scispace - formally typeset
Search or ask a question
Topic

Linear elasticity

About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.


Papers
More filters
Journal ArticleDOI
13 Jul 1977
TL;DR: In this article, the dynamics of the deformation of a viscous ellipsoidal inhomogeneity in a 2-dimensional viscous matrix undergoing a general linear time-dependent flow at infinity are investigated.
Abstract: The theory of the elastic fields round ellipsoidal inclusions and inhomogeneities together with the well-known analogy between linear elasticity and slow incompressible viscous flow are used to develop the governing equations for the finite deformation of a viscous ellipsoidal inhomogeneity in a viscous matrix undergoing a general linear time-dependent flow at infinity. The governing equations are then solved for an inhomogeneity in the form of an elliptic cylinder in a linear two-dimensional flow whose stream lines at infinity are steady. The behaviour of the inhomogeneity under pure shear and simple shear is considered in detail and it is shown that the boundaries of certain deforming inhomogeneities remain unchanged during simple shear. These steady inhomogeneities can appear also in general linear two-dimensional applied flows. In such flows the behaviour is influenced both by the initial shape and orientation of the inhomogeneity and by its viscosity. Inhomogeneities which are rather viscous or subject to an applied flow with high vorticity deform periodically, while most others elongate indefinitely. The patterns of behaviour may be described in terms of a number of regimes which can be classified by considering the singularities of the differential equations governing the variations of shape and orientation of the inhomogeneity, or, equivalently, by studying the invariants of the corresponding one-parameter Lie groups. Finally, some obvious extensions of the treatment are indicated. These make it possible to consider inhomogeneities (such as holes) whose volume does not remain constant, and which have constitutive relations more general than those of a linear viscous material. In this paper we discuss the slow finite deformation of a viscous ellipsoidal inhomogeneity in a matrix of different viscosity. The problem of the deforming inhomogeneity in viscous flow has been treated by a number of workers, but usually with the main interest either in the phenomenon of the ultimate bursting of a drop or in the calculation of the properties of a suspension of such inhomogeneities; for a recent brief review see Hinch (1975). The theories have thus not been concerned primarily with the progressive finite deformation of the inhomogeneity in nonsteady flow, but have dealt with an inhomogeneity which undergoes small or limited

84 citations

Journal ArticleDOI
TL;DR: In this paper, anisotropic linear elastic theory is invoked to provide boundary conditions for the core region, and a first approximation for lattice-point displacements within, and core atoms are then relaxed to a configuration of minimum potential energy by computer.
Abstract: The structuxe of atomically sharp equilibrium cracks in diamond, silicon and germanium is calculated. The treatment considers a long plane crack formed by bond rupture across the (111) cleavage plane, critically loaded in tension. Within a small 'core' region immediately surrounding the crack tip the interatomic interactions are represented by a potential function specially constructed to match macroscopic fracture parameters. Anisotropic linear elastic theory is invoked to provide boundary conditions for the core region, and a first approximation for lattice-point displacements within. The core atoms are then relaxed to a configuration of minimum potential energy by computer. The results indicate that continuum theory is capable of giving remarkably accurate predictions of the crack-tip displacement field, except within about three atom spacings from the tip, despite marked nonlinearity in the interatomic force function. These results are discussed in terms of existing continuum models of crack-tip structure: in particular, Barenblatt's model of a cusp-shaped tip region is found to be inapplicable to diamond-structure crystals. The crack-tip geometry is better pictured as a narrow slit terminated by a single line of bonds close to the rupture point. Brief reference is made to the possible extension of the treatment to other classes of highly brittle solid, especially glassy materials, and to the relevance of the results to some fracture problems of practical importance. The fracture of an ideally brittle solid is essentially an atomic process, in which cohesive bonds are ruptured at the tip of the growing crack. Yet traditionally the rnathematical treatment of the mechanics of fracture propagation has been developed almost exclusively from continuum concepts. The chief reason for this lies in the interest of simplicity, a proper description of the atomic configuration at a crack tip requiring seemingly formidable analysis in terms of a suitable structural model for the given solid. The continuum approach, based on linear elasticity theory, has in fact proved adequate in many fracture-mechanics problems: in particular, the growth of a semi-brittle crack in most 'engineering materials' can be described in terms of a macroscopic 'plastic zone' encasing the tip. Many mechanical properties, on the other hand, are highly sensitive to events occurring over distances no greater than a few interatomic spacings. For instance, the energetics of dislocations in plastic crystals, particularly covalently-bonded crystals, may depend largely on the atomic structure of the dislocation core. The ideally brittle crack provides a similar case, the crack front advancing one atomic

84 citations

Journal ArticleDOI
TL;DR: In this article, the failure of concrete from a mesoscopic point of view was studied using the Delaunay triangulation technique and the effects of mesostructural features such as aggregate grading curve, aggregate volumetric share, and more importantly the controlling parameters of mortar's damage-plasticity constitutive model have been investigated.

84 citations

Journal ArticleDOI
TL;DR: In this article, the authors present a theoretical development to show the sufficient conditions that will insure a finite element displacement analysis to converge to the exact displacement solutions when the size of the elements are progressively reduced.

84 citations

Journal ArticleDOI
TL;DR: In this paper, an improved technique was proposed to determine the uniaxial residual stress, elastic modulus, and yield stress of a linear elastic, perfectly plastic bulk material from the force-displacement curve of one conical indentation test.

84 citations


Network Information
Related Topics (5)
Finite element method
178.6K papers, 3M citations
91% related
Fracture mechanics
58.3K papers, 1.3M citations
88% related
Numerical analysis
52.2K papers, 1.2M citations
88% related
Boundary value problem
145.3K papers, 2.7M citations
85% related
Discretization
53K papers, 1M citations
85% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202386
2022223
2021318
2020317
2019312
2018335