657 results on '"Antiplane shear"'
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2. Damage as a Material Phase Transition.
- Author
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Bucchi, Andrea, De Tommasi, Domenico, Puglisi, Giuseppe, and Saccomandi, Giuseppe
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PHASE transitions ,SHEAR (Mechanics) ,CYCLIC loads ,ENERGY function ,ENERGY density - Abstract
We propose paradigmatic examples to show how material damage phenomena can be efficiently described as a solid-solid phase transition. Starting from the pioneering work of J.L. Ericksen (J. Elast. 5(3):191–201, 1975) and the extensions of R.L. Fosdick and other authors to three-dimensional non linear elasticity, we describe the insurgence of damage as a hard → soft transition between two material states (damage and undamaged) characterized by two different energy wells. We consider the two separate constitutive assumptions of a simple Neo-Hookean type damageable material and a more complex microstructure inspired damageable Gent type material with variable limit threshold of the first invariant. In both cases we study two different deformation shear classes, one homogeneous and the other one inhomogeneous and obtain fully analytic description of the system damage response under cyclic loading. The considered constitutive assumptions and deformation classes are aimed at attaining fully analytic descriptions. On the other hand, we remark that the proposed, Griffith type, variational approach of damage, based on two different energy density functions for the damaged and undamaged material phases, and a resulting non (rank-one) convex energy, can be extended to systems with more complex energy functions, possibly with a larger number of wells representing an increasing degree of damage. [ABSTRACT FROM AUTHOR] more...
- Published
- 2023
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3. Are the direct and indirect BEM/BIEMs equivalent?
- Author
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Chen, Jeng-Tzong, Kao, Jeng-Hong, Kao, Shing-Kai, and Wu, Ting-Ann
- Subjects
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BOUNDARY element methods , *NUMERICAL solutions for linear algebra , *ZETA potential , *DISCRETE systems , *DEGENERATE differential equations - Abstract
For a long time, direct and indirect BEM/BIEMs were always unified and seemed equivalent in real implementation for ensuring the solution. Regarding the solution space and the numerical aspects in linear algebra, it is interesting to find that they are not fully equivalent. To demonstrate this finding, antiplane shear problems containing the elliptical rigid inclusion and hole as well as rigid-line inclusion and line crack were given to demonstrate the non-equivalence between the direct and indirect BEM/BIEMs. It is interesting to find that nonunique boundary densities may yield the unique field solution in both analytical derivation and numerical implementation. The mechanism was analytically studied and numerically performed by using the degenerate kernel and the singular value decomposition technique, respectively. Besides, the Fredholm alternative theorem was employed to examine the solvability condition in both the indirect boundary integral equation method and indirect boundary element method. For continuous system and discrete system, we can explain why the boundary density does not match the exact solution but the field solution is always acceptable when setting ξ 0 = 0 in the beginning of the derivation of BIE. Two approaches, direct and indirect BEM/BIEMs, show the non-equivalence of solution in case of degenerate boundary and degenerate scale. [ABSTRACT FROM AUTHOR] more...
- Published
- 2023
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4. On the refined boundary condition at the edge of a thin elastic strip supported by a Winkler-type foundation under antiplane shear deformation.
- Author
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Prikazchikova, Ludmila, Nolde, Evgeniya, Miszuris, Wiktoria, and Kaplunov, Julius
- Subjects
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STRUCTURAL frame models , *SHEAR (Mechanics) , *BOUNDARY layer (Aerodynamics) , *EQUILIBRIUM - Abstract
The derivation of the boundary conditions is the most challenging part of the asymptotic techniques underlying low-dimensional models for thin elastic structures. At the moment, these techniques do not take into consideration the effect of the environment, e.g., a Winkler foundation, when tackling boundary conditions, and have to be amended. In this paper as an example we consider an antiplane problem for a thin elastic strip contacting with a relatively compliant Winkler foundation. Refined boundary conditions at an edge loaded by prescribed stresses are established using a properly adjusted Saint-Venant's principle. They appear to be useful for advanced structure modelling including analysis of the static equilibrium under self-equilibrated loading. [ABSTRACT FROM AUTHOR] more...
- Published
- 2024
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5. Calculation of Elastic Deflections of Thin Stiff Shells Based on the Finite Element Method out of the Kirchhoff’s Theory
- Author
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Hrant Ararat Gevorgyan
- Subjects
finite element method ,antiplane shear ,plane-spatial problem ,kirchhoff’s hypothesis ,flexion stiffness ,tensor of flexion stiffness ,fractal geometry ,fragment of shell ,Mechanical engineering and machinery ,TJ1-1570 - Abstract
The computational method of determining thin stiff shells deflections formulated on the basis of the plane-spatial problem of the FEM without using Kirchhoff’s hypothesis is developed; in virtue of the geometric properties of the finite element stiffness matrix, a tensor of flexion stiffness is introduced. A linear and a nonlinear modification of the plane-spatial problem of the FEM for calculation of small elastic deflections of thin shells are formulated. An example of calculation of fragment of sloping conical shell is given in accordance with the common principles of two-dimensional domain discretization and some elements of fractal geometry. more...
- Published
- 2018
6. Asymptotic Justification of the Models of Thin Inclusions in an Elastic Body in the Antiplane Shear Problem.
- Author
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Rudoy, E. M., Itou, H., and Lazarev, N. P.
- Abstract
The equilibrium problem for an elastic body having an inhomogeneous inclusion with curvilinear boundaries is considered within the framework of antiplane shear. We assume that there is a power-law dependence of the shear modulus of the inclusion on a small parameter characterizing its width. We justify passage to the limit as the parameter vanishes and construct an asymptotic model of an elastic body containing a thin inclusion. We also show that, depending on the exponent of the parameter, there are the five types of thin inclusions: crack, rigid inclusion, ideal contact, elastic inclusion, and a crack with adhesive interaction of the faces. The strong convergence is established of the family of solutions of the original problem to the solution of the limiting one. [ABSTRACT FROM AUTHOR] more...
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- 2021
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7. Phase-field simulation and coupled criterion link echelon cracks to internal length in antiplane shear.
- Author
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Molnár, Gergely, Doitrand, Aurélien, and Lazarus, Véronique
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POISSON'S ratio , *SPATIAL variation - Abstract
This paper provides a comprehensive numerical analysis of daughter crack localization in pure antiplane shear. Although antiplane shear fracture is important in various industrial applications, understanding the morphology of the resulting fragmentation remains challenging. The paper develops innovative phase-field models to induce the facets using a small spatial variation in the toughness field and examines the impact of numerical and material parameters on the newly formed daughter cracks' shape and spacing. Through meticulous comparison to the coupled criterion, the paper reveals a compelling connection between the internal length-scale of damage regularization, Irwin's length and the facet crack spacing. Furthermore, the effect of Poisson's ratio on the crack form and spacing is investigated: the results reveal a significant influence and showcase comparable initiation distances between the numerical simulations and experimental measurements in pure antiplane loading. • Phase-field models reveal daughter crack morphology in pure antiplane shear. • Link found between regularization length, Irwin's length, and facet crack spacing. • Poisson's ratio's impact on crack form and spacing identified. • Comparisons highlight similar initiation distances to experimental measurements. [ABSTRACT FROM AUTHOR] more...
- Published
- 2024
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8. THE EFFECT OF CRYSTAL SYMMETRIES ON THE LOCALITY OF SCREW DISLOCATION CORES.
- Author
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BRAUN, JULIAN, BUZE, MACIEJ, and ORTNER, CHRISTOPH
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SCREW dislocations , *CRYSTAL symmetry , *KINEMATICS , *AUTOMOBILE defects , *ELASTICITY - Abstract
In linearized continuum elasticity, the elastic strain due to a straight dislocation line decays as O(r-1), where r denotes the distance to the defect core. It is shown in [V. Ehrlacher, C. Ortner, and A. V. Shapeev, Arch. Ration. Mech. Anal., 222 (2016), pp. 1217-1268] that the core correction due to nonlinear and discrete (atomistic) effects decays like O(r-2). In the present work, we focus on screw dislocations under pure antiplane shear kinematics. In this setting we demonstrate that an improved decay O(r-p), p > 2, of the core correction is obtained when crystalline symmetries are fully exploited and possibly a simple and explicit correction of the continuum far-field prediction is made. This result is interesting in its own right as it demonstrates that, in some cases, continuum elasticity gives a much better prediction of the elastic field surrounding a dislocation than expected and moreover has practical implications for atomistic simulation of dislocations cores, which we discuss as well. [ABSTRACT FROM AUTHOR] more...
- Published
- 2019
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9. Analytical study on the mode III stress fields due to blunt notches with cracks.
- Author
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Zappalorto, Michele, Maragoni, Lucio, and Salviato, Marco
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SHEAR (Mechanics) , *SURFACE cracks , *NOTCH strength , *STRESS concentration , *TORSION - Abstract
This work presents an analytical study on the stress fields induced by cracks nucleated at the tip of radiused notches under antiplane shear and torsion loadings. Closed‐form solutions for both shallow and deep notches are derived leveraging a combination of proper curvilinear coordinate systems and the complex potential method for antiplane elasticity. Based on the exact stress field solutions, convenient expressions for the stress intensity factors are derived. The accuracy of all the analytical formulations is verified by comparison with the results from a bulk of numerical analyses. [ABSTRACT FROM AUTHOR] more...
- Published
- 2019
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10. Solution Methods for Functionally Graded Piezoelectric Materials
- Author
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Qin, Qing-Hua and Qin, Qing-Hua
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- 2013
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11. Saint-Venant Decay Problems in Piezoelectricity
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Qin, Qing-Hua and Qin, Qing-Hua
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- 2013
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12. Antiplane Shear
- Author
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Barber, J. R. and Barber, J. R.
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- 2010
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13. Exact solution for the mode III stress fields ahead of cracks initiated at sharp notch tips.
- Author
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Salviato, Marco, Zappalorto, Michele, and Maragoni, Lucio
- Subjects
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STRESS concentration , *SURFACE cracks , *NOTCH effect , *SHEAR (Mechanics) , *TORSION , *FINITE element method - Abstract
Abstract In this work, the exact solution for the stress fields ahead of cracks initiated at sharp notch tips under antiplane shear and torsion loadings is derived in close form, leveraging conformal mapping and the complex potential method for antiplane elasticity. Based on the stress field distributions, relevant expressions for the mode III crack stress intensity factors are derived and their accuracy is discussed in detail taking advantage of a bulk of results from FE analyses. Highlights • General approach closed-form solution for the stress field in anti-plane shear and torsion. • Closed-form solution for V-notches weakened by a crack. • Closed-form solution for Stress Intensity Factor (SIF) and discussion on effect of notch opening, notch depth and crack. [ABSTRACT FROM AUTHOR] more...
- Published
- 2018
- Full Text
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14. Elastic Field of a Heterogeneous Medium Containing Doubly Periodic Cylindrical Inclusions Under Antiplane Shear and its Application.
- Author
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Xu, Y. L., Xiao, J. H., and Shen, Y. Z.
- Subjects
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ELASTIC deformation , *CYLINDRICAL probabilities , *SHEAR (Mechanics) , *BOUNDARY value problems , *RIEMANN surfaces - Abstract
The elastic field of a heterogeneous medium containing doubly periodic cylindrical inclusions is investigated in antiplane shear. The heterogeneous medium is replaced by a homogeneous medium with doubly periodic stresses not related to strains. In the regions corresponding to the inclusions of the heterogeneous medium, an equivalence condition between a problem for the heterogeneous medium (called the original problem) and the corresponding problem for the homogeneous medium (called the equivalent problem) is established. Employing displacement continuity and stress jump conditions, the equivalent problem is formulated as a doubly quasi-periodic Riemann boundary-value problem, which is solved analytically, and the elastic fields in the doubly periodic inclusions and matrix are determined. As an example of application, the present solution is used to evaluate the effective antiplane moduli of composites, which are found to be in good agreement with existing results. [ABSTRACT FROM AUTHOR] more...
- Published
- 2018
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15. Antiplane Shear
- Author
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Sofonea, Mircea and Matei, Andaluzia
- Published
- 2009
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16. ANTIPLANE CRACK IN A PRE-STRESSED FIBER REINFORCED ELASTIC MATERIAL
- Author
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Craciun, Eduard-Marius and Sadowski, Tomasz, editor
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- 2006
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17. STUDY ON DOUBLY PERIODIC RIGID LINE INCLUSIONS UNDER ANTIPLANE SHEAR
- Author
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Xu, Y.L., Huang, L., LIU, G.R., editor, TAN, V.B.C., editor, and HAN, X., editor
- Published
- 2006
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18. Phenomenology of Rubber-Like Materials
- Author
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Saccomandi, Giuseppe, Velarde, Manuel Garcia, editor, Sayir, Mahir, editor, Schneider, Wilhelm, editor, Schrefler, Bernhard, editor, Tasso, Carlo, editor, Saccomandi, Giuseppe, editor, and Ogden, Raymond W., editor more...
- Published
- 2004
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19. A hybrid $$ H ^1\times H (\mathrm {curl})$$ finite element formulation for a relaxed micromorphic continuum model of antiplane shear
- Author
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Ingo Münch, Adam Sky, Michael Neunteufel, Patrizio Neff, and Joachim Schöberl
- Subjects
Curl (mathematics) ,Continuum (topology) ,Applied Mathematics ,Mechanical Engineering ,Mathematical analysis ,Computational Mechanics ,Hilbert space ,Ocean Engineering ,02 engineering and technology ,Antiplane shear ,01 natural sciences ,Finite element method ,010101 applied mathematics ,Computational Mathematics ,symbols.namesake ,020303 mechanical engineering & transports ,Exact solutions in general relativity ,0203 mechanical engineering ,Computational Theory and Mathematics ,symbols ,Uniqueness ,0101 mathematics ,Continuum hypothesis ,Mathematics - Abstract
One approach for the simulation of metamaterials is to extend an associated continuum theory concerning its kinematic equations, and the relaxed micromorphic continuum represents such a model. It incorporates the Curl of the nonsymmetric microdistortion in the free energy function. This suggests the existence of solutions not belonging to $$ H ^1$$ H 1 , such that standard nodal $$ H ^1$$ H 1 -finite elements yield unsatisfactory convergence rates and might be incapable of finding the exact solution. Our approach is to use base functions stemming from both Hilbert spaces $$ H ^1$$ H 1 and $$ H (\mathrm {curl})$$ H ( curl ) , demonstrating the central role of such combinations for this class of problems. For simplicity, a reduced two-dimensional relaxed micromorphic continuum describing antiplane shear is introduced, preserving the main computational traits of the three-dimensional version. This model is then used for the formulation and a multi step investigation of a viable finite element solution, encompassing examinations of existence and uniqueness of both standard and mixed formulations and their respective convergence rates. more...
- Published
- 2021
- Full Text
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20. Antiplane shear crack in a functionally graded material strip with surface elasticity
- Author
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Zhen-Liang Hu, Xian-Fang Li, Ying Yang, and Wei-Li Ma
- Subjects
Materials science ,Mechanical Engineering ,Mathematical analysis ,02 engineering and technology ,Antiplane shear ,01 natural sciences ,Functionally graded material ,Displacement (vector) ,Stress (mechanics) ,020303 mechanical engineering & transports ,0203 mechanical engineering ,0103 physical sciences ,Elasticity (economics) ,Galerkin method ,010301 acoustics ,Stress intensity factor ,Intensity (heat transfer) - Abstract
When the dimension of a structure falls to the micro-/nanoscale, surface effect is significant and plays a key role in affecting the mechanical behavior. This article studies the influence of surface elasticity on the stress intensity factor of an antiplane shear crack embedded in an elastic strip made of functionally graded materials. Surface elasticity is applied on the strip surfaces and crack faces, and classic elasticity is invoked for the strip interior. An antiplane shear crack problem is solved for a symmetric FGM with a crack parallel to the strip surfaces. The associated problem is converted to a hypersingular integro-differential equation for the out-of-plane displacement on the crack faces through the Fourier transform and then to a singular integro-differential equation with Cauchy kernel. The Galerkin method is applied to expand the crack face displacement as a Chebyshev series, and the singular integro-differential equation reduces to a system of algebraic linear equations. Stress intensity factors at the crack tips and the out-of-plane displacement on the crack faces are calculated numerically. It is found that surface elasticity and gradient index strongly alter the bulk stress and its intensity factors near the crack tips. Positive surface shear modulus decreases the mode III stress intensity factors and negative surface shear modulus has an opposite behavior. The influence of the variation of material gradient on the mode III stress intensity factors is expounded in graph. more...
- Published
- 2021
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21. Electro-elastic field of a piezoelectric quasicrystal medium containing two cylindrical inclusions
- Author
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Libin Wang, Hui Jin, Shaker A. Meguid, and Keqiang Hu
- Subjects
Materials science ,Field (physics) ,Mechanical Engineering ,Computational Mechanics ,Conformal map ,02 engineering and technology ,Mechanics ,Antiplane shear ,01 natural sciences ,Piezoelectricity ,010305 fluids & plasmas ,Matrix (mathematics) ,020303 mechanical engineering & transports ,0203 mechanical engineering ,0103 physical sciences ,Boundary value problem ,Phason ,Material properties - Abstract
Considering the piezoelectric effect, the electro-elastic field of an infinite one-dimensional quasicrystal medium with two circular cylindrical inclusions is derived under antiplane shear and inplane electric loading. The boundary value problem of the composite material with circular cylindrical inclusions is analytically solved by the use of the conformal mapping technique and analytical continuation theory. The stresses in the phonon and phason fields and the electric displacements are obtained explicitly in the form of a power series both for the matrix and the inclusions. Some typical examples are analyzed to show the effect of the geometric parameters, material properties, and electro-mechanical loading on the electro-elastic fields in the matrix, inclusions, and interfaces. The limiting cases of circular cavities and rigid circular inclusions have also been investigated and discussed. more...
- Published
- 2021
- Full Text
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22. Energetics in Martensites
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Bruno, O. P., Gladwell, G. M. L., editor, Bahei-El-Din, Yehia A., editor, and Dvorak, George J., editor
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- 2002
- Full Text
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23. Kinking and Curving of Cracks. Maximum Dissipation Criterion
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Marsden, J. E., editor, Sirovich, L., editor, and Gurtin, Morton E.
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- 2000
- Full Text
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24. A boundary value problem of orthotropic electroelastic circular cylinder
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Ákos József Lengyel, István Ecsedi, and Attila Baksa
- Subjects
Physics::Fluid Dynamics ,Materials science ,Traction (engineering) ,Boundary (topology) ,Cylinder ,Boundary value problem ,Mechanics ,Deformation (meteorology) ,Antiplane shear ,Orthotropic material ,Piezoelectricity - Abstract
A boundary value problem of orthotropic piezoelectric solid circular cylinder which is in the state of antiplane shear deformation is studied. The whole boundary surface is loaded by an equilibrium axial traction. This paper gives an analytical solution of the considered antiplane shear deformation. more...
- Published
- 2021
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25. Analyzing size effects in a cracked orthotropic layer under antiplane shear loading
- Author
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Kheng Lim Goh, Judha Purbolaksono, Richardson P Joseph, Chunwei Zhang, Baolin Wang, and Bijan Samali
- Subjects
Crack plane ,Materials science ,Mechanical Engineering ,Surface gradient ,Stiffness ,02 engineering and technology ,Antiplane shear ,Orthotropic material ,01 natural sciences ,Layer thickness ,020303 mechanical engineering & transports ,0203 mechanical engineering ,mental disorders ,0103 physical sciences ,medicine ,medicine.symptom ,Composite material ,010301 acoustics ,Layer (electronics) ,Stress intensity factor - Abstract
Scale-dependent stress intensity factors in an anti-plane cracked orthotropic material layer are evaluated using strain gradient theory. Both volumetric and surface strain gradient material characteristic lengths represented as l and $$l^{'}$$ , respectively, are employed to obtain semi-analytical solutions. The surface strain gradient effect is considered for both positive and negative $$l^{'}$$ values. The layer edges are assumed stress-free and oriented parallel to the crack plane. The presence of orthotropy can either increase or decrease the stress intensity factors depending on if it is greater or smaller than unity. The volumetric strain gradient effect reduces the stress intensity factor and it is more pronounced for smaller layer thickness. It was found that the negative surface gradient leads to a more complaint crack, while the positive surface gradient increases crack stiffness. Overall, the surface gradient effect is less significant in comparison with the volumetric gradient effect. more...
- Published
- 2020
- Full Text
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26. Cracked elastic layer with surface elasticity under antiplane shear loading
- Author
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Xian-Fang Li, Ying Yang, and Zhen-Liang Hu
- Subjects
Stress (mechanics) ,Materials science ,Mechanical Engineering ,Mathematical analysis ,Isotropy ,Constitutive equation ,Computational Mechanics ,Boundary value problem ,Elasticity (economics) ,Galerkin method ,Antiplane shear ,Stress intensity factor - Abstract
A mode-III crack embedded in a homogeneous isotropic elastic layer of nanoscale finite thickness is studied in this article. The classical elasticity incorporating surface elasticity is employed to reduce a nonclassical mixed boundary value problem, where the layer interior obeys the traditional constitutive relation and the surfaces of the layer and the crack are dominated by the surface constitutive relation. Using the Fourier transform, we convert the problem to a hypersingular integro-differential equation for the out-of-plane displacement on the crack faces. By expanding the out-of-plane displacement as series of Chebyshev polynomials, the Galerkin method is invoked to reduce the singular integro-differential equation with Cauchy kernel to a set of algebraic linear equations for the unknown coefficients. An approximate solution is determined, and the influences of surface elasticity on the elastic field and stress intensity factor are examined and displayed graphically. It is shown that surface elasticity decreases the bulk stress and its intensity factor near the crack tips for positive surface shear modulus and gives rise to an opposite trend for a negative surface shear modulus. more...
- Published
- 2020
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27. Singular elastic solutions in corners with spring boundary conditions under anti-plane shear
- Author
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Vladislav Mantic, Víctor Villalba, and Sara Jiménez-Alfaro
- Subjects
Laplace's equation ,Series (mathematics) ,Mathematical analysis ,Linear elasticity ,Computational Mechanics ,02 engineering and technology ,Mathematics::Spectral Theory ,Antiplane shear ,01 natural sciences ,010101 applied mathematics ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Harmonic function ,Mechanics of Materials ,Singular solution ,Modeling and Simulation ,Boundary value problem ,0101 mathematics ,Asymptotic expansion ,Mathematics - Abstract
A new analytical procedure is developed for the deduction of the asymptotic series of the singular solutions in displacements and stresses near the vertex of the linear elastic isotropic corners with the Dirichlet–Robin (fixed-spring) and Neumann–Robin (free-spring) boundary conditions. Under the assumption of antiplane shear loading, the corresponding elastic problem reduces to the Laplace equation for the out-of-plane displacement. In the deduction of such singular solution, the complex variable is used to propose a harmonic function in the form of an asymptotic series including both power and logarithmic terms. This original procedure is suitable for its implementation in a computer algebra software which makes all the necessary symbolic computing, simplifications and rearrangements. This is a key issue due to the fact that the complexity of terms in these series may increase with increasing order of terms. These series are composed by the main terms (also called main singularities), solutions of the corresponding Dirichlet–Neumann or Neumann–Neumann problems, and the associated finite or infinite series of the so-called shadow terms (also called shadow singularities). These terms are determined by solving systems of recursive inhomogeneous Dirichlet–Neumann or Neumann–Neumann problems, respectively. A general classification of the behaviours of the asymptotic series covering all the considered corner problems is introduced. A few examples of the asymptotic series for corners with Dirichlet–Robin and Neumann–Robin boundary conditions are presented to illustrate the capabilities of this procedure. more...
- Published
- 2020
- Full Text
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28. Formation of Shear Bands in Models of Granular Materials
- Author
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Shearer, M., Garaizar, F. X., Gordon, M. K., Gladwell, G. M. L., editor, Fleck, N. A., editor, and Cocks, A. C. F., editor
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- 1997
- Full Text
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29. Plane Waves in Isotropic Fluids and Solids
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Allard, J. F. and Allard, J. F.
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- 1993
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30. A unified solution approach for a large variety of antiplane shear and torsion notch problems: Theory and examples.
- Author
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Salviato, Marco and Zappalorto, Michele
- Subjects
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STRESS concentration , *TORSION , *POLYGONALES , *ELASTICITY , *SCHWARZ-Christoffel transformation - Abstract
In this work, a unified solution approach is proposed for the analytical evaluation of the stress fields close to notches under antiplane shear and torsion loadings, which allows a large variety of notch problems to be tackled. The method is based on the complex potential approach for antiplane elasticity combined with the use of proper conformal mappings. In particular, it is shown that a well defined analytical link does exist between the complex potential to be used to determine stresses and the first derivative of the conformal mapping used to mathematically describe the notch profile. This makes some methodologies such as Schwarz-Christoffel transformation, which allows describing any polygonal domain automatically, very attractive for the direct solution of notch problems. A bulk of solutions are provided to support this finding, from cracks and pointed notches, to radiused notches. In addition, the accuracy of each proposed solution is discussed in detail taking advantage of a bulk of results from FE analyses. [ABSTRACT FROM AUTHOR] more...
- Published
- 2016
- Full Text
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31. Stack of non-uniformly loaded shear cracks in magnetoelectroelastic materials
- Author
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G. E. Tupholme
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Materials science ,Mechanical Engineering ,General Mathematics ,02 engineering and technology ,021001 nanoscience & nanotechnology ,Antiplane shear ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Shear (geology) ,Mechanics of Materials ,General Materials Science ,Composite material ,0210 nano-technology ,Civil and Structural Engineering - Abstract
Detailed expressions are derived in closed-form for the field components at a general point in the deformation of magnetoelectroelastic media by a stack of parallel, antiplane shear cracks to which... more...
- Published
- 2020
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32. Doubly periodic array of coated cylindrical inclusions model and applications for nanocomposites
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Junhua Xiao, Yaoling Xu, and Qiao Tian
- Subjects
Nanocomposite ,Materials science ,Mechanical Engineering ,Computational Mechanics ,Stiffness ,02 engineering and technology ,Antiplane shear ,01 natural sciences ,Finite element method ,010305 fluids & plasmas ,Stress (mechanics) ,Matrix (mathematics) ,020303 mechanical engineering & transports ,0203 mechanical engineering ,0103 physical sciences ,Solid mechanics ,medicine ,Interphase ,Composite material ,medicine.symptom - Abstract
An analytical method is proposed to solve the problem of an infinite elastic matrix containing a doubly periodic array of coated cylindrical inclusions under antiplane shear. The elastic fields in the inclusions, the coatings/interphases and the matrix are derived, which are used to investigate the stresses and the effective stiffness coefficients of the nanofiber composites. Numerical examples demonstrate the size dependence of the stress and the effective stiffness coefficient, and the effects of the interphase thickness and stiffness and array configurations of the inclusions on the effective stiffness coefficient. A finite element analysis is used to benchmark the effective stiffness coefficient predicted by the proposed model, in which excellent agreement is observed. When letting the interphase be thin enough, the proposed coated inclusions model can be used to simulate the zero-thickness interface model, which is validated by the results comparisons of the two models. Instabilities of the stress fields are observed under certain conditions in simulating the zero-thickness interface model. more...
- Published
- 2019
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33. The Stress Intensity Factors of Multiple Inclined Cracks in a Composite Laminate Subjected to In-Plane Loading
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J. Wang and S. Li
- Subjects
010302 applied physics ,Materials science ,Composite number ,Fracture mechanics ,02 engineering and technology ,Surfaces and Interfaces ,Composite laminates ,Condensed Matter Physics ,Antiplane shear ,01 natural sciences ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Mechanics of Materials ,Tension (geology) ,0103 physical sciences ,Shielding effect ,General Materials Science ,Composite material ,Stress intensity factor ,Stress concentration - Abstract
Inclined multiple cracks may appear in composite laminates and sandwich structures. In this paper, we solve the fracture problem of a three-layer sandwich structure which contains multiple inclined cracks in the central layer under tension and antiplane shear. Three types of crack configurations are considered: an isolated crack, a periodic array of inclined cracks with the same length, and two parallel cracks with different lengths. In these cases, we examine the interaction among the cracks under mixed I–II mode and pure mode III based on the stress intensity factors. Then, we apply the solutions to fibre-reinforced composite laminates. The results show that the stress intensity factors of the multiple cracks are significantly affected by the constraining effect of the outer sublaminates and the shielding effect among cracks. For cracks with significantly different sizes, the long crack dominates the stress concentration. This work reveals the influences of the laminate configuration, crack distribution, crack orientation and crack size on the stress concentration at the tips of inclined cracks in the three-layer composite laminate, and the results may be used to analyze the crack propagation in the laminates. more...
- Published
- 2019
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34. Uniform stress state inside a non-elliptical inhomogeneity near an irregularly shaped hole in antiplane shear
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Peter Schiavone and Xu Wang
- Subjects
Physics ,General Mathematics ,Analytic continuation ,Conformal map ,02 engineering and technology ,Mechanics ,State (functional analysis) ,Antiplane shear ,01 natural sciences ,010101 applied mathematics ,Stress (mechanics) ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Mechanics of Materials ,General Materials Science ,0101 mathematics - Abstract
Analytic continuation and conformal mapping techniques are applied to establish that the state of stress inside a non-elliptical elastic inhomogeneity can remain uniform despite the presence of a nearby irregularly shaped hole when the surrounding matrix is subjected to uniform remote antiplane shear stresses. The hole boundary is assumed to be either traction-free or subjected to antiplane line forces. Detailed numerical results are presented to demonstrate the resulting analytical solutions. Our results indicate that in maintaining a uniform stress distribution inside the inhomogeneity, it is permissible for the stresses in the matrix to exhibit either a square root singularity at sharp corners of a hole boundary or a high level of stress concentration at rounded corners of a hole. more...
- Published
- 2019
- Full Text
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35. Scattering of harmonic antiplane shear waves by an arc-shaped interfacial crack in functionally graded annular bi-material guide rail
- Author
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Xiaoxiao Liu, Ming Liu, and Pengpeng Shi
- Subjects
Materials science ,Scattering ,Mechanical Engineering ,General Mathematics ,Aerospace Engineering ,020101 civil engineering ,Ocean Engineering ,02 engineering and technology ,Condensed Matter Physics ,Antiplane shear ,Orthotropic material ,0201 civil engineering ,Arc (geometry) ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Mechanics of Materials ,Automotive Engineering ,Harmonic ,Composite material ,Civil and Structural Engineering - Abstract
The dynamic behavior of an arc-shaped interfacial crack in an orthotropic functionally graded annular bi-material structure is investigated. In order for the analysis to be executable, the material... more...
- Published
- 2019
- Full Text
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36. Asymptotic Analysis of the Crack Tip Stress Field (Consideration of Higher Order Terms)
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Larisa Stepanova
- Subjects
Numerical Analysis ,Asymptotic analysis ,Materials science ,Deformation (mechanics) ,Cauchy stress tensor ,Elastic energy ,Fracture mechanics ,010103 numerical & computational mathematics ,Mechanics ,Antiplane shear ,01 natural sciences ,010101 applied mathematics ,Stress field ,Fracture (geology) ,0101 mathematics - Abstract
This paper presents multi-parameter asymptotic description of the stress field near the tip of a central crack in a linear-elastic plate under: (1) normal tensile stress; (2) transverse shear; (3) mixed mode deformation in the full range of mixed modes of loading, from the opening mode fracture to antiplane shear. A multi-parameter expansion of the stress tensor components including higher order terms has been constructed. All the scale (amplitude) factors—coefficients of the complete Williams asymptotic expansion—have been determined as functions of the crack length and parameters of loading. The expansion constructed and formulas obtained for the expansion coefficients can be used for keeping any preassigned number of terms in asymptotic representations of mechanical fields at a crack tip in a plate. The number of components to keep at different distances from the tip of defect was subjected to analysis. The angles of crack propagation under conditions of mixed-mode loading were calculated using a multi-parameter expansion of stress field by means of (1) the maximum tangential stress criterion and (2) the criterion of minimum elastic strain energy density. more...
- Published
- 2019
- Full Text
- View/download PDF
37. Strain fields in cracked bodies under antiplane shear for a generalised non-hardening material law
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Michele Zappalorto
- Subjects
strain distributions ,Materials science ,non-linear material behaviour ,General Mathematics ,crack ,02 engineering and technology ,Stress distribution ,021001 nanoscience & nanotechnology ,Antiplane shear ,Antiplane shear deformation ,Condensed Matter::Materials Science ,020303 mechanical engineering & transports ,non work-hardening material ,0203 mechanical engineering ,Mechanics of Materials ,Law ,Hardening (metallurgy) ,General Materials Science ,0210 nano-technology - Abstract
An exact, closed form, solution is derived for the non-linear stress distribution in a cracked body under antiplane shear deformation. A generalised, non work-hardening, law is introduced to describe the material behaviour, and the stress and strain fields are derived in closed form. Such a new generalised material law includes the effect of a new parameter, a, which allows the transition from the ideally elastic behaviour (low strain regime) to the pure non-linear behaviour (large strain regime) to be modulated. A discussion is carried out on the features of the new solution and on the behaviour of stresses and strains close to and far away from the crack tip. more...
- Published
- 2019
- Full Text
- View/download PDF
38. Antiplane Shear Waves in Fiber Composites with Structural Nonlinearity
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Vladyslav V. Danishevskyy, Jan Awrejcewicz, and Igor V. Andrianov
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Nonlinear system ,Materials science ,Fiber ,Composite material ,Antiplane shear - Published
- 2021
- Full Text
- View/download PDF
39. Homogenization of piezoelectric planar Willis materials undergoing antiplane shear
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Majd Kosta, René Pernas-Salomón, Daniel Torrent, Alan Muhafra, and Gal Shmuel
- Subjects
dynamic homogenization ,bepress|Engineering ,bepress|Engineering|Mechanical Engineering ,engrXiv|Engineering|Mechanical Engineering ,General Physics and Astronomy ,bepress|Engineering|Aerospace Engineering ,Homogenization (chemistry) ,Causality (physics) ,fiber composites ,bepress|Engineering|Mechanical Engineering|Acoustics, Dynamics, and Controls ,Dispersion (water waves) ,Coupling ,Physics ,piezoelectricity ,Applied Mathematics ,Metamaterial ,Antiplane shear ,Piezoelectricity ,engrXiv|Engineering|Aerospace Engineering ,Computational Mathematics ,Bloch–Floquet waves ,Classical mechanics ,engrXiv|Engineering ,Modeling and Simulation ,Reciprocity (electromagnetism) ,Wills metamaterials ,bepress|Engineering|Mechanical Engineering|Electro-Mechanical Systems ,engrXiv|Engineering|Mechanical Engineering|Electro-Mechanical Systems ,effective properties ,engrXiv|Engineering|Mechanical Engineering|Acoustics, Dynamics, and Controls - Abstract
Homogenization theories provide models that simplify the constitutive description of heterogeneous media while retaining their macroscopic features. These theories have shown how the governing fields can be macroscopically coupled, even if they are microscopically independent. A prominent example is the Willis theory which predicted the strain–momentum coupling in elastodynamic metamaterials. Recently, a theory that is based on the Green’s function method predicted analogous electro–momentum coupling in piezoelectric metamaterials. Here, we develop a simpler scheme for fibrous piezoelectric composites undergoing antiplane shear waves. We employ a source-driven approach that delivers a unique set of effective properties for arbitrary frequency–wavevector pairs. We numerically show how the resultant homogenized model recovers exactly the dispersion of free waves in the composite. We also compute the effective properties in the long-wavelength limit and off the dispersion curves, and show that the resultant model satisfy causality, reciprocity and energy conservation. By contrast, we show how equivalent models that neglect the electromomentum coupling violate these physical laws. more...
- Published
- 2021
40. Antiplane shear of an asymmetric sandwich plate
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Julius Kaplunov, L.A. Prikazchikova, and Mohammed Alkinidri
- Subjects
Physics ,Asymptotic analysis ,Wave propagation ,Mathematical analysis ,General Physics and Astronomy ,Equations of motion ,Harmonic (mathematics) ,02 engineering and technology ,021001 nanoscience & nanotechnology ,Antiplane shear ,Shear (sheet metal) ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Mechanics of Materials ,Dispersion relation ,General Materials Science ,Boundary value problem ,0210 nano-technology ,QA - Abstract
An asymmetric three-layered laminate with prescribed stresses along the faces is considered. The outer layers are assumed to be much stiffer than the inner one. The focus is on long-wave low-frequency anti-plane shear. Asymptotic analysis of the original dispersion relation reveals a low-frequency harmonic supporting a slow quasi-static (or static at the limit) decay along with near cut-off wave propagation. In spite of asymmetry of the problem, the leading order shortened polynomial dispersion relation factorises into two simpler ones corresponding to the fundamental mode and the aforementioned harmonic. The associated 1D equations of motion derived in the paper are also split into two second-order operators in line with the factorisation of the shortened dispersion relation. Asymptotically justified boundary conditions are established using the Saint-Venant’s principle modified by taking into account the high-contrast properties of the laminate. more...
- Published
- 2021
41. Antiplane Shear Deformation of Elastic Cylinders in Contact with a Rigid Foundation
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Csaba Varga, Nicuşor Costea, and Alexandru Kristály
- Subjects
Physics ,Lemma (mathematics) ,Corollary ,Weak solution ,Foundation (engineering) ,Mechanics ,Deformation (engineering) ,Antiplane shear ,Elastic cylinder - Abstract
We analyze the antiplane shear deformation of an elastic cylinder in frictional contact with a rigid foundation, for static processes, under the small deformations hypothesis. Using the KKM lemma due to Fan (see Corollary D.1), we prove that the model has at least one weak solution. Moreover, we present several examples of constitutive laws and friction laws for which our theoretical results are valid. more...
- Published
- 2021
- Full Text
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42. Application of Numerical and Symbolic System for Evaluating Stressed State of Cylindrical Shock Absorber
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B. A. Zhukov, Yu. Yu. Andreeva, and Ya. V. Kalinin
- Subjects
Maple ,business.industry ,Computer science ,Structural engineering ,engineering.material ,Antiplane shear ,Damper ,Shock absorber ,Natural rubber ,Hyperelastic material ,visual_art ,visual_art.visual_art_medium ,engineering ,Boundary value problem ,Deformation (engineering) ,business - Abstract
Rubber-metal products represent one of the most important classes of products used in modern machine building. In most cases, reliability and durability of structures are determined by reliability and durability of component rubber products. Therefore, there are increased requirements for the calculation of rubber products. In the field of operational loads, the rubber is in a highly elastic state; i.e., it relates to elastomers. Since in a highly elastic state the rubber is a low-modulus material and allows for large operational deformations, a nonlinear theory of elasticity must be used to describe the stress–strain state. This paper discusses a specialized Maple-based calculation system that focuses on the calculation of the shear damper. This system helps solve any static problem with finite antiplane shear deformation with mixed boundary conditions and any generalized neo-Hookean potential of the strain energy for areas with a complex configuration. An example of comparing a numerical solution with a known exact solution for Treloar strain energy potential is given. For Fung’s deformation energy potential, a new exact solution obtained by a semi-partial method is given and is also compared to the numerical solution. The results of the compared solutions show the suitability of the proposed Maple-based calculation system. more...
- Published
- 2021
- Full Text
- View/download PDF
43. ANALYSIS OF STABLE SCREW DISLOCATION CONFIGURATIONS IN AN ANTIPLANE LATTICE MODEL.
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HUDSON, T. and ORTNER, C.
- Subjects
- *
STABILITY theory , *DISLOCATIONS in crystals , *LATTICE models (Statistical physics) , *MATHEMATICAL proofs , *APPROXIMATION theory , *MATHEMATICAL analysis , *INVERSE functions - Abstract
We consider a variational antiplane lattice model and demonstrate that at zero temperature, there exist locally stable states containing screw dislocations, given conditions on the distance between the dislocations and on the distance between dislocations and the boundary of the crystal. In proving our results, we introduce approximate solutions which are taken from the theory of dislocations in linear elasticity and use the inverse function theorem to show that local minimizers lie near them. This gives credence to the commonly held intuition that linear elasticity is essentially correct up to a few spacings from the dislocation core. [ABSTRACT FROM AUTHOR] more...
- Published
- 2015
- Full Text
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44. Earthquake Sequence Dynamics at the Interface Between an Elastic Layer and Underlying Half‐Space in Antiplane Shear
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Kali L. Allison, Eric M. Dunham, and Lauren S. Abrahams
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Quantitative Biology::Biomolecules ,Sequence ,Materials science ,010504 meteorology & atmospheric sciences ,Interface (Java) ,Dynamics (mechanics) ,Mechanics ,Half-space ,Antiplane shear ,01 natural sciences ,Geophysics ,Space and Planetary Science ,Geochemistry and Petrology ,Free surface ,Earth and Planetary Sciences (miscellaneous) ,Layer (electronics) ,0105 earth and related environmental sciences - Abstract
We quantify sliding stability and rupture styles for a horizontal interface between an elastic layer and stiffer elastic half-space with a free surface on top and rate-and-state friction on the int... more...
- Published
- 2020
- Full Text
- View/download PDF
45. On the Tykhonov Well-Posedness of an Antiplane Shear Problem
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Mircea Sofonea and Domingo A. Tarzia
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Pure mathematics ,74M15, 74M10, 74G25, 74G30, 49J40, 35M86 ,General Mathematics ,010102 general mathematics ,Boundary (topology) ,Monotonic function ,Weak formulation ,Antiplane shear ,01 natural sciences ,Interpretation (model theory) ,010101 applied mathematics ,Mathematics - Analysis of PDEs ,Compact space ,FOS: Mathematics ,Coulomb ,Boundary value problem ,0101 mathematics ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
We consider a boundary value problem which describes the frictional antiplane shear of an elastic body. The process is static and friction is modeled with a slip-dependent version of Coulomb's law of dry friction. The weak formulation of the problem is in the form of a quasivariational inequality for the displacement field, denoted by $\cP$. We associated to problem $\cP$ a boundary optimal control problem, denoted by $\cQ$. For Problem $\cP$ we introduce the concept of well-posedness and for Problem $\cQ$ we introduce the concept of weakly and weakly generalized well-posedness, both associated to appropriate Tykhonov triples. Our main result are Theorems \ref{t1} and \ref{t2}. Theorem \ref{t1} provides the well-posedness of Problem $\cP$ and, as a consequence, the continuous dependence of the solution with respect to the data. Theorem \ref{t2} provides the weakly generalized well-posedness of Problem $\cQ$ and, under additional hypothesis, its weakly well posedness. The proofs of these theorems are based on arguments of compactness, lower semicontinuity, monotonicity and various estimates. Moreover, we provide the mechanical interpretation of our well-posedness results., 21 pages more...
- Published
- 2020
- Full Text
- View/download PDF
46. Antiplane Shear of an Elastic Body with Elliptic Inclusions Under the Conditions of Imperfect Contact on the Interfaces
- Author
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Volodymyr I. Kushch and V. S. Chernobai
- Subjects
Statistics and Probability ,Series (mathematics) ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Antiplane shear ,01 natural sciences ,010305 fluids & plasmas ,Shear (sheet metal) ,Algebraic equation ,Rate of convergence ,0103 physical sciences ,0101 mathematics ,Elasticity (economics) ,Multipole expansion ,Mathematics ,Stress concentration - Abstract
We study the problem of аntiplane shear of an elastic body containing a finite array of arbitrarily located and oriented elliptic inclusions under the conditions of imperfect mechanical contact on the interfaces. The analytic solution of the problem is obtained by the method of multipole expansions with the use of the technique of complex potentials. By expanding the disturbances of the field of displacements caused by inclusions in a series in the system of elliptic harmonics and using the formulas for their reexpansion and exact validity of all contact conditions, we reduce the boundary-value problem of the theory of elasticity to an infinite system of linear algebraic equations. It is also proved that the reduction method is applicable to the indicated system, the rate of convergence of the solution is investigated, and the accumulated results are compared with the data available from the literature. The presented numerical results of parametric investigations reveal the presence of a strong dependence of stress concentration on the conditions of contact on the interfaces, as well as on the sizes, shapes, and relative positions of the inclusions. more...
- Published
- 2019
- Full Text
- View/download PDF
47. A Yoffe-type moving crack in one-dimensional hexagonal piezoelectric quasicrystals
- Author
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Xian-Fang Li and Y.-B. Zhou
- Subjects
Materials science ,Applied Mathematics ,Fracture mechanics ,02 engineering and technology ,Mechanics ,Moving crack ,Physics::Classical Physics ,Antiplane shear ,01 natural sciences ,Piezoelectricity ,Physics::Geophysics ,Condensed Matter::Materials Science ,020303 mechanical engineering & transports ,Singularity ,0203 mechanical engineering ,Modeling and Simulation ,Electric field ,0103 physical sciences ,Phason ,010301 acoustics ,Electric displacement field - Abstract
A Yoffe-type moving crack in one-dimensional hexagonal piezoelectric quasicrystals is considered. The Fourier transform technique is used to solve a moving crack problem under the action of antiplane shear and inplane electric field. Full elastic stresses of phonon and phason fields and electric fields are derived for a crack running with constant speed in the periodic plane. Obtained results show that the coupled elastic fields inside piezoelectric quasicrystals depend on the speed of crack propagation, and exhibit the usual square-root singularity at the moving crack tip. Electric field and phason stresses do not have singularity and electric displacement and phonon stresses have the inverse square-root singularity at the crack tip for a permeable crack. The field intensity factors and energy release rates are obtained in closed form. The crack velocity does not affect the field intensity factors, but alters the dynamic energy release rate. Bifurcation angle of a moving crack in a 1D hexagonal piezoelectric quasicrystal is evaluated from the viewpoint of energy balance. Obtained results are helpful to better understanding crack advance in piezoelectric quasicrystals. more...
- Published
- 2019
- Full Text
- View/download PDF
48. Non-Uniformly Loaded Row of Moving, Antiplane Shear Cracks in One-Dimensional Piezoelectric Quasicrystals
- Author
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G. E. Tupholme
- Subjects
Materials science ,General Physics and Astronomy ,Quasicrystal ,Composite material ,Antiplane shear ,Piezoelectricity - Published
- 2018
- Full Text
- View/download PDF
49. An analytic solution for the problem of two symmetrical edge cracks emanating from a circular hole with surface effect under antiplane shear
- Author
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Junhua Xiao, Yaoling Xu, and Fucheng Zhang
- Subjects
Strain energy release rate ,Materials science ,Mechanical Engineering ,Computational Mechanics ,Conformal map ,02 engineering and technology ,Mechanics ,Edge (geometry) ,021001 nanoscience & nanotechnology ,Antiplane shear ,Shear (sheet metal) ,Condensed Matter::Materials Science ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Solid mechanics ,Fracture (geology) ,0210 nano-technology ,Stress intensity factor - Abstract
A theoretical study is performed on the fracture characteristics for the problem of two symmetrical edge cracks emanating from a circular hole with surface effect under far-field antiplane shear loading. Based on the theory of Gurtin–Murdoch surface model, a rigorous analytical solution of the stress intensity factor and the strain energy release rate at a crack tip is presented by using the complex potential function and a conformal mapping technique. When the cracked hole becomes nano-sized, the stress intensity factor and the strain energy release rate show significant size dependence. The interaction effects between cracks and hole on the stress intensity factor and the strain energy release rate are discussed in providing numerical examples. more...
- Published
- 2018
- Full Text
- View/download PDF
50. Nonuniformly Loaded Stack of Antiplane Shear Cracks in One-Dimensional Piezoelectric Quasicrystals
- Author
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G. E. Tupholme
- Subjects
Materials science ,Article Subject ,Deformation (mechanics) ,General Engineering ,02 engineering and technology ,Mechanics ,021001 nanoscience & nanotechnology ,Antiplane shear ,Piezoelectricity ,Stress (mechanics) ,Condensed Matter::Materials Science ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Isotropic solid ,lcsh:TA401-492 ,lcsh:Materials of engineering and construction. Mechanics of materials ,General Materials Science ,Phason ,Dislocation ,0210 nano-technology ,Electric displacement field - Abstract
Representations in a closed form are derived, using an extension to the method of dislocation layers, for the phonon and phason stress and electric displacement components in the deformation of one-dimensional piezoelectric quasicrystals by a nonuniformly loaded stack of parallel antiplane shear cracks. Their dependence upon the polar angle in the region close to the tip of a crack is deduced, and the field intensity factors then follow. These exhibit that the phenomenon of crack shielding is dependent upon the relative spacing of the cracks. The analogous analyses, that have not been given previously, involving non-piezoelectric or non-quasicrystalline or simply elastic materials can be straightforwardly considered as special cases. Even when the loading is uniform and the crack is embedded in a purely elastic isotropic solid, no explicit representations have been available before for the components of the field at points other than directly ahead of a crack. Typical numerical results are graphically displayed. more...
- Published
- 2018
- Full Text
- View/download PDF
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