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Journal articles on the topic 'Elastodynamics'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 July 2024

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1

Achenbach, Jan D. "Reciprocity and Related Topics in Elastodynamics." Applied Mechanics Reviews 59, no. 1 (2006): 13–32. http://dx.doi.org/10.1115/1.2110262.

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Reciprocity theorems in elasticity theory were discovered in the second half of the 19th century. For elastodynamics they provide interesting relations between two elastodynamic states, say states A and B. This paper will primarily review applications of reciprocity relations for time-harmonic elastodynamic states. The paper starts with a brief introduction to provide some historical and general background, and then proceeds in Sec. 2 to a brief discussion of static reciprocity for an elastic body. General comments on waves in solids are offered in Sec. 3, while Sec. 4 provides a brief summary of linearized elastodynamics. Reciprocity theorems are stated in Sec. 5. For some simple examples the concept of virtual waves is introduced in Sec. 6. A virtual wave is a wave motion that satisfies appropriate conditions on the boundaries and is a solution of the elastodynamic equations. It is shown that combining the desired solution as state A with a virtual wave as state B provides explicit results for state A. Basic elastodynamic states are discussed in Sec. 7. These states play an important role in the formulation of integral representations and integral equations, as shown in Sec. 8. Reciprocity in 1-D and full-space elastodynamics are discussed in Secs. 910, respectively. Applications to a half-space and a layer are reviewed in Secs. 1112. Section 13 is concerned with reciprocity of coupled acousto-elastic systems. The paper is completed with a brief discussion of reciprocity for piezoelectric systems. There are 61 references cited in this review article.

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2

Biswal, Swagatika, and Prakash Chandra Mishra. "Piston Compression Ring Elastodynamics and Ring–Liner Elastohydrodynamic Lubrication Correlation Analysis." Lubricants 10, no. 12 (2022): 356. http://dx.doi.org/10.3390/lubricants10120356.

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Friction loss in an internal combustion engine largely depends on elastohydrodynamic lubrication. The piston compression ring is a contributor to such parasitic losses in the piston subsystem. The complex elastodynamics of the ring are responsible for the transient and regime-altering film that affects the elastohydrodynamic lubrication of the ring liner contact conjunction. The current paper will discuss the ring radial, lateral deformation, and axial twist, and its effect on the film profile of the compression ring and its subsequent effect on tribological characteristics like elastohydrodynamic pressure, friction, and lubricant. A finite difference technique is used to solve the elastohydrodynamic issue of elastodynamic piston compression by introducing the elastodynamically influenced film thickness into the lubrication model. The results show that consideration of the elastodynamics predicts a 23.53% reduction in friction power loss in the power stroke due to the elastodynamic ring compared to the rigid ring. The elastodynamic effect improves the lubricant oil flow into the conjunction. A finite element simulation predicts a von-Mises stress of 0.414 N/mm2, and a maximum deformation of 0.513 µm at the core and coating interface is observed at the ring–ring groove contact. The sustainability of EHL in this case largely depends on the ring–liner elastodynamics.

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3

Srivastava, Ankit. "Causality and passivity in elastodynamics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2180 (2015): 20150256. http://dx.doi.org/10.1098/rspa.2015.0256.

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What are the constraints placed on the constitutive tensors of elastodynamics by the requirements that the linear elastodynamic system under consideration be both causal (effects succeed causes) and passive (system does not produce energy)? The analogous question has been tackled in other areas but in the case of elastodynamics its treatment is complicated by the higher order tensorial nature of its constitutive relations. In this paper, we clarify the effect of these constraints on highly general forms of the elastodynamic constitutive relations. We show that the satisfaction of passivity (and causality) directly requires that the hermitian parts of the transforms (Fourier and Laplace) of the time derivatives of the constitutive tensors be positive semi-definite. Additionally, the conditions require that the non-hermitian parts of the Fourier transforms of the constitutive tensors be positive semi-definite for positive values of frequency. When major symmetries are assumed these definiteness relations apply simply to the real and imaginary parts of the relevant tensors. For diagonal and one-dimensional problems, these positive semi-definiteness relationships reduce to simple inequality relations over the real and imaginary parts, as they should. Finally, we extend the results to highly general constitutive relations which include the Willis inhomogeneous relations as a special case.

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4

Shragge, Jeffrey, and Tugrul Konuk. "Tensorial elastodynamics for isotropic media." GEOPHYSICS 85, no. 6 (2020): T359—T373. http://dx.doi.org/10.1190/geo2020-0074.1.

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Numerical solutions of 3D isotropic elastodynamics form the key computational kernel for many isotropic elastic reverse time migration and full-waveform inversion applications. However, real-life scenarios often require computing solutions for computational domains characterized by non-Cartesian geometry (e.g., free-surface topography). One solution strategy is to compute the elastodynamic response on vertically deformed meshes designed to incorporate irregular topology. Using a tensorial formulation, we have developed and validated a novel system of semianalytic equations governing 3D elastodynamics in a stress-velocity formulation for a family of vertically deformed meshes defined by Bézier interpolation functions between two (or more) nonintersecting surfaces. The analytic coordinate definition also leads to a corresponding analytic free-surface boundary condition (FSBC) as well as expressions for wavefield injection and extraction. Theoretical examples illustrate the utility of the tensorial approach in generating analytic equations of 3D elastodynamics and the corresponding FSBCs for scenarios involving free-surface topography. Numerical examples developed using a fully staggered grid with a mimetic finite-difference formulation demonstrate the ability to model the expected full-wavefield behavior, including complex free-surface interactions.

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5

Qin, Shaopeng, Gaofeng Wei, Zheng Liu, and Xuehui Shen. "Elastodynamic Analysis of Functionally Graded Beams and Plates Based on Meshless RKPM." International Journal of Applied Mechanics 13, no. 04 (2021): 2150043. http://dx.doi.org/10.1142/s1758825121500435.

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In this paper, the reproducing kernel particle method (RKPM) is innovatively extended to the elastodynamic analysis of functionally graded material (FGM). The elastodynamics governing equations of FGM are solved by using the RKPM. The penalty factor method is used to solve the displacement boundary conditions, and the Newmark-[Formula: see text] method is used to discretize the time. The influence of the penalty factor and the scaling parameter is discussed, and the stability and convergence of the RKPM are analyzed. Finally, the correctness of meshless RKPM to solve the elastodynamics of FGM is verified by numerical examples of the functionally graded beams and plates.

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6

Patra, Subir, Hossain Ahmed, Mohammadsadegh Saadatzi, and Sourav Banerjee. "Experimental verification and validation of nonlocal peridynamic approach for simulating guided Lamb wave propagation and damage interaction." Structural Health Monitoring 18, no. 5-6 (2019): 1789–802. http://dx.doi.org/10.1177/1475921719833754.

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In this article, experimental verification and validation of a peridynamics-based simulation technique, called peri-elastodynamics, are presented while simulating the guided Lamb wave propagation and wave–damage interaction for ultrasonic nondestructive evaluation and structural health monitoring applications. Peri-elastodynamics is a recently developed elastodynamic computation tool where material particles are assumed to interact with the neighboring particles nonlocally, distributed within an influence zone. First, in this article, peri-elastodynamics was used to simulate the Lamb wave modes and their interactions with the damages in a three-dimensional plate-like structure, while the accuracy and the efficacy of the method were verified using the finite element simulation method (FEM). Next, the peri-elastodynamics results were validated with the experimental results, which showed that the newly developed method is more accurate and computationally cheaper than the FEM to be used for computational nondestructive evaluation and structural health monitoring. Specifically, in this work, peri-elastodynamics was used to accurately simulate the in-plane and out-of-plane symmetric and anti-symmetric guided Lamb wave modes in a pristine plate and was extended to investigate the wave–damage interaction with damage (e.g. a crack) in the plate. Experiments were designed keeping all the simulation parameters consistent. The accuracy of the proposed technique is confirmed by performing error analysis on symmetric and anti-symmetric Lamb wave modes compared to the experimental results for pristine and damaged plates.

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7

Wang, Jiawei. "Incompressible limit of nonisentropic Hookean elastodynamics." Journal of Mathematical Physics 63, no. 6 (2022): 061506. http://dx.doi.org/10.1063/5.0080539.

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We study the incompressible limit of the compressible nonisentropic Hookean elastodynamics with general initial data in the whole space [Formula: see text]. First, we obtain the uniform estimates of the solutions in [Formula: see text] for s > d/2 + 1 being even and the existence of classic solutions on a time interval independent of the Mach number. Then, we prove that the solutions converge to the incompressible elastodynamic equations as the Mach number tends to zero.

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8

Patnaik, Sansit, and Fabio Semperlotti. "A generalized fractional-order elastodynamic theory for non-local attenuating media." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2238 (2020): 20200200. http://dx.doi.org/10.1098/rspa.2020.0200.

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This study presents a generalized elastodynamic theory, based on fractional-order operators, capable of modelling the propagation of elastic waves in non-local attenuating solids and across complex non-local interfaces. Classical elastodynamics cannot capture hybrid field transport processes that are characterized by simultaneous propagation and diffusion. The proposed continuum mechanics formulation, which combines fractional operators in both time and space, offers unparalleled capabilities to predict the most diverse combinations of multiscale, non-local, dissipative and attenuating elastic energy transport mechanisms. Despite the many features of this theory and the broad range of applications, this work focuses on the behaviour and modelling capabilities of the space-fractional term and on its effect on the elastodynamics of solids. We also derive a generalized fractional-order version of Snell’s Law of refraction and of the corresponding Fresnel’s coefficients. This formulation allows predicting the behaviour of fully coupled elastic waves interacting with non-local interfaces. The theoretical results are validated via direct numerical simulations.

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9

Konuk, Tugrul, and Jeffrey Shragge. "Tensorial elastodynamics for anisotropic media." GEOPHYSICS 86, no. 4 (2021): T293—T303. http://dx.doi.org/10.1190/geo2020-0156.1.

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Elastic wavefield solutions computed by finite-difference (FD) methods in complex anisotropic media are essential elements of elastic reverse time migration and full-waveform inversion analyses. Cartesian formulations of such solution methods, though, face practical challenges when aiming to represent curved interfaces (including free-surface topography) with rectilinear elements. To forestall such issues, we have developed a general strategy for generating solutions of tensorial elastodynamics for anisotropic media (i.e., tilted transversely isotropic or even lower symmetry) in non-Cartesian computational domains. For the specific problem of handling free-surface topography, we define an unstretched coordinate mapping that transforms an irregular physical domain to a regular computational grid on which FD solutions of the modified equations of elastodynamics are straightforward to calculate. Our fully staggered grid (FSG) with a mimetic FD (MFD) (FSG + MFD) approach solves the velocity-stress formulation of the tensorial elastic wave equation in which we compute the stress-strain constitutive relationship in Cartesian coordinates and then transform the resulting stress tensor to generalized coordinates to solve the equations of motion. The resulting FSG + MFD numerical method has a computational complexity comparable with Cartesian scenarios using a similar FSG + MFD numerical approach. Numerical examples demonstrate that our solution can simulate anisotropic elastodynamic field solutions on irregular geometries; thus, it is a reliable tool for anisotropic elastic modeling, imaging, and inversion applications in generalized computational domains including handling free-surface topography.

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10

Lu, Xiang Yang, and Jin Hu. "Approximate Elastodynamic Directional-Cloak with Isotropous Homogeneous Material." Advanced Materials Research 634-638 (January 2013): 2787–90. http://dx.doi.org/10.4028/www.scientific.net/amr.634-638.2787.

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Recently, the transformation method has been extended to control solid elastic waves in case of high frequency or small material gradient. An important device in practice, the approximate elastodynamic directional-cloak with isotropic homogeneous materials, can be designed based on this method. In this paper, this device’s design method is discussed in detail and its effect on cloaking arbitrary shaped obstacles is explored. It is also shown that this useful device cannot be designed based on the conventional transformation elastodynamics. Examples are conceived and validated by numerical simulations.

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11

Fradkin, Larissa, Audrey Kamta Djakou, Chris Prior, Michel Darmon, Sylvain Chatillon, and Pierre Calmon. "The alternative Kirchhoff approximation in elastodynamics with applications in ultrasonic nondestructive testing." ANZIAM Journal 62 (April 25, 2021): 406–22. http://dx.doi.org/10.21914/anziamj.v62.14357.

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The Kirchhoff approximation is widely used to describe the scatter of elastodynamic waves. It simulates the scattered field as the convolution of the free-space Green’s tensor with the geometrical elastodynamics approximation to the total field on the scatterer surface and, therefore, cannot be used to describe nongeometrical phenomena, such as head waves. The aim of this paper is to demonstrate that an alternative approximation, the convolution of the far-field asymptotics of the Lamb’s Green’s tensor with incident surface tractions, has no such limitation. This is done by simulating the scatter of a critical Gaussian beam of transverse motions from an infinite plane. The results are of interest in ultrasonic nondestructive testing. doi:10.1017/S1446181120000036

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12

Shahab, Shima, and Alper Erturk. "Coupling of experimentally validated electroelastic dynamics and mixing rules formulation for macro-fiber composite piezoelectric structures." Journal of Intelligent Material Systems and Structures 28, no. 12 (2016): 1575–88. http://dx.doi.org/10.1177/1045389x16672732.

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Piezoelectric structures have been used in a variety of applications ranging from vibration control and sensing to morphing and energy harvesting. In order to employ the effective 33-mode of piezoelectricity, interdigitated electrodes have been used in the design of macro-fiber composites which employ piezoelectric fibers with rectangular cross section. In this article, we present an investigation of the two-way electroelastic coupling (in the sense of direct and converse piezoelectric effects) in bimorph cantilevers that employ interdigitated electrodes for 33-mode operation. A distributed-parameter electroelastic modeling framework is developed for the elastodynamic scenarios of piezoelectric power generation and dynamic actuation. Mixing rules (i.e. rule of mixtures) formulation is employed to evaluate the equivalent and homogenized properties of macro-fiber composite structures. The electroelastic and dielectric properties of a representative volume element (piezoelectric fiber and epoxy matrix) between two neighboring interdigitated electrodes are then coupled with the global electro-elastodynamics based on the Euler–Bernoulli kinematics accounting for two-way electromechanical coupling. Various macro-fiber composite bimorph cantilevers with different widths are tested for resonant dynamic actuation and power generation with resistive shunt damping. Excellent agreement is reported between the measured electroelastic frequency response and predictions of the analytical framework that bridges the continuum electro-elastodynamics and mixing rules formulation.

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13

TAKANO, Yasunari, Tomonobu GOTO, and Shinichi NISHINO. "A Finite Volume Scheme for Elastodynamic Equations. 1st Report. Algorithm for Elastodynamics." Transactions of the Japan Society of Mechanical Engineers Series A 64, no. 626 (1998): 2471–76. http://dx.doi.org/10.1299/kikaia.64.2471.

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14

Li, Duo, Shinjiro Sueda, Debanga R. Neog, and Dinesh K. Pai. "Thin skin elastodynamics." ACM Transactions on Graphics 32, no. 4 (2013): 1–10. http://dx.doi.org/10.1145/2461912.2462008.

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15

Ostoja-Starzewski, Martin. "Ignaczak equation of elastodynamics." Mathematics and Mechanics of Solids 24, no. 11 (2018): 3674–713. http://dx.doi.org/10.1177/1081286518757284.

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The development of linear elastodynamics in pure stress-based formulation began over half-a-century ago as an alternative to the classical displacement-based treatment that came into existence two centuries ago in the school of mathematical physics in France. While the latter approach – fundamentally based on the Navier displacement equation of motion – remains the conventional setting for analysis of wave propagation in elastic bodies, the stress-based formulation and the advantages it offers in elastodynamics and its various extensions remain much less known. Since the key mathematical results of that formulation, as well as a series of applications, originated with J. Ignaczak in 1959 and 1963, the key relation is named the Ignaczak equation of elastodynamics. This review article presents the main ideas and results in the stress-based formulation from a common perspective, including (i) a history of early attempts to find a pure stress language of elastodynamics, (ii) a proposal to use such a language in solving the natural traction initial-boundary value problems of the theory, and (iii) various applications of the stress language to elastic wave propagation problems. Finally, various extensions of the Ignaczak equation of elastodynamics focused on dynamics of solids with interacting fields of different nature (classical or micropolar thermoelastic, fluid-saturated porous, piezoelectro-elastic) as well as nonlinear problems are reviewed.

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16

Elhaddad, M., N. Zander, S. Kollmannsberger, A. Shadavakhsh, V. Nübel, and E. Rank. "Finite Cell Method: High-Order Structural Dynamics for Complex Geometries." International Journal of Structural Stability and Dynamics 15, no. 07 (2015): 1540018. http://dx.doi.org/10.1142/s0219455415400180.

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In this contribution, the finite cell method (FCM) is applied to solve transient problems of linear elastodynamics. The mathematical formulation of FCM for linear elastodynamics is presented, following from the weak formulation of the initial/boundary-value problem. Semi-discrete time integration schemes are briefly discussed, and the choice of implicit time integration is justified. A 1D benchmark problem is solved using FCM, illustrating the method's ability to solve problems of linear elastodynamics obtaining high rates of convergence. Furthermore, a numerical example of transient analysis from an industrial application is solved using FCM. The numerical results are compared to the results obtained using state-of-the-art commercial software, employing linear finite elements, in conjunction with explicit time integration. The results illustrate the potential of FCM as a powerful tool for transient analysis in elastodynamics, offering a high degree of accuracy at a moderate computational effort.

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17

CHEW, W. C., and Q. H. LIU. "PERFECTLY MATCHED LAYERS FOR ELASTODYNAMICS: A NEW ABSORBING BOUNDARY CONDITION." Journal of Computational Acoustics 04, no. 04 (1996): 341–59. http://dx.doi.org/10.1142/s0218396x96000118.

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The use of perfectly matched layers (PML) has recently been introduced by Berenger as a material absorbing boundary condition (ABC) for electromagnetic waves. In this paper, we will first prove that a fictitious elastodynamic material half-space exists that will absorb an incident wave for all angles and all frequencies. Moreover, the wave is attenuative in the second half-space. As a consequence, layers of such material could be designed at the edge of a computer simulation region to absorb outgoing waves. Since this is a material ABC, only one set of computer codes is needed to simulate an open region. Hence, it is easy to parallelize such codes on multiprocessor computers. For instance, it is easy to program massively parallel computers on the SIMD (single instruction multiple data) mode for such codes. We will show two- and three-dimensional computer simulations of the PML for the linearized equations of elastodynamics. Comparison with Liao’s ABC will be given.

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18

Zhang, Z. H., Z. J. Yang, and J. H. Li. "An Adaptive Polygonal Scaled Boundary Finite Element Method for Elastodynamics." International Journal of Computational Methods 13, no. 02 (2016): 1640015. http://dx.doi.org/10.1142/s0219876216400156.

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An adaptive polygonal scaled boundary finite element method (APSBFEM) is developed for elastodynamics. Flexible polygonal meshes are generated from background Delaunay triangular meshes and used to calculate structure’s dynamic responses. In each time step, a posteriori-type energy error estimator is employed to locate the polygonal subdomains with exceeding spatial discretization error, then edge midpoints of the corresponding triangles are inserted into the background. A new Delaunay triangular mesh and a polygonal mesh are regenerated successively. The state variables, including displacement, velocity and acceleration are mapped from the old polygonal mesh to the new one by a simple algorithm. A benchmark elastodynamic problem is modeled to validate the developed method. The results show that the adaptive meshes are capable of capturing the steep stress regions, and the dynamic responses agree well with those from the adaptive finite element method and the polygonal scaled boundary finite element method without adaptivity using fine meshes.

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19

Kube, Christopher M. "Elastodynamic property closures of elastic waves in polycrystalline materials." Journal of the Acoustical Society of America 155, no. 3_Supplement (2024): A290. http://dx.doi.org/10.1121/10.0027539.

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In polycrystalline materials like many metals, grainy microstructures significantly influence elastodynamics. Bulk waves scattering at grain boundaries cause attenuation and speed variation in waves. This depends on grain characteristics, including local elasticity and spatial properties. These are modeled statistically to homogenize the microstructure or elastodynamic fields, within bounds. For example, the elasticity of a homogenized medium can't exceed that of individual grains. 'Property closure' is the range within which microstructures yield specific properties like Young's modulus. This presentation introduces property closures for modeling elastic wave properties, specifically attenuation and velocity, in metal alloys. The focus is on the modeling framework and integrating microstructure statistics. An excting prospect of this work is in linking measurable wave properties with other physical quantities dependent on microstructure.

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20

Norris, A. N., and A. L. Shuvalov. "Elastodynamics of radially inhomogeneous spherically anisotropic elastic materials in the Stroh formalism." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2138 (2011): 467–84. http://dx.doi.org/10.1098/rspa.2011.0463.

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A method for solving elastodynamic problems in radially inhomogeneous elastic materials with spherical anisotropy is presented, i.e. materials having c ijkl = c ijkl ( r ) in a spherical coordinate system { r , θ , ϕ }. The time-harmonic displacement field u ( r , θ , ϕ ) is expanded in a separation of variables form with dependence on θ , ϕ described by vector spherical harmonics with r -dependent amplitudes. It is proved that such separation of variables solution is generally possible only if the spherical anisotropy is restricted to transverse isotropy (TI) with the principal axis in the radial direction, in which case the amplitudes are determined by a first-order ordinary differential system. Restricted forms of the displacement field, such as u ( r , θ ), admit this type of separation of variables solution for certain lower material symmetries. These results extend the Stroh formalism of elastodynamics in rectangular and cylindrical systems to spherical coordinates.

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21

Turnbull, R., R. Rahmani, and H. Rahnejat. "The effect of outer ring elastodynamics on vibration and power loss of radial ball bearings." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 234, no. 4 (2020): 707–22. http://dx.doi.org/10.1177/1464419320951398.

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Ball bearings are an integral part of many machines and mechanisms and often determine their performance limits. Vibration, friction and power loss are some of the key measures of bearing performance. Therefore, there have been many predictive analyses of bearing performance with emphasis on various aspects. The current study presents a mathematical model, incorporating bearing dynamics, mechanics of rolling element-to-races contacts as well as the elastodynamics of the bearing outer ring as a focus of the study. It is shown that the bearing power loss in cage cycles increases by as much as 4% when the flexibility of the outer ring is taken into account as a thick elastic ring, based on Timoshenko beam theory as opposed to the usual assumption of a rigid ring in other studies. Geometric optimisation has shown that the lifetime power consumption can be reduced by 1.25%, which is a significant source of energy saving when considering the abundance of machines using rolling element bearings. The elastodynamics of bearing rings significantly affects the radial bearing clearance through increased roller loads and generated contact pressures. The flexible ring dynamics is shown to generate surface waviness through global elastic wave propagation, not hitherto taken into account in contact dynamics of rollers-to-raceways which are generally considered to be subjected to only localised Hertzian deflection. The elastodynamic behaviour reduces the elastohydrodynamic film thickness, affecting contact friction, wear, fatigue, vibration, noise and inefficiency.

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22

Sakhr, Jamal, and Blaine A. Chronik. "Harmonic Standing-Wave Excitations of Simply-Supported Isotropic Solid Elastic Circular Cylinders: Exact 3D Linear Elastodynamic Response." International Journal of Applied Mechanics 12, no. 06 (2020): 2050060. http://dx.doi.org/10.1142/s175882512050060x.

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The vibration of a solid elastic cylinder is one of the classical applied problems of elastodynamics. Many fundamental forced-vibration problems involving solid elastic cylinders have not yet been studied or solved using the full three-dimensional (3D) theory of linear elasticity. One such problem is the steady-state forced-vibration response of a simply-supported isotropic solid elastic circular cylinder subjected to two-dimensional harmonic standing-wave excitations on its curved surface. In this paper, we exploit certain recently-obtained particular solutions to the Navier–Lamé equation and exact matrix algebra to construct an exact closed-form 3D elastodynamic solution to the problem. The method of solution is direct and demonstrates a general approach that can be applied to solve other similar forced-vibration problems involving elastic cylinders. The obtained analytical solution is then applied to a specific numerical example, where it is used to determine the frequency response of the displacement field in some low wave number excitation cases. In each case, the solution generates a series of resonances that are in exact correspondence with a subset of the natural frequencies of the simply-supported cylinder. The analytical solution is also used to compute the resonant mode shapes in some selected asymmetric excitation cases. The studied problem is of general interest both as an exactly-solvable 3D elastodynamics problem and as a benchmark forced-vibration problem involving a solid elastic cylinder.

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23

Luo, Shichao, and Yinan Cui. "Elastodynamics Field of Non-Uniformly Moving Dislocation: From 3D to 2D." Crystals 12, no. 3 (2022): 363. http://dx.doi.org/10.3390/cryst12030363.

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Molecular dynamics (MD) and experiments indicate that the high-speed dislocations dominate the plasticity properties of crystal materials under high strain rate. New physical features arise accompanied with the increase in dislocation speed, such as the “Lorentz contraction” effect of moving screw dislocation, anomalous nucleation, and annihilation in dislocation interaction. The static description of the dislocation is no longer applicable. The elastodynamics fields of non-uniformly moving dislocation are significantly temporal and spatially coupled. The corresponding mathematical formulas of the stress fields of three-dimensional (3D) and two-dimensional (2D) dislocations look quite different. To clarify these differences, we disclose the physical origin of their connections, which is inherently associated with different temporal and spatial decoupling strategies through the 2D and 3D elastodynamics Green tensor. In this work, the fundamental relationship between 2D and 3D dislocation elastodynamics is established, which has enlightening significance for establishing general high-speed dislocation theory, developing a numerical calculation method based on dislocation elastodynamics, and revealing more influences of dislocation on the macroscopic properties of materials.

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24

Lindell, I. V., and A. P. Kiselev. "Polyadic Methods in Elastodynamics." Progress In Electromagnetics Research 31 (2001): 113–54. http://dx.doi.org/10.2528/pier00051701.

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25

Norris, Andrew. "Transformation acoustics and elastodynamics." Journal of the Acoustical Society of America 128, no. 4 (2010): 2427. http://dx.doi.org/10.1121/1.3508670.

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26

Weaver, R. L. "Spectral statistics in elastodynamics." Journal of the Acoustical Society of America 85, no. 3 (1989): 1005–13. http://dx.doi.org/10.1121/1.397484.

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27

Hungria, Allan, Daniele Prada, and Francisco-Javier Sayas. "HDG methods for elastodynamics." Computers & Mathematics with Applications 74, no. 11 (2017): 2671–90. http://dx.doi.org/10.1016/j.camwa.2017.08.016.

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JONES, D. S. "Boundary Integrals in Elastodynamics." IMA Journal of Applied Mathematics 34, no. 1 (1985): 83–97. http://dx.doi.org/10.1093/imamat/34.1.83.

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29

Zielonka, M. G., M. Ortiz, and J. E. Marsden. "Variationalr-adaption in elastodynamics." International Journal for Numerical Methods in Engineering 74, no. 7 (2008): 1162–97. http://dx.doi.org/10.1002/nme.2205.

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30

M�ller, K. H. "Elastodynamics in parabolic cylinders." ZAMP Zeitschrift f�r angewandte Mathematik und Physik 39, no. 5 (1988): 748–52. http://dx.doi.org/10.1007/bf00948735.

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Epstein, Marcelo, and Jędrzej Śniatycki. "Fermat's principle in elastodynamics." Journal of Elasticity 27, no. 1 (1992): 45–56. http://dx.doi.org/10.1007/bf00057859.

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32

Li, Houguo, and Kefu Huang. "Some Invariant Solutions of Two-Dimensional Elastodynamics in Linear Homogeneous Isotropic Materials." Advances in Applied Mathematics and Mechanics 5, no. 2 (2013): 212–21. http://dx.doi.org/10.4208/aamm.12-m1257.

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AbstractInvariant solutions of two-dimensional elastodynamics in linear homogeneous isotropic materials are considered via the group theoretical method. The second order partial differential equations of elastodynamics are reduced to ordinary differential equations under the infinitesimal operators. Three invariant solutions are constructed. Their graphical figures are presented and physical meanings are elucidated in some cases.

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Solyaev, Yury. "Steady-State Crack Growth in Nanostructured Quasi-Brittle Materials Governed by Second Gradient Elastodynamics." Applied Sciences 13, no. 10 (2023): 6333. http://dx.doi.org/10.3390/app13106333.

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Abstract:

The elastodynamic stress field near a crack tip propagating at a constant speed in isotropic quasi-brittle material was investigated, taking into account the strain gradient and inertia gradient effects. An asymptotic solution for a steady-state Mode-I crack was developed within the simplified strain gradient elasticity by using a representation of the general solution in terms of Lamé potentials in the moving framework. It was shown that the derived solution predicts the nonsingular stress state and smooth opening profile for the growing cracks that can be related to the presence of the fracture process zone in the micro-/nanostructured quasi-brittle materials. Note that similar asymptotic solutions have been derived previously only for Mode-III cracks (under antiplane shear loading). Thus, the aim of this study is to show the possibility of analytical assessments on the elastodynamic crack tip fields for in-plane loading within gradient theories. By using the derived solution, we also performed analysis of the angular distribution of stresses and tractions for the moderate speed of cracks. It was shown that the usage of the maximum principal stress criterion within second gradient elastodynamics allows us to describe a directional stability of Mode-I crack growth and an increase in the dynamic fracture toughness with the crack propagation speed that were observed in the experiments with quasi-brittle materials. Therefore, the possibility of the effective application of regularized solutions of strain gradient elasticity for the refined analysis of dynamic fracture processes in the quasi-brittle materials with phenomenological assessments on the cohesive zone effects is shown.

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Martin, P. A. "Antiplane anisotropic elastodynamics: Babinet’s principle." Mechanics Research Communications 125 (October 2022): 103973. http://dx.doi.org/10.1016/j.mechrescom.2022.103973.

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35

Coclite, G. M., F. Maddalena, G. Puglisi, M. Romano, and G. Saccomandi. "The Gardner Equation in Elastodynamics." SIAM Journal on Applied Mathematics 81, no. 6 (2021): 2346–61. http://dx.doi.org/10.1137/21m1407537.

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Humphrey, J. D., and S. Na. "Elastodynamics and Arterial Wall Stress." Annals of Biomedical Engineering 30, no. 4 (2002): 509–23. http://dx.doi.org/10.1114/1.1467676.

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Tarantino, Angelo Marcello. "Crack Propagation in Finite Elastodynamics." Mathematics and Mechanics of Solids 10, no. 6 (2005): 577–601. http://dx.doi.org/10.1177/1081286505036421.

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Joumaa, Hady, Martin Ostoja-Starzewski, and Paul Demmie. "Elastodynamics in micropolar fractal solids." Mathematics and Mechanics of Solids 19, no. 2 (2012): 117–34. http://dx.doi.org/10.1177/1081286512454557.

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39

Böhm, F. "Elastodynamics of Cars and Tires." Vehicle System Dynamics 27, sup001 (1997): 123–35. http://dx.doi.org/10.1080/00423119708969649.

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40

Zecca, V., and A. Kamel. "Elastodynamics on clustered vector multiprocessors." ACM SIGARCH Computer Architecture News 18, no. 3b (1990): 281–90. http://dx.doi.org/10.1145/255129.255166.

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41

Al-Attar, David, and Ophelia Crawford. "Particle relabelling transformations in elastodynamics." Geophysical Journal International 205, no. 1 (2016): 575–93. http://dx.doi.org/10.1093/gji/ggw032.

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42

Cui, Yinan, Giacomo Po, Yves-Patrick Pellegrini, Markus Lazar, and Nasr Ghoniem. "Computational 3-dimensional dislocation elastodynamics." Journal of the Mechanics and Physics of Solids 126 (May 2019): 20–51. http://dx.doi.org/10.1016/j.jmps.2019.02.008.

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43

Matyukevich, S. I., and B. A. Plamenevskiĭ. "Elastodynamics in domains with edges." St. Petersburg Mathematical Journal 18, no. 03 (2007): 459–511. http://dx.doi.org/10.1090/s1061-0022-07-00957-0.

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Blanchard, Antoine, Themistoklis P. Sapsis, and Alexander F. Vakakis. "Non-reciprocity in nonlinear elastodynamics." Journal of Sound and Vibration 412 (January 2018): 326–35. http://dx.doi.org/10.1016/j.jsv.2017.09.039.

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45

Kienzler, R., and G. Herrmann. "On conservation laws in elastodynamics." International Journal of Solids and Structures 41, no. 13 (2004): 3595–606. http://dx.doi.org/10.1016/j.ijsolstr.2004.01.018.

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46

Chandrasekharaiah, D. S. "A complete solution in elastodynamics." Acta Mechanica 84, no. 1-4 (1990): 185–90. http://dx.doi.org/10.1007/bf01176096.

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Hulbert, Gregory M. "Discontinuity-capturing operators for elastodynamics." Computer Methods in Applied Mechanics and Engineering 96, no. 3 (1992): 409–26. http://dx.doi.org/10.1016/0045-7825(92)90073-s.

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48

Bao, Gang, Guanghui Hu, Yavar Kian, and Tao Yin. "Inverse source problems in elastodynamics." Inverse Problems 34, no. 4 (2018): 045009. http://dx.doi.org/10.1088/1361-6420/aaaf7e.

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49

Neale, K. W. "Boundary element method in elastodynamics." Canadian Journal of Civil Engineering 18, no. 3 (1991): 535. http://dx.doi.org/10.1139/l91-066.

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Lindell, I. V., and A. P. Kiselev. "Polyadic Methods in Elastodynamics - Abstract *." Journal of Electromagnetic Waves and Applications 14, no. 12 (2000): 1627–28. http://dx.doi.org/10.1163/156939300x00392.

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