Journal articles: 'Isotropic material'

1

GRIGOR’EV, Yu M., та A. M. YAKOVLEV. "Transversally isotropic elastic material applicable for permafrost rocks: а case study". Arctic and Subarctic Natural Resources 28, № 2 (2023): 337–45. http://dx.doi.org/10.31242/2618-9712-2023-28-2-337-345.

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In this paper we present the principles for a new method of quaternion factorization of the equilibrium equations for the transversally isotropic elasticity. Natural and artificial materials have anisotropy of physical properties. Many of them have transversal isotropy of elastic properties. Transversally isotropic materials are used in many technologies and industries, for example, in rock mechanics under permafrost conditions. Mathematical description of such materials involves the model of a transversally-isotropic material with 5 independent elastic constants. The equations of this model are more complicated than those for isotropic elasticity, and their analysis causes much more difficulties. One of the methods for analyzing such equations is factorization, i.e. reduction to the solution of simpler first-order equations.

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2

Selfridge, A. R. "Approximate Material Properties in Isotropic Materials." IEEE Transactions on Sonics and Ultrasonics 32, no. 3 (1985): 381–94. http://dx.doi.org/10.1109/t-su.1985.31608.

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3

Hanson, M. T. "The Elastic Potentials for Coplanar Interaction Between an Infinitesimal Prismatic Dislocation Loop and a Circular Crack for Transverse Isotropy." Journal of Applied Mechanics 59, no. 2S (1992): S72—S78. http://dx.doi.org/10.1115/1.2899510.

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This paper gives a closed-form evaluation in terms of elementary functions for the title problem of coplanar dislocation—crack interaction. The two cases of an external and internal crack are considered and the potential for each is found for an isotropic material. The similarity between isotropy and transverse isotropy is discussed in the beginning sections and is used to write the corresponding potential for a transversely isotropic material from the isotropic result.

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4

Czarnecki, Sławomir. "Isotropic Material Design." Computational Methods in Science and Technology 21, no. 2 (2015): 49–64. http://dx.doi.org/10.12921/cmst.2015.21.02.001.

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Abousleiman, Younane, and Shailesh Ekbote. "Solutions for the Inclined Borehole in a Porothermoelastic Transversely Isotropic Medium." Journal of Applied Mechanics 72, no. 1 (2005): 102–14. http://dx.doi.org/10.1115/1.1825433.

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A porothermoelastic solution of the general problem of the inclined borehole in a transversely isotropic porous material is presented herein and compared with the isotropic porothermoelastic solution. The governing equations are outlined for the case of general anisotropy and specialized for a transversely isotropic poroelastic material under nonhydrostatic and nonisothermal in situ conditions. A superposition scheme is employed to obtain the analytical solutions within the isotropic and transversely isotropic poromechanics theory. The borehole generator is assumed to coincide with the material axis of symmetry, in the case of transverse isotropy, yet subjected to a three-dimensional state of stress. A systematic analysis has been carried out to evaluate the effect of the anisotropy of the poromechanical material parameters as well as the thermal material properties on stress and pore pressure distributions and the potential impact on the overall stability of deep wellbore drilling.

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Shiah, Y. C., and W. X. Sun. "On the Efficiency of Analyzing 3D Anisotropic, Transversely Isotropic, and Isotropic Bodies in BEM." Journal of Mechanics 26, no. 4 (2010): 483–91. http://dx.doi.org/10.1017/s1727719100004688.

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ABSTRACTDue to a lack of closed-form solutions for three dimensional anisotropic bodies, the computational burden of evaluating the fundamental solutions in the boundary element method (BEM) has been a research focus over the years. In engineering practice, transversely isotropic material has gained popularity in the use of composites. As a degenerate case of the generally anisotropic material, transverse isotropy still needs to be treated separately to ease the computations. This paper aims to investigate the computational efficiency of the BEM implementations for 3D anisotropic, transversely isotropic, and isotropic bodies. For evaluating the fundamental solutions of 3D anisotropy, the explicit formulations reported in [1,2] are implemented. For treating transversely isotropic materials, numerous closed form solutions have been reported in the literature. For the present study, the formulations presented by Pan and Chou [3] are particularly employed. At the end, a numerical example is presented to compare the computational efficiency of the three cases and to demonstrate how the CPU time varies with the number of meshes.

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7

Tang, Shuang Qing, and Xing Xia. "Stress Analysis of Isotropic Material Flywheel Battery Rotor." Applied Mechanics and Materials 532 (February 2014): 519–23. http://dx.doi.org/10.4028/www.scientific.net/amm.532.519.

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The strength of metal materials is far less than the new composite material, such as carbon fiber. However, the price of the metal material and manufacturing cost are much lower than composite materials, which makes isotropic material much more practical for flywheel rotor. Through the stress analysis of isotropic material rotor, we can optimize the parameters of the rotor, thus for isotropic material provides the basis for the design of the rotor for flywheel battery.

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8

Wang, Zhi-Qiao, and Yu Wang. "A Natural Generalization of Linear Isotropic Relations with Seth-Hill Strain Tensors to Transversely Isotropic Materials at Finite Strains." Mathematical Problems in Engineering 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/7473046.

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Hooke’s law was naturally generalized to finite strains by Hill in 1978, by introducing the Seth-Hill strain and its conjugate stress. This paper presents the transversely isotropic relations, which are not only a natural extension of Hill’s theory from isotropic materials to transversely isotropic materials, but also the natural generalization of the transversely isotropic Hooke’s law from infinitesimal strains to moderate strains. This generalization introduces a class of transversely isotropic hyperelastic models, which are adopted to investigate the uniaxial stretch and the simple shear problems. Results show that the material responses for different constitutive equations are significantly different; the stiffening or softening behaviors of materials at moderate deformations can be described by the appropriate model with proper material parameters.

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Cauvin, Alix, and Rene B. Testa. "Elastoplastic material with isotropic damage." International Journal of Solids and Structures 36, no. 5 (1999): 727–46. http://dx.doi.org/10.1016/s0020-7683(98)00043-2.

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10

Limbert, Georges, and John Middleton. "A transversely isotropic viscohyperelastic material." International Journal of Solids and Structures 41, no. 15 (2004): 4237–60. http://dx.doi.org/10.1016/j.ijsolstr.2004.02.057.

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11

Panchal, Rekha, and Richa Sharma. "Thermal elastic-plastic transition of functionally graded thick-walled pressurized rotating cylinder fabricated from transversely isotropic material." Structural Integrity and Life 25, Special Issue A (2025): S75—S83. https://doi.org/10.69644/ivk-2025-sia-0075.

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In this paper, elastic-plastic stress analysis is done for a pressurized thick-walled functionally graded cylinder rotating along its axis with angular velocity ꞷ so that the collapse of the cylinder under loading can be avoided. The problem is formulated for functionally graded transversely isotropic material by using Seth’s transition theory. Results are analysed theoretically and discussed numerically. From this analysis, it has been concluded that the cylinder made up of functionally graded transversely isotropic material (beryl) has less circumferential stresses than cylinder of transversely isotropic material (magnesium) and isotropic material (steel). Thus, transversely isotropic material (beryl) is safe as compared to the cylinder made up of transversely isotropic material (magnesium) and isotropic material (steel).

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12

Белкин, Антон Эдуардович. "Modeling of rectification of a nonlinear-elastic cylindrical layer taking into account the change in the direction of transversal isotropy." Herald of Tver State University. Series: Applied Mathematics, no. 2(69) (July 24, 2023): 17–27. http://dx.doi.org/10.26456/vtpmk687.

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В статье рассмотрена математическая модель деформации тела из несжимаемого трансверсально-изотропного нелинейно-упругого материала. Особое внимание в статье уделяется векторной характеристике трансверсально-изотропного тела, указывающей направление оси трансверсальной изотропии, а также изменению данной характеристики при деформации. Отмечается, что при деформации определённого вида трансверсально-изотропный материал ведёт себя как материал Трелоара. Исследуется частный случай задачи о деформации несжимаемого трансверсально-изотропного нелинейно-упругого цилиндрического слоя, для этого случая получено точное аналитическое решение задачи. The article considers a mathematical model of the deformation of a body made of an incompressible transversally isotropic nonlinear elastic material. Particular attention is paid to the vector characteristic of a transversally isotropic body, which indicates the direction of the axis of transversal isotropy, as well as to the change in this characteristic during deformation. It is noted that under deformation of a certain type, a transversely isotropic material behaves like a Treloar material. A special case of the problem of deformation of an incompressible transversally isotropic nonlinear elastic cylindrical layer is studied, and an exact analytical solution of the problem is obtained for this case.

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13

Odom, Edwin M., and Donald F. Adams. "An investigation of the isotropy of epoxy polymers." Journal of Materials Research 7, no. 12 (1992): 3352–58. http://dx.doi.org/10.1557/jmr.1992.3352.

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Measurements of the engineering constants E, G, and v are routinely made for polymeric materials. If these materials are isotropic, these measurements should satisfy the relationship G = E/2(1 + v). However, many past measurements have indicated that this relationship is not satisfied. This raises questions about the assumptions of material isotropy and the applicability of Hooke's law. The methods used to measure these engineering constants for a number of different polymers are first described. Then, new results obtained in the current investigation are presented, indicating that the elastic constants do in fact satisfy the isotropic relationship for strains up to 0.5%. However, it is shown that at strain levels above this level, the relationship between stress and strain is nonlinear.

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14

Sharma, Sanjeev, Ila Sahay, and Ravindra Kumar. "Thermo elastic-plastic transition of transversely isotropic thick-walled circular cylinder under internal and external pressure." Multidiscipline Modeling in Materials and Structures 10, no. 2 (2014): 211–27. http://dx.doi.org/10.1108/mmms-03-2013-0026.

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Purpose – The purpose of this paper is to provide the guidance on a design and integrity evaluation of a cylinder under pressure, for which stress analysis has been done for transversely isotropic thick-walled circular cylinder under internal and external pressure with thermal effects. Design/methodology/approach – Transition theory has been used to evaluate plastic stresses based on the concept of generalized principal Lebesgue strain measure which simplifies the constitutive equations and helps to achieve better agreement between the theoretical and experimental results. Findings – It can be concluded that circular cylinder with thermal effects under internal and external pressure made of isotropic material (steel) is on the safer side of the design as compared to the cylinder made of transversely isotropic material (i.e. magnesium and beryl) because percentage increase in effective pressure required for initial yielding to become fully plastic is high for isotropic material (steel) as compared to transversely isotropic material (i.e. magnesium and beryl). It can also be concluded that out of two transversely isotropic materials, beryl is better choice for design of cylinder as compared to magnesium material because percentage increase in effective pressure required for initial yielding to become fully plastic is high for beryl as compared to magnesium. Originality/value – A detailed investigation of thermal transversely isotropic thick-walled circular cylinder under internal and external pressure has been done which leads to the idea of “stress saving” that minimizes the possibility of fracture of cylinder.

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15

Pankaj, Thakur. "Elastic-plastic transition stresses in a transversely isotropic thick-walled cylinder subjected to internal pressure and steady-state temperature." Thermal Science 13, no. 4 (2009): 107–18. http://dx.doi.org/10.2298/tsci0904107p.

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Elastic-plastic transitional stresses in a transversely isotropic thick-walled cylinder subjected to internal pressure and steady-state temperature have been derived by using Seth's transition theory. The combined effects of pressure and temperature has been presented graphically and discussed. It has been observed that at room temperature, thick-walled cylinder made of isotropic material yields at a high pressure at the internal surface as compared to cylinder made of transversely isotropic material. With the introduction of thermal effects isotropic/transversely isotropic cylinder yields at a lower pressure whereas cylinder made of isotropic material requires less percentage increase in pressure to become fully-plastic from its initial yielding as compared to cylinder made of transversely isotropic material.

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16

Theocaris, Pericles S. "Effect of Swelling on the Failure Mode of Foamy Materials." Applied Mechanics Reviews 48, no. 10 (1995): 696–706. http://dx.doi.org/10.1115/1.3005051.

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A study was undertaken for the mode of failure of open- or closed-cell cellular materials depending on the variation of the relative density of the material because of swelling or variation of its porosity. The cellular materials or foams were considered as transversely isotropic, an assumption which corresponds well with their mechanical behavior. Using a tensor failure polynomial criterion, and as such the elliptic paraboloid failure criterion was considered, for the study of the mode of failure of closed-cell foams of different relative densities, it was established that the failure behavior of the swelled material changes drastically its failure mode by becoming a tension strong material from a compression-strong one. Furthermore, there is a critical value of the relative density for each material where the substance passes through a quasi-isotropic state and the foam behaves like an isotropic material, where triaxiality phenomena are significant.

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17

Shi, Dongai, Yuan Lin, and Timothy C. Ovaert. "Indentation of an Orthotropic Half-Space by a Rigid Ellipsoidal Indenter." Journal of Tribology 125, no. 2 (2003): 223–31. http://dx.doi.org/10.1115/1.1537743.

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Anisotropic materials represent a unique class of materials, including crystals, wood, thin-films, and composites. Existing work in the literature has provided the engineering community with an in-depth understanding of isotropic contact mechanics, and the methodologies for solving isotropic contact problems have been fully developed. Anisotropic material systems, however, are more complex and their analysis is less fully-developed in the literature. Presented here is the analysis of indentation by a rigid ellipsoidal indenter against an orthotropic half-space, with the surface of the half-space parallel to two of the axes of material symmetry, derived from stress equilibrium. A numerical method has been used to solve for the contact parameters (contact dimensions and normal approach) for both orthotropic and transversely isotropic material systems.

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18

Mikata, Y. "Analytical treatment on the effective material properties of a composite material with spheroidal and ellipsoidal inhomogeneities in an isotropic matrix." Journal of Micromechanics and Molecular Physics 01, no. 03n04 (2016): 1640012. http://dx.doi.org/10.1142/s2424913016400129.

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Effective material properties of a composite with spheroidal and ellipsoidal inhomogeneities in an isotropic matrix are investigated analytically using the dilute approximation and the Mori–Tanaka approximation together with the Eshelby's equivalent inclusion method. Both uniaxially aligned and uniformly randomly oriented spheroidal and ellipsoidal inhomogeneities are treated. For a spheroid, both oblate and prolate spheroidal inhomogeneities are considered. It is analytically shown that a composite with uniaxially aligned anisotropic ellipsoidal inhomogeneities in an isotropic matrix is anisotropic in general in thermal conductivity. It is also analytically shown that a composite with uniformly randomly oriented anisotropic ellipsoidal inhomogeneities in an isotropic matrix is exactly isotropic in thermal conductivity. Various special cases are also treated for the effective thermal conductivity of a composite with ellipsoidal and spheroidal inhomogeneities. Similar results are also obtained for the effective elastic moduli. Newly obtained expressions for the effective elastic moduli of a composite with isotropic spheroidal inhomogeneities are rather involved. Conversely, an effective thermal conductivity of a composite with anisotropic ellipsoidal inhomogeneities is relatively simple. An effective thermal conductivity of a composite with isotropic spheroidal inhomogeneities reduces to a known result (Kerner, E. H. [1956] “The electrical conductivity of composite media,” Proceedings of the Physical Society London Section B 69, 802–807; Hashin, Z. and Shtrikman, S. [1962] “A variational approach to the theory of the effective magnetic permeability of multiphase materials,” Journal of Applied Physics 33, 3125–3131.) as the spheroid aspect ratio approaches 1 (i.e., a sphere). The effective thermal conductivity of a composite with uniformly randomly oriented isotropic spheroidal inhomogeneities in an isotropic matrix obtained in this paper as a special case is similar to the one obtained by Hatta and Taya (Hatta, H. and Taya, M. [1985] “Effective thermal conductivity of a misoriented short fiber composite,” Journal Applied Physics 58, 2478–2486.) in some respects, but is different. Numerical results are shown for a composite with oblate spheroidal voids in an isotropic matrix.

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19

Arimitsu, Yutaka, Kazumi Nishioka, and Toyomitsu Senda. "A Study of Saint-Venant’s Principle for Composite Materials by Means of Internal Stress Fields." Journal of Applied Mechanics 62, no. 1 (1995): 53–58. http://dx.doi.org/10.1115/1.2895883.

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It is well known that end effects in a composite material do not always decay as they do in a homogeneous and isotropic material, but there is no unified explanation for this difference. We note that the stress field in a composite material can be resolved into two kinds: one is the stress distribution in an isotropic and homogeneous reference system where Saint-Venant’s principle is satisfied and the other is the internal stress field induced by the incompatibility. Considering that the incompatibility is proportional to the difference between the elastic compliances of the components or to the deviation from isotropy, we propose, based on an argument concerning the dislocations associated with the incompatibility, a reason why end effects may survive to a long distance in a composite material.

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20

Bohrer, Rubens, and Il Yong Kim. "Multi-material topology optimization considering isotropic and anisotropic materials combination." Structural and Multidisciplinary Optimization 64, no. 3 (2021): 1567–83. http://dx.doi.org/10.1007/s00158-021-02941-z.

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21

Latorre, Marcos, and Francisco Javier Montáns. "Material-symmetries congruency in transversely isotropic and orthotropic hyperelastic materials." European Journal of Mechanics - A/Solids 53 (September 2015): 99–106. http://dx.doi.org/10.1016/j.euromechsol.2015.03.007.

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22

Girimaji, S. S., and S. B. Pope. "Material-element deformation in isotropic turbulence." Journal of Fluid Mechanics 220 (November 1990): 427–58. http://dx.doi.org/10.1017/s0022112090003330.

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The evolution of infinitesimal material line and surface elements in homogeneous isotropic turbulence is studied using velocity-gradient data generated by direct numerical simulations (DNS). The mean growth rates of length ratio (l) and area ratio (A) of material elements are much smaller than previously estimated by Batchelor (1952) owing to the effects of vorticity and of non-persistent straining. The probability density functions (p.d.f.'s) of l/〈l〉 and A/〈A〉 do not attain stationarity as hypothesized by Batchelor (1952). It is shown analytically that the random variable l/〈l〉 cannot be stationary if the variance and integral timescale of the strain rate along a material line are non-zero and DNS data confirm that this is indeed the case. The application of the central limit theorem to the material element evolution equations suggests that the standardized variables $\hat{l}(\equiv (\ln l - \langle \ln l\rangle)/({\rm var} l)^{\frac{1}{2}})$ and Â(≡(ln A − 〈ln A〉)/(var A)½) should attain stationary distributions that are Gaussian for all Reynolds numbers. The p.d.f.s of $\hat{l}$ and Â calculated from DNS data appear to attain stationary shapes that are independent of Reynolds number. The stationary values of the flatness factor and super-skewness of both $\hat{l}$ and Â are in close agreement with those of a Gaussian distribution. Moreover, the mean and variance of ln l (and ln A) grow linearly in time (normalized by the Kolmogorov timescale, τη), at rates that are nearly independent of Reynolds number. The statistics of material volume-element deformation are also studied and are found to be nearly independent of Reynolds number. An initially spherical infinitesimal volume of fluid deforms into an ellipsoid. It is found that the largest and the smallest of the principal axes grow and shrink respectively, exponentially in time at comparable rates. Consequently, to conserve volume, the intermediate principal axis remains approximately constant.The performance of the stochastic model of Girimaji & Pope (1990) for the velocity gradients is also studied. The model estimates of the growth rates of 〈ln l〉 and 〈ln A〉 are close to the DNS values. The growth rate of the variances are estimated by the model to within 17%. The stationary distributions of $\hat{l}$ and Â obtained from the model agree very well with those calculated from DNS data. The model also performs well in calculating the statistics of material volume-element deformation.

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23

Münch, Ingo, Patrizio Neff, and Werner Wagner. "Microstructural behaviour of transversal isotropic material." PAMM 8, no. 1 (2008): 10559–60. http://dx.doi.org/10.1002/pamm.200810559.

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24

Norris, Andrew. "The isotropic material closest to a given anisotropic material." Journal of Mechanics of Materials and Structures 1, no. 2 (2006): 223–38. http://dx.doi.org/10.2140/jomms.2006.1.223.

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25

Stauden, Thomas, Florentina Niebelschütz, Katja Tonisch, et al. "Isotropic Etching of SiC." Materials Science Forum 600-603 (September 2008): 651–54. http://dx.doi.org/10.4028/www.scientific.net/msf.600-603.651.

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Isotropic etching of silicon carbide was achieved using a capacitive coupled parallel plate reactor in plasma etching mode and SF6 at elevated substrate temperatures. It was observed to be remarkable at substrate temperatures above 350°C. The influence of chamber pressure, masking materials, rf-power and substrate temperature were analyzed. Thereby, 8.5° off-axis oriented 4HSiC wafers exhibit a larger vertical and lateral etching rate compared to on-axis oriented SiC wafers. Additionally, the erosion of nitrogen containing masking material results in a reduction of the etching rates.

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Vorobyeva, Alexandra, Qifeng Wang, Dieter Klatt, Kenneth Shull, Eric J. Perreault, and Thomas Royston. "Rayleigh-Lamb wave propagation in a prestressed transversely isotropic viscoelastic waveguide: Inverse modeling challenges." Journal of the Acoustical Society of America 155, no. 3_Supplement (2024): A291. http://dx.doi.org/10.1121/10.0027544.

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The functional role and structure of skeletal muscle results in anisotropy in both material properties and imposed stresses, as well as waveguide effects. Dynamic elastography reconstruction methods for estimating muscle tissue viscoelastic properties that are rooted in assumptions of isotropy and bulk wave motion may produce inaccurate estimates. The superposition of axially-aligned orthotropy (transverse isotropy) in material properties and axially-aligned prestress conditions due to passive stretch or muscle activation makes it difficult to independently discern how much of the apparent anisotropy is due to the muscle material or the imposed stress field. Furthermore, this stress field may result in large strain conditions that require use of higher order terms in the stress-strain relationship. The significance of this confounding condition and strategies for decoupling material and stress-based anisotropy are investigated with a series of numerical finite element and experimental elastography studies using scanning laser Doppler vibrometry and magnetic resonance elastography. Shear and Rayleigh-Lamb wave motion is studied in a polymeric muscle phantom that is in the shape of a rectangular rod and has either isotropic or transversely isotropic material properties under zero stress conditions. [Funding support: NIH AR071162]

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Tsvetkov, S. V. "Non-Linear Constitutive Equations for Transversely Isotropic Materials Belonging to the С∞ and С∞h Symmetry Groups". Herald of the Bauman Moscow State Technical University. Series Natural Sciences, № 84 (червень 2019): 46–59. http://dx.doi.org/10.18698/1812-3368-2019-3-46-59.

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Transversely isotropic materials feature infinite-order symmetry axes. Depending on which other symmetry elements are found in the material structure, five symmetry groups may be distinguished among transversely isotropic materials. We consider constitutive equations for these materials. These equations connect two symmetric second-order tensors. Two types of constitutive equations describe the properties of these five material groups. We derived constitutive equations for materials belonging to the C∞ and C∞h symmetry groups in the tensor function form. To do this, we used corollaries of Curie's Symmetry Principle. This makes it possible to obtain a fully irreducible form of the tensor function.

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Chen, Wenjiong, Liyong Tong, and Shutian Liu. "Design of periodic unit cell in cellular materials with extreme properties using topology optimization." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 232, no. 10 (2016): 852–69. http://dx.doi.org/10.1177/1464420716652638.

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This paper presents a topology optimization method to design periodic unit cell in cellular materials with extreme properties using a moving iso-surface threshold method. The aim is to determine the optimal distribution of material within the periodic unit cell. The effective properties of cellular material are obtained by using a finite element-based homogenization method. The penalty function approach is introduced to construct the objective function for designing material with extreme properties under condition of square or isotropic symmetry. New characteristic response functions of moving iso-surface threshold are proposed for maximum shear or bulk modulus, maximum shear modulus or negative Poisson’s ratio under isotropic symmetry. Several examples are presented and the results are compared to those obtained with the solid isotropic material with penalization method to demonstrate the validity of the method. A series of new and interesting microstructures with extreme properties are found and presented.

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Avetisyan, A. S., H. S. Jilavyan, and As Zh Khurshudyan. "Averaged Controllability Of Transversely Isotropic Ambartsumyan Plate." Mechanics - Proceedings of National Academy of Sciences of Armenia 75, no. 1 (2022): 124–35. http://dx.doi.org/10.54503/0002-3051-2022.75.1-2-124.

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In this paper we study the averaged controllability of Ambartsumyan plate made of a transversely isotropic material. Governing equations are based on assumptions of particular theory of anisotropic plates developed by S. A. Ambartsumyan specifically for describing the deformation of anisotropic plates made of material with isotropy plane which, at each point of the plate, is parallel to its middle plane. The Green’s function approach is applied to express the plate normal displacement by means of material parameters (density, Young moduli in both directions of isotropy) which are assumed to be uniformly distributed random variables. Eventually, the averaged controllability condition is reduced to an infinite system of linear constraints with respect to the control action. Three types of particular (heuristic) solutions of the truncated version of the infinite system are discussed. Determination of control parameters is reduced to the solution of a problem of nonlinear programming.

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Khoshini, Mohammad, Arman Khoshghalb, and Nasser Khalili. "Compressive behaviour of very dense structured granular geo-materials." E3S Web of Conferences 92 (2019): 09002. http://dx.doi.org/10.1051/e3sconf/20199209002.

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The isotropic compression behaviour of dense structured geo-materials and the associated degradation at failure is addressed in a non-qualitative manner. To this end, the general behaviour of fully de-structured geo-materials, e.g. sands, as an accepted reference is thoroughly investigated. The parameters affecting the behaviour of de-structured materials such as mineralogy, gradation and fines content, and relative density are discussed. The isotropic compression behaviour of a weathered weak sandstone, representative of a structured granular geo-material, is then investigated along the isotropic compression stress path under a range of pressures from nil to 100 MPa. Both structured and fully de-structured states of the material are tested implementing the proposed quantification method. The effect of structure on the compressibility of the material is found to be tangible. By plotting the specific volume versus natural log of the mean effective stress, the onset of structure collapse and the successive degradation of the structure are captured. By increasing the pressure, compaction bands throughout the sample increasingly develop and the compression curve asymptotically approaches to that of the fully degraded state of the material. At elevated pressures, the rate of compressibility will increase significantly due to particle crushing.

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Ghlawat, Vikash, Devinder Singh Pathania, Richa Sharma, Arvind Kumar, and Khursheed Alam. "Evaluation of thermal stresses in transversely isotropic piezoelectric disc with rotation and internal pressure." Structural Integrity and Life 24, no. 2 (2024): 172–77. http://dx.doi.org/10.69644/ivk-2024-02-0172.

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The paper deals with the analytical solution of transitional stresses in thin rotating disc composed of piezoelectric material under temperature and internal pressure. The stresses are evaluated in the rotating disc by using transition theory of Seth. The electric displacement relations and stresses are computed by using stress strain relations. The non-homogeneous differential equation is derived by substituting the obtained relations into the equilibrium equation. The formulated differential equation is solved with specified boundary conditions, applied pressure, electric displacement and stresses. Obtained results are exhibited graphically, analysed numerically and it is then concluded that transversely isotropic beryl is better than transversely isotropic magnesium material and transversely isotropic piezoelectric materials BaTiO4 and PZT-4.

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Ghamkhar, Madiha, Ahmad N. Al-Kenani, and Naveed Hussain. "Structural Study of Four-Layered Cylindrical Shell Comprising Ring Support." Symmetry 16, no. 7 (2024): 812. http://dx.doi.org/10.3390/sym16070812.

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In this work, the vibration analysis of a layered, cylinder-shaped shell is undertaken. The structure of the shell layers is composed of functionally graded and isotropic materials. The vibrations of four-layered cylindrical shells with a ring support along the axial direction are investigated in this research. The two internal layers are composed of isotropic materials, and the external two layers are composed of functionally graded materials. The outer functionally graded material layers considered are stainless steel, zirconia, and nickel. The inner two isotropic layers considered are aluminum and stainless steel. The shell frequency equation is acquired by employing the Rayleigh–Ritz method under the shell theory of Sanders. The trigonometric volume fraction law is used to sort the functionally graded material composition of the FGM layers. The natural frequencies are attained under two boundary conditions, namely simply supported–simply supported and clamped–clamped.

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Theocaris, Pericles S. "The Plane Hydrostatic Test as a Means for Selecting Appropriate Failure Criteria in Fibre Composites." Engineering Plastics 1, no. 1 (1993): 147823919300100. http://dx.doi.org/10.1177/147823919300100102.

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Biaxial tests in anisotropic plates of composite materials do not provide a conclusive evidence for the selection of the appropriate version of the failure tensor polynomial criterion (FTP). On the other hand triaxial tests, which could be decisive, present difficulties and inaccuracies when anisotropic materials should be tested. It was shown in this paper that a simple biaxial hydrostatic test in the transverse isotropic plane of a transversely isotropic material constitutes an accurate technique to decide which version of the criterion is valid. It was proved that the anisotropy along the strong stress axis of the material increases considerably the differences in failure in the transverse isotropic plane between the various criteria and it constitutes a safe test for deciding the validity of the appropriate criterion. Tests in biaxial hydrostatic tension or compression with different composite materials indicated clearly the superiority of the elliptic paraboloid failure surface criterion (EPFS).

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Theocaris, Pericles S. "The Plane Hydrostatic Test as a Means for Selecting Appropriate Failure Criteria in Fibre Composites." Polymers and Polymer Composites 1, no. 1 (1993): 3–17. http://dx.doi.org/10.1177/096739119300100102.

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Biaxial tests in anisotropic plates of composite materials do not provide a conclusive evidence for the selection of the appropriate version of the failure tensor polynomial criterion (FTP). On the other hand triaxial tests, which could be decisive, present difficulties and inaccuracies when anisotropic materials should be tested. It was shown in this paper that a simple biaxial hydrostatic test in the transverse isotropic plane of a transversely isotropic material constitutes an accurate technique to decide which version of the criterion is valid. It was proved that the anisotropy along the strong stress axis of the material increases considerably the differences in failure in the transverse isotropic plane between the various criteria and it constitutes a safe test for deciding the validity of the appropriate criterion. Tests in biaxial hydrostatic tension or compression with different composite materials indicated clearly the superiority of the elliptic paraboloid failure surface criterion (EPFS).

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35

Liu, Long, Ji Wan Kim, Ran Zheng, Gil Ho Yoon, and Bing Yi. "Multi-material topology optimization of phononic crystal considering isotropic/anisotropic materials." Computers & Structures 302 (October 2024): 107479. http://dx.doi.org/10.1016/j.compstruc.2024.107479.

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36

Kumar, Rajneesh, and Vijay Chawla. "Three-dimensional fundamental solution in transversely isotropic thermoelastic diffusion material." Theoretical and Applied Mechanics 39, no. 2 (2012): 165–84. http://dx.doi.org/10.2298/tam1202163k.

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The aim of the present investigation is to study the fundamental solution for three dimensional problem in transversely isotropic thermoelastic diffusion medium. After applying the dimensionless quantities, two displacement functions are introduced to simplify the basic threedimensional equations of thermoelastic diffusion with transverse isotropy for the steady state problem. Using the operator theory, we have derived the general expression for components of displacement, mass concentration, temperature distribution and stress components. On the basis of general solution, three dimensional fundamental solutions for a point heat source in an infinite thermoelastic diffusion media is obtained by introducing four new harmonic functions. From the present investigation, a special case of interest is also deduced to depict the effect of diffusion.

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37

Susek, Waldemar, Andrzej Dukata, and Patrycja Pomarańska. "A Formal Approach to the Extraction of Permittivity and Permeability of Isotropic and Anisotropic Media Using the TM11 Mode in Rectangular Waveguides." Electronics 12, no. 13 (2023): 2899. http://dx.doi.org/10.3390/electronics12132899.

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Based on our previous work on the propagation of electromagnetic waves in a layered medium placed in a rectangular waveguide, we present the theory of using the TE10 and TM11 modes to determine the complex parameters of isotropic and anisotropic media. The Nicolson–Ross–Weir method was used. The cases of isotropic, uniaxial, and biaxial materials were considered. It has been shown that the TM11 mode can be used to extract parameters of non-magnetic uniaxial anisotropy media by a single measurement, without changing the sample position. This is not possible with the previously used TE10 mode. It is also possible to use the TM11 mode to quickly determine whether a material is isotropic or not. Experimental results are presented for some isotropic materials.

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38

Kühn, M., W. John, and R. Weigel. "Analytical calculation of intrinsic shielding effectiveness for isotropic and anisotropic materials based on measured electrical parameters." Advances in Radio Science 12 (November 10, 2014): 83–89. http://dx.doi.org/10.5194/ars-12-83-2014.

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Abstract. This contribution contains the mechanisms for calculation of magnetic shielding effectiveness from material samples, based on measured electrical parameters. For this, measurement systems for the electrical conductivity of high and low conductive material samples with respect to the direction of current flow are presented and discussed. Also a definition of isotropic and anisotropic materials with electrical circuit diagrams is given. For prediction of shielding effectiveness for isotropic and anisotropic materials, several analytical models are presented. Also adaptions to gain a near field solution are part of this contribution. All analytical models will also be validated with an adequate measurement system.

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Rose, Joseph L., Adnan Nayfeh, and Aleksander Pilarski. "Surface Waves for Material Characterization." Journal of Applied Mechanics 57, no. 1 (1990): 7–11. http://dx.doi.org/10.1115/1.2888328.

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Analyses are presented for the propagation of harmonic surface waves on a transversely isotropic layer rigidly bonded to a transversely isotropic substrate of different material. The layer-substrate system is also assumed to be in contact with a liquid and inviscid space. The propagation takes place along an axis of symmetry of both the layer and the substrate. Exact closed-form solutions for the characteristic dispersion relations are presented. Numerical results are presented for material combinations of three classes of centrifugally cast stainless steel material. Results clearly demonstrate the influence of the layer thickness on the propagation speed and, hence, provide a means of material characterization.

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Miroshnichenko, I. P., and V. P. Sizov. "GENERAL SCALARIZATION METHOD OF DYNAMIC ELASTIC FIELDS IN TRANSVERSALLY ISOTROPIC MEDIA AND ITS NEW APPLICATIONS." Vestnik of Don State Technical University 18, no. 3 (2018): 258–64. http://dx.doi.org/10.23947/1992-5980-2018-18-3-258-264.

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Introduction. An efficient technique of tensor field scalarization is successfully used while investigating tensor elastic fields of displacements, stresses and deformations in the layered structures of different materials, including transversally isotropic composites. These fields can be expressed through the scalar potentials corresponding to the quasi-longitudinal, quasi-transverse, and transverse-only waves. Such scalarization is possible if the objects under consideration are tensors relating to the subgroup of general coordinate conversions, when the local affine basis has one invariant vector that coincides with the material symmetry axis of the material. At this, the known papers consider structures where this vector coincides with the normal to the boundary between layers. However, other cases of the mutual arrangement of the material symmetry axis of the material and the boundaries between layers are of interest on the practical side.Materials and Methods. The work objective is further development of the scalarization method application in the boundary value problems of the dynamic elasticity theory for the cases of an arbitrary arrangement of the material symmetry axis relative to the boundary between layers. The present research and methodological apparatus are developed through the general technique of scalarization of the dynamic elastic fields of displacements, stresses and strains in the transversally isotropic media.Research Results. New design ratios for the determination of the displacement fields, stresses and deformations in the transversally isotropic media are obtained for the cases of an arbitrary arrangement of the material symmetry axes of the layer materials with respect to the boundaries between layers. Discussion and Conclusions. The present research and methodological apparatus are successfully used in determining the stress-strain state in the layered structures of transversally isotropic materials, and in analyzing the diagnosis results of the state of the plane-layered and layered cylindrical structures under operation.

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41

Darkwa, K. "Quasi-isotropic laminated phase-change material system." Applied Energy 84, no. 6 (2007): 599–607. http://dx.doi.org/10.1016/j.apenergy.2007.02.001.

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42

Chandrakanth, S., and P. C. Pandey. "An isotropic damage model for ductile material." Engineering Fracture Mechanics 50, no. 4 (1995): 457–65. http://dx.doi.org/10.1016/0013-7944(94)00214-3.

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43

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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BERZBORN, Marco, and Michael VORLäNDER. "Inference of the acoustic properties of transversely isotropic porous materials." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 270, no. 3 (2024): 8339–44. http://dx.doi.org/10.3397/in_2024_4080.

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Transversely isotropic porous materials are well represented by equivalent fluid models based on semi-phenomenological models such as the Johnson-Champoux-Allard-Lafarge (JCAL) model and a set of material parameters. Direct measurements of these parameters, however, are often difficult or time consuming. As an alternative, inverse estimation methods provide a simple and fast framework to identify the JCAL model parameters, since they can be performed on single impedance tube measurements. In this work, we present a stochastic inverse identification method of the JCAL parameters for transversely isotropic materials. We consider the flow resistance and characteristic viscous length and the static tortuosity to be anisotropic and the frame to be fully rigid, resulting in nine unique parameters to be identified. The method is based on reflection factor measurements of a material in different orientations corresponding the transverse and isotropic principal axes. Hence, a priori knowledge of the orientation of the principal axes of the material is required. Results of the parameter inference are presented based on experimental data for a glass wool sample.

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Slota, Jan, Ivan Gajdos, Emil Spišák, and Marek Šiser. "Springback Prediction of Stretching Process using Finite Element Analysis for DP600 Steel Sheet." Acta Mechanica et Automatica 11, no. 1 (2017): 5–8. http://dx.doi.org/10.1515/ama-2017-0001.

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Abstract Springback phenomenon is well predicted for some mild steel materials, but not for steels with higher strength. One of the most used tools to stamping optimization is usage of finite element analysis. In order to accurate describe the real behaviour of the materials for stamping of vehicle panels, the application of proper hardening rule seems to be crucial. Due to higher accuracy of predicted results, high strength steel sheets are usually modelled by means of kinematic or mixed isotropic-kinematic hardening models. In this paper the springback prediction of advanced high strength steel DP600 by numerical simulation was investigated. Through cyclic tension-compression tests, the material characterization has been performed for DP600 steel sheet. Different hardening models (isotropic, kinematic and mixed isotropic-kinematic) used in the simulations were compared with expreriment. The Yoshida–Uemori model succesfully describe the kinematic behaviour of the material and provided more accurate results than others.

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Mittleman, J., R. Roberts, and R. B. Thompson. "Scattering of Longitudinal Elastic Waves From an Anisotropic Spherical Shell." Journal of Applied Mechanics 62, no. 1 (1995): 150–58. http://dx.doi.org/10.1115/1.2895896.

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An exact solution for scattering of ultrasound from a spherically orthotropic shell is presented. The shell is assumed to be embedded in an isotropic elastic medium, and the core surrounded by the shell is also assumed to be isotropic. The shell itself is assumed to be “spherically orthotropic,” with five independent elastic constants (the spherical analog of a transversely isotropic material in Cartesian coordinates). Field equations for this material are presented, and these equations are shown to be separable. Working with the displacement vector, we find that the radius dependent part of the solution satisfies coupled second-order ordinary differential equations. This system of equations is solved using the method of Frobenius, and results in four independent series determined by material properties to within a multiplicative constant. Use of boundary conditions expressed in terms of stresses and displacements at the inner and outer shell radii completes the solution. Numerical results for a range of shell elastic constants show that this solution matches known analytic results in the special case of isotropy and matches previously developed finite difference results for anisotropic elastic constants. The effect of shell anisotropy on far-field scattering amplitude is explored for an incident plane longitudinal wave.

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Usal, Melek. "On Continuum Damage Modeling of Fiber Reinforced Viscoelastic Composites with Microcracks in terms of Invariants." Mathematical Problems in Engineering 2015 (2015): 1–15. http://dx.doi.org/10.1155/2015/624750.

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A continuum damage model is developed for the linear viscoelastic behavior of composites with microcracks consisting of an isotropic matrix reinforced by two arbitrarily independent and inextensible fiber families. Despite the fact that the matrix material is isotropic, the model in consideration bears the characteristic of directed media included in the transverse isotropy symmetry group solely due to its fibers distributions and the existence of microcracks. Using the basic laws of continuum damage mechanics and equations belonging to kinematics and deformation geometries of fibers, the constitutive functions have been obtained. It has been detected as a result of the thermodynamic constraints that the stress potential function is dependent on two symmetric tensors and two vectors, whereas the dissipative stress function is dependent on four symmetric tensors and two vectors. To determine arguments of the constitutive functionals, findings relating to the theory of invariants have been used as a method because of the fact that isotropy constraint is imposed on the material. As a result the linear constitutive equations of elastic stress, dissipative stress, and strain energy density release rate have been written in terms of material coordinate description. Using these expressions, total stress has been found.

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Bansal, Savita, and Satya Bir Singh. "Investigation of creep in anisotropic cylinder using plane stress condition." Structural Integrity and Life 25, no. 1 (2025): 106–10. https://doi.org/10.69644/ivk-2025-01-0106.

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Creep response is investigated in an anisotropic cylinder under plane stress condition using constitutive equations of anisotropic creep theory and Sherby’s law, on a thick-walled cylinder of orthotropic material under constant internal pressure. Radial and tangential stress distribution in the cylinder have been calculated and compared for two different cases of anisotropy with that of an isotropic material. It is concluded that anisotropy leads to nominal variation in stress distribution in the thick-walled cylinder under plane stress condition. The study, however, reveals that under plane stress condition, isotropic materials show lesser creep response than anisotropic material and are found to be better from the engineering design point of view.

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Islam, Md Shahidul, and Hideo Koguchi. "813 Effect of Singularity at Vertex in Transversely Isotropic Piezoelectric Dissimilar Material Joints." Proceedings of Conference of Hokuriku-Shinetsu Branch 2010.47 (2010): 293–94. http://dx.doi.org/10.1299/jsmehs.2010.47.293.

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WU, YUE-XIU, and QUAN-SHENG LIU. "THE ANALYSIS OF DYNAMICAL RESPONSE OF TRANSVERSELY ISOTROPIC MATERIAL UNDER BLASTING LOAD." International Journal of Modern Physics B 22, no. 09n11 (2008): 1443–48. http://dx.doi.org/10.1142/s0217979208046906.

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To understand the dynamic response of transversely isotropic material under explosion load, the analysis is done with the help of ABAQUS software and the constitutive equations of transversely isotropic material with different angle of isotropic section. The result is given: when the angle of isotropic section is settled, the velocity and acceleration of measure points decrease with the increasing distance from the explosion borehole. The velocity and acceleration in the loading direction are larger than those in the normal direction of the loading direction and their attenuation are much faster. When the angle of isotropic section is variable, the evolution curves of peak velocity and peak acceleration in the loading direction with the increasing angles are notching parabolic curves. They get their minimum values when the angle is equal to 45 degree. But the evolution curves of peak velocity and peak acceleration in the normal direction of the loading direction with the increasing angles are overhead parabolic curves. They get their maximum values when the angle is equal to 45 degree.

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Journal articles on the topic 'Isotropic material'

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