Log in

Relevant bibliographies by topics / Tensor of elasticity / Journal articles

To see the other types of publications on this topic, follow the link: Tensor of elasticity.

Journal articles on the topic 'Tensor of elasticity'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Tensor of elasticity.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Milton, Graeme W., and Andrej V. Cherkaev. "Which Elasticity Tensors are Realizable?" Journal of Engineering Materials and Technology 117, no. 4 (October 1, 1995): 483–93. http://dx.doi.org/10.1115/1.2804743.

Full text

Abstract:

It is shown that any given positive definite fourth order tensor satisfying the usual symmetries of elasticity tensors can be realized as the effective elasticity tensor of a two-phase composite comprised of a sufficiently compliant isotropic phase and a sufficiently rigid isotropic phase configured in an suitable microstructure. The building blocks for constructing this composite are what we call extremal materials. These are composites of the two phases which are extremely stiff to a set of arbitrary given stresses and, at the same time, are extremely compliant to any orthogonal stress. An appropriately chosen subset of the extremal materials are layered together to form the composite with elasticity tensor matching the given tensor.

APA, Harvard, Vancouver, ISO, and other styles

2

He, Q. C. "A Remarkable Tensor in Plane Linear Elasticity." Journal of Applied Mechanics 64, no. 3 (September 1, 1997): 704–7. http://dx.doi.org/10.1115/1.2788952.

Full text

Abstract:

It is shown that any two-dimensional elastic tensor can be orthogonally and uniquely decomposed into a symmetric tensor and an antisymmetric tensor. To within a scalar multiplier, the latter turns out to be equal to the right-angle rotation on the space of two-dimensional second-order symmetric tensors. On the basis of these facts, several useful results are derived for the traction boundary value problem of plane linear elasticity.

APA, Harvard, Vancouver, ISO, and other styles

3

Sutcliffe, S. "Spectral Decomposition of the Elasticity Tensor." Journal of Applied Mechanics 59, no. 4 (December 1, 1992): 762–73. http://dx.doi.org/10.1115/1.2894040.

Full text

Abstract:

The elasticity tensor in anisotropic elasticity can be regarded as a symmetric linear transformation on the nine-dimensional space of second-order tensors. This allows the elasticity tensor to be expressed in terms of its spectral decomposition. The structures of the spectral decompositions are determined by the sets of invariant subspaces that are consistent with material symmetry. Eigenvalues always depend on the values of the elastic constants, but the eigenvectors are, in part, independent of these values. The structures of the spectral decompositions are presented for the classical symmetry groups of crystallography, and numerical results are presented for representative materials in each group. Spectral forms for the equilibrium equations, the acoustic tensor, and the stored energy function are also derived.

APA, Harvard, Vancouver, ISO, and other styles

4

Kochetov, Mikhail, and Michael A. Slawinski. "Estimating effective elasticity tensors from Christoffel equations." GEOPHYSICS 74, no. 5 (September 2009): WB67—WB73. http://dx.doi.org/10.1190/1.3155163.

Full text

Abstract:

We consider the problem of obtaining the orientation and elasticity parameters of an effective tensor of particular symmetry that corresponds to measurable traveltime and polarization quantities. These quantities — the wavefront-slowness and polarization vectors — are used in the Christoffel equation, a characteristic equation of the elastodynamic equation that brings seismic concepts to our formulation and relates experimental data to the elasticity tensor. To obtain an effective tensor of particular symmetry, we do not assume its orientation; thus, the regression using the residuals of the Christoffel equation results in a nonlinear optimization problem. We find the absolute extremum and, to avoid numerical instability of a global search, obtain an accurate initial guess using the tensor of given symmetry closest to the generally anisotropic tensor obtained from data by linear regression. The issue is twofold. First, finding the closest tensor of particular symmetry without assuming its orientation is challenging. Second, the closest tensor is not the effective tensor in the sense of regression because the process of finding it carries neither seismic concepts nor statistical information; rather, it relies on an abstract norm in the space of elasticity tensors. To include seismic concepts and statistical information, we distinguish between the closest tensor of particular symmetry and the effective one; the former is the initial guess to search for the latter.

APA, Harvard, Vancouver, ISO, and other styles

5

Diner, Çağrı. "The Structure of Moment Tensors in Transversely Isotropic Focal Regions." Bulletin of the Seismological Society of America 109, no. 6 (September 24, 2019): 2415–26. http://dx.doi.org/10.1785/0120180316.

Full text

Abstract:

Abstract Full moment tensor inversion has become a standard method for understanding the mechanisms of earthquakes as the resolution of the inversion process increases. Thus, it is important to know the possible forms of non–double‐couple (non‐DC) moment tensors, which can be obtained because of either the different source mechanisms or the anisotropy of the focal regions. In this study, the form of the moment tensors of seismic sources occurring in transversely isotropic (TI) focal regions is obtained using the eigendecomposition of the elasticity tensor. More precisely, a moment tensor is obtained as a linear combination of the eigenspaces of TI elasticity tensor in which the coefficients of the terms are the corresponding eigenvalues multiplied with the projection of the potency tensor onto the corresponding eigenspaces. Moreover, the eigendecomposition method is also applied to obtain the three different forms of moment tensors in isotropic focal regions, in particular, for the shear source, tensile source, and for any type of potency tensor whose rank is three. This linear algebra point of view makes the structure of the moment tensors more apparent; for example, a shear source tensor is an eigenvector of isotropic elasticity tensor, and hence the resulting moment tensor is proportional to its shear source tensor. Moreover, a geometric interpretation for the scalar seismic moment, which is the norm of the moment tensor, for anisotropic focal regions is achieved through the eigendecomposition method. This method also gives a simple way to quantify the percentage of the isotropic component of the moment tensor of shear sources in TI focal regions. Hence, the complexities in the moment tensor introduced by the anisotropy of the focal region and by the source mechanism can be differentiated.

APA, Harvard, Vancouver, ISO, and other styles

6

Lazar, Markus, and Giacomo Po. "On Mindlin’s isotropic strain gradient elasticity: Green tensors, regularization, and operator-split." Journal of Micromechanics and Molecular Physics 03, no. 03n04 (September 2018): 1840008. http://dx.doi.org/10.1142/s2424913018400088.

Full text

Abstract:

The theory of Mindlin’s isotropic strain gradient elasticity of form II is reviewed. Three-dimensional and two-dimensional Green tensors and their first and second derivatives are derived for an unbounded medium. Using an operator-split in Mindlin’s strain gradient elasticity, three-dimensional and two-dimensional regularization function tensors are computed, which are the three-dimensional and two-dimensional Green tensors of a tensorial Helmholtz equation. In addition, a length scale tensor is introduced, which is responsible for the characteristic material lengths of strain gradient elasticity. Moreover, based on the Green tensors of Mindlin’s strain gradient elasticity, point, line and double forces are studied.

APA, Harvard, Vancouver, ISO, and other styles

7

Suchocki, Cyprian. "A Finite Element Implementation of Knowles Stored-Energy Function: Theory, Coding and Applications." Archive of Mechanical Engineering 58, no. 3 (January 1, 2011): 319–46. http://dx.doi.org/10.2478/v10180-011-0021-7.

Full text

Abstract:

A Finite Element Implementation of Knowles Stored-Energy Function: Theory, Coding and Applications This paper contains the full way of implementing a user-defined hyperelastic constitutive model into the finite element method (FEM) through defining an appropriate elasticity tensor. The Knowles stored-energy potential has been chosen to illustrate the implementation, as this particular potential function proved to be very effective in modeling nonlinear elasticity within moderate deformations. Thus, the Knowles stored-energy potential allows for appropriate modeling of thermoplastics, resins, polymeric composites and living tissues, such as bone for example. The decoupling of volumetric and isochoric behavior within a hyperelastic constitutive equation has been extensively discussed. An analytical elasticity tensor, corresponding to the Knowles stored-energy potential, has been derived. To the best of author's knowledge, this tensor has not been presented in the literature yet. The way of deriving analytical elasticity tensors for hyperelastic materials has been discussed in detail. The analytical elasticity tensor may be further used to develop visco-hyperelastic, nonlinear viscoelastic or viscoplastic constitutive models. A FORTRAN 77 code has been written in order to implement the Knowles hyperelastic model into a FEM system. The performance of the developed code is examined using an exemplary problem.

APA, Harvard, Vancouver, ISO, and other styles

8

Le Quang, Hung, Qi-Chang He, and Nicolas Auffray. "Classification of first strain-gradient elasticity tensors by symmetry planes." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2251 (July 2021): 20210165. http://dx.doi.org/10.1098/rspa.2021.0165.

Full text

Abstract:

First strain-gradient elasticity is a generalized continuum theory capable of modelling size effects in materials. This extended capability comes from the inclusion in the mechanical energy density of terms related to the strain-gradient. In its linear formulation, the constitutive law is defined by three elasticity tensors whose orders range from four to six. In the present contribution, the symmetry properties of the sixth-order elasticity tensors involved in this model are investigated. If their classification with respect to the orthogonal symmetry group is known, their classification with respect to symmetry planes is still missing. This last classification is important since it is deeply connected with some identification procedures. The classification of sixth-order elasticity tensors in terms of invariance properties with respect to symmetry planes is given in the present contribution. Precisely, it is demonstrated that there exist 11 reflection symmetry classes. This classification is distinct from the one obtained with respect to the orthogonal group, according to which there exist 17 different symmetry classes. These results for the sixth-order elasticity tensor are very different from those obtained for the classical fourth-order elasticity tensor, since in the latter case the two classifications coincide. A few numerical examples are provided to illustrate how some different orthogonal classes merge into one reflection class.

APA, Harvard, Vancouver, ISO, and other styles

9

Truman, C. E. "An Introduction to Tensor Elasticity." Strain 39, no. 4 (November 2003): 161–65. http://dx.doi.org/10.1046/j.1475-1305.2003.00089.x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Desmorat, R., N. Auffray, B. Desmorat, B. Kolev, and M. Olive. "Generic separating sets for three-dimensional elasticity tensors." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2226 (June 2019): 20190056. http://dx.doi.org/10.1098/rspa.2019.0056.

Full text

Abstract:

We define a generic separating set of invariant functions (a.k.a. a weak functional basis ) for tensors. We then produce two generic separating sets of polynomial invariants for three-dimensional elasticity tensors, one consisting of 19 polynomials and one consisting of 21 polynomials (but easier to compute), and a generic separating set of 18 rational invariants. As a by-product, a new integrity basis for the fourth-order harmonic tensor is provided.

APA, Harvard, Vancouver, ISO, and other styles

11

Itin, Yakov. "Irreducible matrix resolution for symmetry classes of elasticity tensors." Mathematics and Mechanics of Solids 25, no. 10 (April 20, 2020): 1873–95. http://dx.doi.org/10.1177/1081286520913596.

Full text

Abstract:

In linear elasticity, a fourth-order elasticity (stiffness) tensor of 21 independent components completely describes deformation properties elastic constants of a material. The main goal of the current work is to derive a compact matrix representation of the elasticity tensor that correlates with its intrinsic algebraic properties. Such representation can be useful in design of artificial materials. Owing to Voigt, the elasticity tensor is conventionally represented by a (6 × 6) symmetric matrix. In this paper, we construct two alternative matrix representations that conform with the irreducible decomposition of the elasticity tensor. The 3 × 7 matrix representation is in correspondence with the permutation transformations of indices and with the general linear transformation of the basis. An additional representation of the elasticity tensor by two scalars and three 3 × 3 matrices is suitable to describe the irreducible decomposition under the rotation transformations. We present the elasticity tensor of all crystal systems in these compact matrix forms and construct the hierarchy diagrams based on this representation.

APA, Harvard, Vancouver, ISO, and other styles

12

Chen, Zhongming, Yannan Chen, Liqun Qi, and Wennan Zou. "Two irreducible functional bases of isotropic invariants of a fourth-order three-dimensional symmetric and traceless tensor." Mathematics and Mechanics of Solids 24, no. 10 (March 8, 2019): 3092–102. http://dx.doi.org/10.1177/1081286519835246.

Full text

Abstract:

The elasticity tensor is one of the most important fourth-order tensors in mechanics. Fourth-order three-dimensional symmetric and traceless tensors play a crucial role in the study of the elasticity tensor. In this paper, we present two isotropic irreducible functional bases for a fourth-order three-dimensional symmetric and traceless tensor. One of them is exactly the minimal integrity basis introduced by Smith and Bao in 1997. It has nine homogeneous polynomial invariants of degrees two, three, four, five, six, seven, eight, nine and ten, respectively. We prove that it is also an irreducible functional basis. The second irreducible functional basis also has nine homogeneous polynomial invariants. It has no quartic invariant but has two sextic invariants. The other seven invariants are the same as those of the Smith–Bao basis. Hence, the second irreducible functional basis is not contained in any minimal integrity basis.

APA, Harvard, Vancouver, ISO, and other styles

13

Bóna, Andrej. "Symmetry characterization and measurement errors of elasticity tensors." GEOPHYSICS 74, no. 5 (September 2009): WB75—WB78. http://dx.doi.org/10.1190/1.3184013.

Full text

Abstract:

It is often desirable to approximate a full anisotropic tensor, given by 21 independent parameters, by one with a higher symmetry. If one considers measurement errors of an elasticity tensor, the standard approaches of finding the best approximation by a higher symmetric tensor do not produce the most likely tensor. To find such a tensor, I replace the distance metric used in previous studies with one based on probability distribution functions of the errors of the measured quantities. In the case of normally distributed errors, the most likely tensor with higher symmetries coincides with the closest higher symmetric tensor, using a deviation-scaled Euclidean metric.

APA, Harvard, Vancouver, ISO, and other styles

14

Rasolofosaon, Patrick N. J., and Bernard E. Zinszner. "Comparison between permeability anisotropy and elasticity anisotropy of reservoir rocks." GEOPHYSICS 67, no. 1 (January 2002): 230–40. http://dx.doi.org/10.1190/1.1451647.

Full text

Abstract:

We developed new experimental and theoretical tools for the measurement and the characterization of arbitrary elasticity tensors and permeability tensors in rocks. They include an experimental technique for the 3‐D visualization of hydraulic invasion fronts in rock samples by monitoring the injection of salt solutions by X‐ray tomography, and a technique for inverting the complete set of the six coefficients of the permeability tensor from invasion front images. In addition, a technique for measuring the complete set of the 21 elastic coefficients, a technique allowing the identification and the orientation in the 3‐D space of the symmetry elements (planes, axes), and a technique for approximating the considered elastic tensor by a tensor of simpler symmetry with the quantification of the error induced by such an approximation have been developed. We apply these tools to various types of reservoir rocks and observed quite contrasted behaviors. In some rocks, the elastic anisotropy and the hydraulic anisotropy are closely correlated, for instance in terms of the symmetry directions. This is the case when elastic anisotropy and hydraulic anisotropy share the same cause (e.g., layering, fractures). In contrast, in some other rocks, hydraulic properties and elastic properties are clearly uncorrelated. These results highlight the challenge we have to face in order to estimate the rock permeability and to monitor the fluid flow from seismic measurements in the field.

APA, Harvard, Vancouver, ISO, and other styles

15

Nikabadze, Mikhail, and Armine Ulukhanyan. "Some Applications of Eigenvalue Problems for Tensor and Tensor–Block Matrices for Mathematical Modeling of Micropolar Thin Bodies." Mathematical and Computational Applications 24, no. 1 (March 22, 2019): 33. http://dx.doi.org/10.3390/mca24010033.

Full text

Abstract:

The statement of the eigenvalue problem for a tensor–block matrix (TBM) of any orderand of any even rank is formulated, and also some of its special cases are considered. In particular,using the canonical presentation of the TBM of the tensor of elastic modules of the micropolartheory, in the canonical form the specific deformation energy and the constitutive relations arewritten. With the help of the introduced TBM operator, the equations of motion of a micropolararbitrarily anisotropic medium are written, and also the boundary conditions are written down bymeans of the introduced TBM operator of the stress and the couple stress vectors. The formulationsof initial-boundary value problems in these terms for an arbitrary anisotropic medium are given.The questions on the decomposition of initial-boundary value problems of elasticity and thin bodytheory for some anisotropic media are considered. In particular, the initial-boundary problems of themicropolar (classical) theory of elasticity are presented with the help of the introduced TBM operators(tensors–operators). In the case of an isotropic micropolar elastic medium (isotropic and transverselyisotropic classical media), the TBM operator (tensors–operators) of cofactors to TBM operators(tensors–tensors) of the initial-boundary value problems are constructed that allow decomposinginitial-boundary value problems. We also find the determinant and the tensor of cofactors to the sumof six tensors used for decomposition of initial-boundary value problems. From three-dimensionaldecomposed initial-boundary value problems, the corresponding decomposed initial-boundary valueproblems for the theories of thin bodies are obtained.

APA, Harvard, Vancouver, ISO, and other styles

16

Sokolova, M. Yu, and D. V. Khristich. "FINITE STRAINS OF NONLINEAR ELASTIC ANISOTROPIC MATERIALS." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 70 (2021): 103–16. http://dx.doi.org/10.17223/19988621/70/9.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

17

COWIN, STEPHEN C. "PROPERTIES OF THE ANISOTROPIC ELASTICITY TENSOR." Quarterly Journal of Mechanics and Applied Mathematics 42, no. 2 (1989): 249–66. http://dx.doi.org/10.1093/qjmam/42.2.249.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

COWIN, STEPHEN C. "PROPERTIES OF THE ANISOTROPY ELASTICITY TENSOR." Quarterly Journal of Mechanics and Applied Mathematics 46, no. 3 (1993): 539. http://dx.doi.org/10.1093/qjmam/46.3.539-a.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Truman, C. E. "An Introduction to Tensor Elasticity II." Strain 40, no. 2 (May 2004): 67–72. http://dx.doi.org/10.1111/j.1475-1305.2004.00121.x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Itin, Yakov. "Quadratic Invariants of the Elasticity Tensor." Journal of Elasticity 125, no. 1 (January 15, 2016): 39–62. http://dx.doi.org/10.1007/s10659-016-9569-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Calisti, V., A. Lebée, A. A. Novotny, and J. Sokolowski. "Sensitivity of the Second Order Homogenized Elasticity Tensor to Topological Microstructural Changes." Journal of Elasticity 144, no. 2 (May 2021): 141–67. http://dx.doi.org/10.1007/s10659-021-09836-6.

Full text

Abstract:

AbstractThe multiscale elasticity model of solids with singular geometrical perturbations of microstructure is considered for the purposes, e.g., of optimum design. The homogenized linear elasticity tensors of first and second orders are considered in the framework of periodic Sobolev spaces. In particular, the sensitivity analysis of second order homogenized elasticity tensor to topological microstructural changes is performed. The derivation of the proposed sensitivities relies on the concept of topological derivative applied within a multiscale constitutive model. The microstructure is topologically perturbed by the nucleation of a small circular inclusion that allows for deriving the sensitivity in its closed form with the help of appropriate adjoint states. The resulting topological derivative is given by a sixth order tensor field over the microstructural domain, which measures how the second order homogenized elasticity tensor changes when a small circular inclusion is introduced at the microscopic level. As a result, the topological derivatives of functionals for multiscale models can be obtained and used in numerical methods of shape and topology optimization of microstructures, including synthesis and optimal design of metamaterials by taking into account the second order mechanical effects. The analysis is performed in two spatial dimensions however the results are valid in three spatial dimensions as well.

APA, Harvard, Vancouver, ISO, and other styles

22

Cowin, Stephen C. "The relationship between the elasticity tensor and the fabric tensor." Mechanics of Materials 4, no. 2 (July 1985): 137–47. http://dx.doi.org/10.1016/0167-6636(85)90012-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Felício Fuck, Rodrigo, and Ilya Tsvankin. "Analysis of the symmetry of a stressed medium using nonlinear elasticity." GEOPHYSICS 74, no. 5 (September 2009): WB79—WB87. http://dx.doi.org/10.1190/1.3157251.

Full text

Abstract:

Velocity variations caused by subsurface stress changes play an important role in monitoring compacting reservoirs and in several other applications of seismic methods. A general way to describe stress- or strain-induced velocity fields is by employing the theory of nonlinear elasticity, which operates with third-order elastic (TOE) tensors. These sixth-rank strain-sensitivity tensors, however, are difficult to manipulate because of the large number of terms involved in the algebraic operations. Thus, even evaluation of the anisotropic symmetry of a medium under stress/strain proves to be a challenging task. We employ a matrix representation of TOE tensors that allows computation of strain-related stiffness perturbations from a linear combination of [Formula: see text] matrices scaled by the components of the strain tensor. In addition to streamlining the numerical algorithm, this approach helps to predict strain-induced symmetry using relatively straightforward algebraic considerations. For example, our analysis shows that a transversely isotropic (TI) medium acquires orthorhombic symmetry if one of the principal directions of the strain tensor is aligned with the symmetry axis. Otherwise, the strained TI medium can become monoclinic or even triclinic.

APA, Harvard, Vancouver, ISO, and other styles

24

Jaric, Jovo, and Dragoslav Kuzmanovic. "On damage tensor in linear anisotropic elasticity." Theoretical and Applied Mechanics 44, no. 2 (2017): 141–54. http://dx.doi.org/10.2298/tam170306018j.

Full text

Abstract:

In this paper, the anisotropic linear damage mechanics is presented starting from the principle of strain equivalence. The authors have previously derived damage tensor components in terms of elastic parameters of undamaged (virgin) material in closed form solution. Here, making use of this paper, we derived elasticity tensor as a function of damage tensor also in closed form. The procedure we present here was applied for several crystal classes which are subjected to hexagonal, orthotropic, tetragonal, cubic and isotropic damage. As an example isotropic system is considered in order to present some possibility to evaluate its damage parameters.

APA, Harvard, Vancouver, ISO, and other styles

25

Auffray, N., B. Kolev, and M. Olive. "Handbook of bi-dimensional tensors: Part I: Harmonic decomposition and symmetry classes." Mathematics and Mechanics of Solids 22, no. 9 (May 23, 2016): 1847–65. http://dx.doi.org/10.1177/1081286516649017.

Full text

Abstract:

To investigate complex physical phenomena, bi-dimensional models are often an interesting option. It allows spatial couplings to be produced while keeping them as simple as possible. For linear physical laws, constitutive equations involve the use of tensor spaces. As a consequence the different types of anisotropy that can be described are encoded in tensor spaces involved in the model. In the present paper, we solve the general problem of computing symmetry classes of constitutive tensors in [Formula: see text] using mathematical tools coming from representation theory. The power of this method is illustrated through the tensor spaces of Mindlin strain-gradient elasticity.

APA, Harvard, Vancouver, ISO, and other styles

26

Lazar, Markus, and Helmut Kirchner. "The Eshelby tensor in nonlocal elasticity and in nonlocal micropolar elasticity." Journal of Mechanics of Materials and Structures 1, no. 2 (June 1, 2006): 325–37. http://dx.doi.org/10.2140/jomms.2006.1.325.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

BAERHEIM, REIDAR. "HARMONIC DECOMPOSITION OF THE ANISOTROPIC ELASTICITY TENSOR." Quarterly Journal of Mechanics and Applied Mathematics 46, no. 3 (1993): 391–418. http://dx.doi.org/10.1093/qjmam/46.3.391.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Federico, Salvatore, Alfio Grillo, and Shoji Imatani. "The linear elasticity tensor of incompressible materials." Mathematics and Mechanics of Solids 20, no. 6 (October 6, 2014): 643–62. http://dx.doi.org/10.1177/1081286514550576.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Kuznetsov, V. V. "Canonical tensor in the theory of elasticity." Journal of Applied Mechanics and Technical Physics 28, no. 5 (1988): 778–80. http://dx.doi.org/10.1007/bf00912034.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Bona, Andrej, and Michael A. Slawinski. "Comparison of two inversions for elasticity tensor." Journal of Applied Geophysics 65, no. 1 (June 2008): 6–9. http://dx.doi.org/10.1016/j.jappgeo.2008.03.002.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Atchonouglo, K., G. de Saxcé, and M. Ban. "2D ELASTICITY TENSOR INVARIANTS, INVARIANTS DEFINITE POSITIVE CRITERIA." Advances in Mathematics: Scientific Journal 10, no. 8 (August 6, 2021): 2999–3012. http://dx.doi.org/10.37418/amsj.10.8.1.

Full text

Abstract:

In this paper, we constructed relationships with the differents 2D elasticity tensor invariants. Indeed, let ${\bf A}$ be a 2D elasticity tensor. Rotation group action leads to a pair of Lax in linear elasticity. This pair of Lax leads to five independent invariants chosen among six. The definite positive criteria are established with the determined invariants. We believe that this approach finds interesting applications, as in the one of elastic material classification or approaches in orbit space description.

APA, Harvard, Vancouver, ISO, and other styles

32

Jaric, Jovo, Dragoslav Kuzmanovic, and Zoran Golubovic. "On tensors of elasticity." Theoretical and Applied Mechanics 35, no. 1-3 (2008): 119–36. http://dx.doi.org/10.2298/tam0803119j.

Full text

Abstract:

An objective of this paper is to reconcile the "symmetry" approach with the "symmetry groups" approach as these two different points of view presently coexist in the literature. Here we will be concerned exclusively with linearly elastic materials. The starting point for an analysis of the inherent symmetry of elastic materials is the notion of a symmetry transformation. Particularly, we paid attention to the compliance tensor for cubic and hexagonal crystals.

APA, Harvard, Vancouver, ISO, and other styles

33

Lazar, Markus. "Micromechanics and dislocation theory in anisotropic elasticity." Journal of Micromechanics and Molecular Physics 01, no. 02 (July 2016): 1650011. http://dx.doi.org/10.1142/s2424913016500119.

Full text

Abstract:

In this work, dislocation master-equations valid for anisotropic materials are derived in terms of kernel functions using the framework of micromechanics. The second derivative of the anisotropic Green tensor is calculated in the sense of generalized functions and decomposed into a sum of a [Formula: see text]-term plus a Dirac [Formula: see text]-term. The first term is the so-called “Barnett-term” and the latter is important for the definition of the Green tensor as fundamental solution of the Navier equation. In addition, all dislocation master-equations are specified for Somigliana dislocations with application to 3D crack modeling. Also the interior Eshelby tensor for a spherical inclusion in an anisotropic material is derived as line integral over the unit circle.

APA, Harvard, Vancouver, ISO, and other styles

34

CIARLET, PHILIPPE G., GIUSEPPE GEYMONAT, and FRANÇOISE KRASUCKI. "A NEW DUALITY APPROACH TO ELASTICITY." Mathematical Models and Methods in Applied Sciences 22, no. 01 (January 2012): 1150003. http://dx.doi.org/10.1142/s0218202512005861.

Full text

Abstract:

The displacement-traction problem of three-dimensional linearized elasticity can be posed as three different minimization problems, depending on whether the displacement vector field, or the stress tensor field, or the strain tensor field, is the unknown. The objective of this paper is to put these three different formulations of the same problem in a new perspective, by means of Legendre–Fenchel duality theory. More specifically, we show that both the displacement and strain formulations can be viewed as Legendre–Fenchel dual problems to the stress formulation. We also show that each corresponding Lagrangian has a saddle-point, thus fully justifying this new duality approach to elasticity.

APA, Harvard, Vancouver, ISO, and other styles

35

CIARLET, PHILIPPE G., PATRICK CIARLET, OANA IOSIFESCU, STEFAN SAUTER, and JUN ZOU. "LAGRANGE MULTIPLIERS IN INTRINSIC ELASTICITY." Mathematical Models and Methods in Applied Sciences 21, no. 04 (April 2011): 651–66. http://dx.doi.org/10.1142/s0218202511005167.

Full text

Abstract:

In an intrinsic approach to three-dimensional linearized elasticity, the unknown is the linearized strain tensor field (or equivalently the stress tensor field by means of the constitutive equation), instead of the displacement vector field in the classical approach. We consider here the pure traction problem and the pure displacement problem and we show that, in each case, the intrinsic approach leads to a quadratic minimization problem constrained by Donati-like relations (the form of which depends on the type of boundary conditions considered). Using the Babuška-Brezzi inf-sup condition, we then show that, in each case, the minimizer of the constrained minimization problem found in an intrinsic approach is the first argument of the saddle-point of an ad hoc Lagrangian, so that the second argument of this saddle-point is the Lagrange multiplier associated with the corresponding constraints. Such results have potential applications to the numerical analysis and simulation of the intrinsic approach to three-dimensional linearized elasticity.

APA, Harvard, Vancouver, ISO, and other styles

36

Boehler, J. P., A. A. Kirillov, and E. T. Onat. "On the polynomial invariants of the elasticity tensor." Journal of Elasticity 34, no. 2 (February 1994): 97–110. http://dx.doi.org/10.1007/bf00041187.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Federico, Salvatore. "Volumetric-Distortional Decomposition of Deformation and Elasticity Tensor." Mathematics and Mechanics of Solids 15, no. 6 (June 19, 2009): 672–90. http://dx.doi.org/10.1177/1081286509105591.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Romanishin, I. "TOMOGRAPHY OF STRESS TENSOR FIELD BY ACOUSTIC ELASTICITY." Nondestructive Testing and Evaluation 15, no. 6 (December 1998): 361–71. http://dx.doi.org/10.1080/10589750008952879.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Nazarov, S. A. "Elasticity polarization tensor, surface enthalpy, and Eshelby theorem." Journal of Mathematical Sciences 159, no. 2 (May 2009): 133–67. http://dx.doi.org/10.1007/s10958-009-9432-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Vaz, E. G. L. R., and Irene Brito. "Analysing the elasticity difference tensor of general relativity." General Relativity and Gravitation 40, no. 9 (February 1, 2008): 1947–66. http://dx.doi.org/10.1007/s10714-008-0615-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

B�na, Andrej, Ioan Bucataru, and Michael A. Slawinski. "Characterization of Elasticity-Tensor Symmetries Using SU(2)." Journal of Elasticity 75, no. 3 (June 2004): 267–89. http://dx.doi.org/10.1007/s10659-004-7192-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Auffray, N., B. Kolev, and M. Petitot. "On Anisotropic Polynomial Relations for the Elasticity Tensor." Journal of Elasticity 115, no. 1 (June 19, 2013): 77–103. http://dx.doi.org/10.1007/s10659-013-9448-z.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Olive, M., B. Kolev, B. Desmorat, and R. Desmorat. "Harmonic Factorization and Reconstruction of the Elasticity Tensor." Journal of Elasticity 132, no. 1 (October 17, 2017): 67–101. http://dx.doi.org/10.1007/s10659-017-9657-y.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Olive, M., B. Kolev, and N. Auffray. "A Minimal Integrity Basis for the Elasticity Tensor." Archive for Rational Mechanics and Analysis 226, no. 1 (May 24, 2017): 1–31. http://dx.doi.org/10.1007/s00205-017-1127-y.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Lazar, Markus, and Helmut O. K. Kirchner. "The Eshelby stress tensor, angular momentum tensor and dilatation flux in gradient elasticity." International Journal of Solids and Structures 44, no. 7-8 (April 2007): 2477–86. http://dx.doi.org/10.1016/j.ijsolstr.2006.07.018.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Lazar, Markus, and Helmut O. K. Kirchner. "The Eshelby stress tensor, angular momentum tensor and scaling flux in micropolar elasticity." International Journal of Solids and Structures 44, no. 14-15 (July 2007): 4613–20. http://dx.doi.org/10.1016/j.ijsolstr.2006.11.043.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

LANCIA, M. R., G. VERGARA CAFFARELLI, and P. PODIO-GUIDUGLI. "NULL LAGRANGIANS IN LINEAR ELASTICITY." Mathematical Models and Methods in Applied Sciences 05, no. 04 (June 1995): 415–27. http://dx.doi.org/10.1142/s0218202595000255.

Full text

Abstract:

The concept of null Lagrangian is exploited in the context of linear elasticity. In particular, it is shown that the stored energy functional can always be split into a null Lagrangian and a remainder; the null Lagrangian vanishes if and only if the elasticity tensor obeys the Cauchy relations, and is therefore determined by only 15 independent moduli (the so-called “rari-constant” theory of elasticity).

APA, Harvard, Vancouver, ISO, and other styles

48

Van Goethem, Nicolas. "Incompatibility-governed singularities in linear elasticity with dislocations." Mathematics and Mechanics of Solids 22, no. 8 (May 19, 2016): 1688–95. http://dx.doi.org/10.1177/1081286516642817.

Full text

Abstract:

The purpose of this paper is to prove the relation [Formula: see text] relating the elastic strain [Formula: see text] and the contortion tensor [Formula: see text], related to the density tensor of mesoscopic dislocations. Here, the dislocations are given by a finite family of closed Lipschitz curves in [Formula: see text]. Moreover the fields are singular at the dislocations, and, in particular, the strain is non square integrable. Moreover, the displacement fields show a constant jump around each isolated dislocation loop. This relation is called after E. Kröner who first derived the same formula for smooth fields at the macroscale.

APA, Harvard, Vancouver, ISO, and other styles

49

Xiao, B., and J. Feng. "Higher order elastic tensors of crystal structure under non-linear deformation." Journal of Micromechanics and Molecular Physics 04, no. 04 (December 2019): 1950007. http://dx.doi.org/10.1142/s2424913019500073.

Full text

Abstract:

The higher-order elastic tensors can be used to characterize the linear and non-linear mechanical properties of crystals at ultra-high pressures. Besides the widely studied second-order elastic constants, the third- and fourth-order elastic constants are sixth and eighth tensors, respectively. The independent tensor components of them are completely determined by the symmetry of the crystal. Using the relations between elastic constants and sound velocity in solid, the independent elastic constants can be measured experimentally. The anisotropy in elasticity of crystal structures is directly determined by the independent elastic constants.

APA, Harvard, Vancouver, ISO, and other styles

50

Hu, Jun, and Shangyou Zhang. "Finite element approximations of symmetric tensors on simplicial grids in ℝn: The lower order case." Mathematical Models and Methods in Applied Sciences 26, no. 09 (July 26, 2016): 1649–69. http://dx.doi.org/10.1142/s0218202516500408.

Full text

Abstract:

In this paper, we construct, in a unified fashion, lower order finite element subspaces of spaces of symmetric tensors with square-integrable divergence on a domain in any dimension. These subspaces are essentially the symmetric tensor finite element spaces of order [Formula: see text] from [Finite element approximations of symmetric tensors on simplicial grids in [Formula: see text]: The higher order case, J. Comput. Math. 33 (2015) 283–296], enriched, for each [Formula: see text]-dimensional simplex, by [Formula: see text] face bubble functions in the symmetric tensor finite element space of order [Formula: see text] from [Finite element approximations of symmetric tensors on simplicial grids in [Formula: see text]: The higher order case, J. Comput. Math. 33 (2015) 283–296] when [Formula: see text], and by [Formula: see text] face bubble functions in the symmetric tensor finite element space of order [Formula: see text] from [Finite element approximations of symmetric tensors on simplicial grids in [Formula: see text]: The higher order case, J. Comput. Math. 33 (2015) 283–296] when [Formula: see text]. These spaces can be used to approximate the symmetric matrix field in a mixed formulation problem where the other variable is approximated by discontinuous piecewise [Formula: see text] polynomials. This in particular leads to first-order mixed elements on simplicial grids with total degrees of freedom per element [Formula: see text] plus [Formula: see text] in 2D, 48 plus 6 in 3D. The previous record of the degrees of freedom of first-order mixed elements is, 21 plus 3 in 2D, and 156 plus 6 in 3D, on simplicial grids. We also derive, in a unified way which is completely different from those used in [D. Arnold, G. Awanou and R. Winther, Finite elements for symmetric tensors in three dimensions, Math. Comput. 77 (2008) 1229–1251; D. N. Arnold and R. Winther, Mixed finite element for elasticity, Number Math. 92 (2002) 401–419], a family of Arnold–Winther mixed finite elements in any space dimension. One example in this family is the Raviart–Thomas elements in one dimension, the second example is the mixed finite elements for linear elasticity in two dimensions due to Arnold and Winther, the third example is the mixed finite elements for linear elasticity in three dimensions due to Arnold, Awanou and Winther.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!