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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, a mixed-stabilized finite element formulation is presented based on a multiscale variational principle and is presented in two different forms: coarse-scale and fine-scale.
Abstract: In this paper we present a mixed stabilized finite element formulation that does not lock and also does not exhibit unphysical oscillations near the incompressible limit. The new mixed formulation is based on a multiscale variational principle and is presented in two different forms. In the first form the displacement field is decomposed into two scales, coarse-scale and fine-scale, and the fine-scale variables are eliminated at the element level by the static condensation technique. The second form is obtained by simplifying the first form, and eliminating the fine-scale variables analytically yet retaining their effect that results with additional (stabilization) terms. We also derive, in a consistent manner, an expression for the stabilization parameter. This derivation also proves the equivalence between the classical mixed formulation with bubbles and the Galerkin least-squares type formulations for the equations of linear elasticity. We also compare the performance of this new mixed stabilized formulation with other popular finite element formulations by performing numerical simulations on three well known test problems.
60 citations
TL;DR: This work finds that xfem is the most suitable when the mesh if coarse, and methods based on Cartesian grids are best when a very fine mesh can be used, and Finite element methods are good compromises with high flexibility.
60 citations
TL;DR: In this paper, a method for determining fractured rock masse properties is given on the basis of a homogenisation approach, based on the homogenized constitutive model of the rock mass considered as a heterogeneous medium constituted of intact rock and of fractures.
Abstract: A method for determining fractured rock masse properties is given on the basis of a homogenisation approach The homogenized constitutive model of the rock mass considered as a heterogeneous medium constituted of intact rock and of fractures, is studied numerically using Finite Element Method The constitutive model of the rock masse, elastic properties, ultimate strength and hardening law, were determined assuming linear elasticity and Mohr-Coulomb strength criterion for intact rock and for fractures
60 citations
TL;DR: A polylogarithmic bound in the local number of degrees of freedom is proven for the condition number of the preconditioned operator in the constant coefficient case and the algorithm is scalable, parallel, and robust with respect to material heterogeneities.
Abstract: Balancing Neumann-Neumann methods are extented to mixed formulations of the linear elasticity system with discontinuous coefficients, discretized with mixed finite or spectral elements with discontinuous pressures. These domain decomposition methods implicitly eliminate the degrees of freedom associated with the interior of each subdomain and solve iteratively the resulting saddle point Schur complement using a hybrid preconditioner based on a coarse mixed elasticity problem and local mixed elasticity problems with natural and essential boundary conditions. A polylogarithmic bound in the local number of degrees of freedom is proven for the condition number of the preconditioned operator in the constant coefficient case. Parallel and serial numerical experiments confirm the theoretical results, indicate that they still hold for systems with discontinuous coefficients, and show that our algorithm is scalable, parallel, and robust with respect to material heterogeneities. The results on heterogeneous general problems are also supported in part by our theory.
60 citations
TL;DR: In this article, a meso-mechanical model for the numerical analysis of concrete specimens in 3D has been proposed, where concrete is represented as a composite material with the larger aggregates embedded in a mortar-plus-aggregates matrix.
Abstract: A meso-mechanical model for the numerical analysis of concrete specimens in 3 D has been recently proposed. In this approach, concrete is represented as a composite material with the larger aggregates embedded in a mortar-plus-aggregates matrix. Both continuum-type components are considered linear elastic, while the possibilities of failure are provided with the systematic use of zero-thickness interface elements equipped with a cohesive fracture constitutive law. These elements are inserted along all potential crack planes in the mesh a priori of the analysis. In this paper, the basic features of the model are summarized, and then results of calculations are presented, which include uniaxial tension and compression loading of 14-aggregate cubical specimen along X, Y and Z axes. The results confirm the consistency of the approach with physical phenomena and well-known features of concrete behaviour, and show low scatter when different loading directions are considered. Those cases can also be considered as different specimens subjected to the same type of loading.
60 citations