyen Dinh, i Nguyen Van Thuong. "Adhesive contact between two-dimensional anisotropic elastic bodies". Vietnam Journal of Mechanics 45, nr 4 (28.12.2023): 318–33. http://dx.doi.org/10.15625/0866-7136/19700.

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Adhesion plays a vital role in the design of smart and intelligent high-tech devices such as modern optical, microelectromechanical, and biomedical systems. However, in the literature, adhesive contact is mostly considered for contact of rigid substrates and transversely isotropic and isotropic elastic materials. The composite materials are increasingly used in the mart and intelligent high-tech devices. Since the composite materials are generally anisotropic and contact bodies are all deformable, it is more practical to consider the adhesive contact of two anisotropic elastic materials. In this paper, an adhesive contact model of anisotropic elastic bodies is established, and the closed-form solutions for two-dimensional adhesive contact of two anisotropic elastic bodies are derived. The full-field solutions and the relation for the contact region and applied force are developed using the Stroh complex variable formalism, the analytical continuation method, and concepts of the JKR adhesive model. We will show that the frictionless contact of two anisotropic elastic materials is just a special case of the present contact problem, and its solutions can be obtained by setting the work of adhesion equal to zero. In addition, we also show that our present solutions are valid for the problems of indentation by a rigid punch on an elastic half-space through a proper placement of the contact radius and the corresponding material constant. Numerical results are provided to demonstrate the accuracy, applicability, and versatility of the developed solutions.

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38

Yen, Wen J., i Chyanbin Hwu. "Interactions Between Dislocations and Anisotropic Elastic Elliptical Inclusions". Journal of Applied Mechanics 61, nr 3 (1.09.1994): 548–54. http://dx.doi.org/10.1115/1.2901494.

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A general field solution for the stresses and displacements of the interactions between dislocations and inclusions has been derived in this paper by applying the Stroh’s formalism and the Muskhelishvili’s method of analytical continuation. The solutions are valid for general elastic anisotropic media under two-dimensional deformation. The interaction energy between dislocations and elastic inclusions is obtained explicitly. The solutions in general are expressed in series form for elastic inclusions. However, for the special cases when the elastic inclusions are replaced by a hole or rigid inclusion, simple closed-form solutions are derived. The general solutions are verified by considering the isotropic media since it is the only solution available in the literature. For the general anisotropic media, a series of contour diagrams for the glide component of the force on a dislocation are provided in this paper to study the effects of inclusion hardness, shape, and matrix anisotropy.

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39

Cheng, Jiao, i Qidong Zhang. "Optical, Electronic Properties and Anisotropy in Mechanical Properties of “X” Type Carbon Allotropes". Materials 13, nr 9 (1.05.2020): 2079. http://dx.doi.org/10.3390/ma13092079.

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Based on first-principle calculations, the mechanical anisotropy and the electronic and optical properties of seven kinds of carbon materials are investigated in this work. These seven materials have similar structures: they all have X-type structures, with carbon atoms or carbon clusters at the center and stacking towards the space. A calculation of anisotropy shows that the order of elastic anisotropy in terms of the shear modulus, Young’s modulus and Poisson’s ratio of these seven carbon materials with similar structure is diamond < supercubane < T carbon < Y carbon < TY carbon < cubane-diyne < cubane-yne. As these seven carbon materials exhibit cubic symmetry, Young’s modulus has the same anisotropy in some major planes, so the order of elastic anisotropy in the Young’s modulus of these seven main planes is (111) plane < (001) plane = (010) plane = (100) plane < (011) plane = (110) plane = (101) plane. It is also due to the fact that their crystal structure has cubic symmetry that the elastic anisotropy in the shear modulus and the Poisson’s ratio of these seven carbon materials on the seven major planes are the same. Among the three propagation directions of [100], [110], and [111], the [110] propagation direction’s anisotropic ratio of the sound velocity of TY carbon is the largest, while the anisotropic ratio of the sound velocity of cubane-diyne on the [100] propagation direction is the smallest. In addition, not surprisingly, the diamond has the largest Debye temperature, while the TY carbon has the smallest Debye temperature. Finally, TY carbon, T carbon and cubane-diyne are also potential semiconductor materials for photoelectric applications owing to their higher or similar absorption coefficients to GaAs in the visible region.

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40

Ting, T. C. T., i D. M. Barnett. "Classifications of surface waves in anisotropic elastic materials". Wave Motion 26, nr 3 (listopad 1997): 207–18. http://dx.doi.org/10.1016/s0165-2125(97)00027-9.

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41

Bruno, L., i A. Poggialini. "Elastic characterization of anisotropic materials by speckle interferometry". Experimental Mechanics 45, nr 3 (czerwiec 2005): 205–12. http://dx.doi.org/10.1007/bf02427943.

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42

Han, Deren, H. H. Dai i Liqun Qi. "Conditions for Strong Ellipticity of Anisotropic Elastic Materials". Journal of Elasticity 97, nr 1 (20.05.2009): 1–13. http://dx.doi.org/10.1007/s10659-009-9205-5.

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43

Ting, T. C. T. "Longitudinal and transverse waves in anisotropic elastic materials". Acta Mechanica 185, nr 3-4 (19.05.2006): 147–64. http://dx.doi.org/10.1007/s00707-006-0333-8.

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44

Furukawa, Tomonari, i Jan Wei Pan. "Stochastic identification of elastic constants for anisotropic materials". International Journal for Numerical Methods in Engineering 81, nr 4 (13.08.2009): 429–52. http://dx.doi.org/10.1002/nme.2700.

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45

Ma, He, Xiaoyou Li, Wei Jiang i Xudong Zhang. "First-Principles Investigation of Structural Stability, Mechanical, Anisotropic, and Thermodynamic Properties of CeT2Al20 Intermetallics". Zeitschrift für Naturforschung A 73, nr 12 (27.11.2018): 1157–67. http://dx.doi.org/10.1515/zna-2018-0265.

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AbstractFirst-principles calculations were carried out to explore the structural stability, elastic moduli, ductile or brittle behaviour, anisotropy, dynamical stability, and thermodynamic properties of pure Al and CeT2Al20 (T = Ti, V, Cr, Nb, and Ta) intermetallics. The calculated formation enthalpy and phonon frequencies confirm that these intermetallics satisfy the conditions for structural stability. The elastic constants Cij, elastic moduli B, G, and E, and the hardness Hv indicate these intermetallics have higher hardness and the better resistance against deformation than pure Al. The values of Poisson’s ratio (v) and B/G indicate that CeT2Al20 intermetallics are all brittle materials. The anisotropic constants and acoustic velocities confirm that CeT2Al20 intermetallics are all anisotropic, but CeV2Al20, CeNb2Al20, and CeTa2Al20 are nearly isotropic. Importantly, the calculated thermodynamic parameters show that CeT2Al20 intermetallics exhibit better thermodynamic properties than pure Al at high temperature.

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46

Obermayer, Thomas, Christian Krempaszky i Ewald Werner. "Analysis of Texture and Anisotropic Elastic Properties of Additively Manufactured Ni-Base Alloys". Metals 12, nr 11 (21.11.2022): 1991. http://dx.doi.org/10.3390/met12111991.

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Additive manufacturing of metallic materials generates strong crystallographic textures, leading to anisotropic elastic properties on the macroscopic scale. The impact of the processing parameters on the resulting texture requires suitable techniques for the prediction and the experimental determination of elastic properties to exploit the anisotropy in the design process. Within this study mechanical as well as microstructure based approaches are applied on a batch of specimens manufactured from IN718 by selective laser melting to assess the elastic behavior on macroscropic scale. Tensile loading experiments and the impulse excitation technique are applied for the determination of elastic properties without additional constitutive data. Furthermore, the elastic behavior is estimated from single-crystal elastic properties and texture data measured by electron backscatter diffraction and high energy X-ray diffraction. The results of the applied approaches are discussed and compared, allowing also to assess the homogeneity of the elastic properties within the batch of specimens.

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47

Schreyer, H. L., i Q. H. Zuo. "Anisotropic Yield Surfaces Based on Elastic Projection Operators". Journal of Applied Mechanics 62, nr 3 (1.09.1995): 780–85. http://dx.doi.org/10.1115/1.2897014.

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Although most materials are anisotropic to some extent, most yield surfaces are either chosen to be isotropic or to be a smooth anisotropic surface with no connection to the elastic anisotropic features. Here, the elastic projection operators obtained from the spectral decomposition of the elasticity tensor are used to define anisotropic yield surfaces with a yield surface defined for each of the projection operators. The advantages of the approach are (1) plastic deformation modes are associated with the elastic anisotropic behavior, (2) the spectral decomposition of the tangent tensor is readily available for a bifurcation analysis, (3) the composite yield surface has vertices which are thought to be important for predicting plastic buckling, and (4) the contributions to plastic deformations from each yield surface are uncoupled. The result is a theory that is actually quite simple but yet reflects some of the observed features for materials to yield in specific modes.

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48

Cowin, Steven C. "Propagation of Kelvin Modes". Mathematics and Mechanics of Solids 1, nr 1 (marzec 1996): 25–43. http://dx.doi.org/10.1177/108128659600100103.

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The Kelvin modes of isotropic elasticity are the dilatational mode and the deviatoric mode. Kelvin modes may be defined for all the anisotropic elastic symmetries. It is shown here that any plane wave may be considered as the sum of propagating Kelvin modes, but that the only Kelvin mode that will propagate by itself as a plane wave in any anisotropic elastic material (except a material with triclinic symmetry) is a single simple shear mode. However, other Kelvin modes may propagate in special elastic materials and single simple shear modes may propagate in special triclinic materials. These results generalized the paradigm of the shear and pressure waves of linear isotropic elasticity to all plane waves in anisotropic elasticity.

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49

Kleschev, A. A. "Anisotropic solid cylindrical waveguides". Transactions of the Krylov State Research Centre 3, nr 401 (5.07.2022): 139–44. http://dx.doi.org/10.24937/2542-2324-2022-3-401-139-144.

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Object and purpose of research. The article studies the behavior of anisotropic elastic bodies of cylindrical shape (orthotropic shell and transversely isotropic rod). The intention is to find the phase velocities of elastic waves in these bodies using thin shell approximations and a rigorous approach based on the dynamic theory of elasticity using "Debye type" potentials. In previous studies of anisotropic structures, anisotropic media or anisotropic half-spaces were used. Materials and methods. Both an approximate thin shell method and a rigorous approach based on the dynamic theory of elasticity and "Debye type" potentials are used in the paper. Main results. Equations for finding the phase velocities of elastic waves in anisotropic cylindrical bodies are obtained. Phase velocities of longitudinal and bending waves in anisotropic cylindrical rod are calculated. Conclusion. As a result of the conducted research relations for calculating the phase velocities of elastic waves in an orthotropic shell and a transversely isotropic rod were found.

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50

Faraci, David, Francesco Mendicino, Angela Vincenti i Claudia Comi. "Wave Polarization Control in Anisotropic Locally Resonant Materials". Applied Sciences 13, nr 19 (28.09.2023): 10797. http://dx.doi.org/10.3390/app131910797.

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Elastic wave propagation in solids can be controlled and manipulated by properly designed metamaterials. In particular, polarization conversion can be obtained by using anisotropic materials. In this paper, we propose a three-component locally resonant material with non-symmetrically coated inclusions, and we study the effect of the anisotropic equivalent mass on band gap formation and the polarization conversion of elastic waves. The equivalent frequency-dependent mass tensor is obtained through the two-scale homogenization approach. The study of the eigenvalues of the mass tensor enables to predict band gaps and polarization bands, as well as identifying a priori the effect of different geometric and material parameters, thus opening the way to metamaterial optimization.

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