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Solid mechanics and its applications
01 Jan 1990-
About: The article was published on 1990-01-01 and is currently open access. It has received 320 citations till now. The article focuses on the topics: Solid mechanics.
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TL;DR: In this paper, the main ingredients and assumptions of developing macroscopic inelastic constitutive equations, mainly for metals and low strain cyclic conditions, have been discussed, with some comparisons with the previous ones, including more recent developments that offer potential new capabilities.
1,414 citations
TL;DR: In this article, a non-singular, self-consistent framework for computing the stress field and the total elastic energy of a general dislocation microstructure was developed, in which the driving force defined as the negative derivative of the total energy with respect to the dislocation position, is equal to the force produced by stress, through the Peach-Koehler formula.
Abstract: We develop a non-singular, self-consistent framework for computing the stress field and the total elastic energy of a general dislocation microstructure. The expressions are self-consistent in that the driving force defined as the negative derivative of the total energy with respect to the dislocation position, is equal to the force produced by stress, through the Peach–Koehler formula. The singularity intrinsic to the classical continuum theory is removed here by spreading the Burgers vector isotropically about every point on the dislocation line using a spreading function characterized by a single parameter a, the spreading radius. A particular form of the spreading function chosen here leads to simple analytic formulations for stress produced by straight dislocation segments, segment self and interaction energies, and forces on the segments. For any value a > 0 , the total energy and the stress remain finite everywhere, including on the dislocation lines themselves. Furthermore, the well-known singular expressions are recovered for a = 0 . The value of the spreading radius a can be selected for numerical convenience, to reduce the stiffness of the dislocation equations of motion. Alternatively, a can be chosen to match the atomistic and continuum energies of dislocation configurations.
403 citations
TL;DR: In this paper, the authors investigated the stress distribution between two adjacent opening-mode fractures as a function of the fracture spacing to layer thickness ratio using a three-layer elastic model with a fractured central layer.
362 citations
TL;DR: In this paper, the authors used large-scale three-dimensional discrete dislocation simulations (DDS) to explicitly model the deformation behavior of micrometer-scale Ni microcrystals in the size range of 0.5-20μm.
293 citations
TL;DR: In this paper, an implicit level set algorithm is proposed to locate the free boundary for a propagating hydraulic fracture, which exploits the local tip asymptotic behavior, applicable at the computational length scale, in order to locate a free boundary.
290 citations
References
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46,339 citations
Book•
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01 Jan 1934
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Abstract: Chapter 1: Stresses and Strains Chapter 2: Foundations of Plasticity Chapter 3: Elasto-Plastic Bending and Torsion Chapter 4: Plastic Analysis of Beams and Frames Chapter 5: Further Solutions of Elasto-Plastic Problems Chapter 6: Theory of the Slipline Field Chapter 7: Steady Problems in Plane Strain Chapter 8: Non-Steady Problems in Plane Strain
20,724 citations
Book•
01 Jan 1989
TL;DR: In this article, the methodes are numeriques and the fonction de forme reference record created on 2005-11-18, modified on 2016-08-08.
Abstract: Keywords: methodes : numeriques ; fonction de forme Reference Record created on 2005-11-18, modified on 2016-08-08
17,327 citations
"Solid mechanics and its application..." refers background in this paper
...Many finite element books are available, such as the books by Reddy [4], Onate [5], Zienkiewicz [6], Hughes [7], Hinton [8], just to name a few....
[...]
TL;DR: In this paper, it is shown that to answer several questions of physical or engineering interest, it is necessary to know only the relatively simple elastic field inside the ellipsoid.
Abstract: It is supposed that a region within an isotropic elastic solid undergoes a spontaneous change of form which, if the surrounding material were absent, would be some prescribed homogeneous deformation. Because of the presence of the surrounding material stresses will be present both inside and outside the region. The resulting elastic field may be found very simply with the help of a sequence of imaginary cutting, straining and welding operations. In particular, if the region is an ellipsoid the strain inside it is uniform and may be expressed in terms of tabulated elliptic integrals. In this case a further problem may be solved. An ellipsoidal region in an infinite medium has elastic constants different from those of the rest of the material; how does the presence of this inhomogeneity disturb an applied stress-field uniform at large distances? It is shown that to answer several questions of physical or engineering interest it is necessary to know only the relatively simple elastic field inside the ellipsoid.
11,784 citations
Book•
01 Jan 1985
TL;DR: In this paper, the physical properties of crystals systematically in tensor notation are presented, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them.
Abstract: First published in 1957, this classic study has been reissued in a paperback version that includes an additional chapter bringing the material up to date. The author formulates the physical properties of crystals systematically in tensor notation, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them. The mathematical groundwork is laid in a discussion of tensors of the first and second ranks. Tensors of higher ranks and matrix methods are then introduced as natural developments of the theory. A similar pattern is followed in discussing thermodynamic and optical aspects.
8,520 citations