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Linear elasticity

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


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TL;DR: In this paper, the effects of material inhomogeneity on the response of linearly elastic isotropic hollow circular cylinders or disks under uniform internal or external pressure were investigated, and the results were illustrated using a specific radially inhomogeneous material model for which explicit exact solutions were obtained.
Abstract: The purpose of this research is to investigate the effects of material inhomogeneity on the response of linearly elastic isotropic hollow circular cylinders or disks under uniform internal or external pressure. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e., materials with spatially varying properties tailored to satisfy particular engineering applications. The analog of the classic Lame problem for a pressurized homogeneous isotropic hollow circular cylinder or disk is considered. The special case of a body with Young"s modulus depending on the radial coordinate only, and with constant Poisson"s ratio, is examined. It is shown that the stress response of the inhomogeneous cylinder (or disk) is significantly different from that of the homogeneous body. For example, the maximum hoop stress does not, in general, occur on the inner surface in contrast with the situation for the homogeneous material. The results are illustrated using a specific radially inhomogeneous material model for which explicit exact solutions are obtained.

259 citations

Journal ArticleDOI
26 Jul 2010
TL;DR: A simple geometric model for elasticity: distance between the differential of a deformation and the rotation group is advocated, and the intuition of previous work that these ideas are "like" elasticity is shown to be spot on.
Abstract: We advocate a simple geometric model for elasticity: distance between the differential of a deformation and the rotation group. It comes with rigorous differential geometric underpinnings, both smooth and discrete, and is computationally almost as simple and efficient as linear elasticity. Owing to its geometric non-linearity, though, it does not suffer from the usual linearization artifacts. A material model with standard elastic moduli (Lame parameters) falls out naturally, and a minimizer for static problems is easily augmented to construct a fully variational 2nd order time integrator. It has excellent conservation properties even for very coarse simulations, making it very robust.Our analysis was motivated by a number of heuristic, physics-like algorithms from geometry processing (editing, morphing, parameterization, and simulation). Starting with a continuous energy formulation and taking the underlying geometry into account, we simplify and accelerate these algorithms while avoiding common pitfalls. Through the connection with the Biot strain of mechanics, the intuition of previous work that these ideas are "like" elasticity is shown to be spot on.

259 citations

Journal ArticleDOI
TL;DR: In this article, the use of fracture mechanics for the plate bonding technique is presented, and a linear and a nonlinear approach are presented for a realistic shear-deformation curve for numerical calculations.
Abstract: This paper presents the use of fracture mechanics for the plate bonding technique. Plates of steel or carbon-fibre reinforced plastic are bonded with an epoxy adhesive to rectangular concrete prisms and loaded in shear up to failure, what is normally known in fracture mechanics as mode II failure. In this special application a linear and a nonlinear approach are presented. The nonlinear equation derived for a realistic shear-deformation curve can only be used for numerical calculations. However, for simplified shear-deformation curves, the derived formula can be solved analytically. Results from tests, which are compared with the theory, are also presented.

259 citations

Journal ArticleDOI
TL;DR: In this paper, a shear-lag model for carbon nanotube-reinforced polymer composites using a multiscale approach is developed for axisymmetric problems, and the resulting formulas are derived in closed forms.

258 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson ratio, nu, becomes independent of Nu(s) as the percolation threshold is approached.
Abstract: A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.

258 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202386
2022223
2021318
2020317
2019312
2018335