Topic
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 elastic shear modulus, Gmax, was defined for small strain ranges having their limits with the order of 0.001%, below which the response was found to be practically linear elastic.
97 citations
TL;DR: In this paper, a discontinuous Galerkin method for linear elasticity is proposed, which derives from the Hellinger-Reissner variational principle with the addition of stabilization terms analogous to those previously considered by others for the Navier-Stokes equations and a scalar Poisson equation.
Abstract: We analyze a discontinuous Galerkin method for linear elasticity. The discrete formulation derives from the Hellinger-Reissner variational principle with the addition of stabilization terms analogous to those previously considered by others for the Navier-Stokes equations and a scalar Poisson equation. For our formulation, we first obtain convergence in a mesh-dependent norm and in the natural mesh-independent BD norm. We then prove a generalization of Korn's second inequality which allows us to strengthen our results to an optimal, mesh-independent BV estimate for the error.
97 citations
TL;DR: In this article, the authors proposed a new concept based on a Taylor expansion of the constitutively dependent quantities with respect to the center of the element, which is called hourglass stabilization part of the residual force vector.
96 citations
TL;DR: In this paper, the importance of the use of a Poisson's function in appropriate circumstances is demonstrated, and interpretation methods for coping with error-sensitive data or small strains are also described.
Abstract: The Poisson's ratio of a material is strictly defined only for small strain linear elastic behavior. In practice, engineering strains are often used to calculate Poisson's ratio in place of the mathematically correct true strains with only very small differences resulting in the case of many engineering amterials. The engineering strain definition is often used even in the inelastic region, for example, in metals during plastic yielding. However, for highly nonlinear elastic materials, such as many biomaterials, smart materials and microstructured materials, this convenient extension may be misleading, and it becomes advantageous to define a strainvarying Poisson's function. This is analogous to the use of a tangent modulus for stiffness. An important recent application of such a Poisson's function is that of auxetic materials that demonstrate a negative Poisson's ratio and are often highly strain dependent. In this paper, the importance of the use of a Poisson's function in appropriate circumstances is demonstrated. Interpretation methods for coping with error-sensitive data or small strains are also described.
96 citations
SIDI1
TL;DR: In this paper, a closed-form rigorous solution for interfacial stress in simply supported beams strengthened with bonded prestressed FRP plates and subjected to a uniformly distributed load, arbitrarily positioned single point load, or two symmetric point loads is developed using linear elastic theory and including the variation in FRP plate fibre orientation.
96 citations