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 article, a two-dimensional finite element analysis of composite bonded single-lap joints was presented, where six-node interface elements compatible with eight-node isoparametric plane solid elements were placed between the adherends and the adhesive, at the midplane of the adhesive and at the interfaces between different oriented layers of the adhereds.
77 citations
01 Jan 1995
TL;DR: A numerical method is presented here that directly uses images of the microstructure to compute the composite overall properties, as well as the local distribution of stresses and strains, without requiring further geometrical interpretation by the user.
Abstract: The effective properties of composite materials are strongly influenced by the geometry of their microstructures, which can be extremely complex. Most of the numerical simulations known to the authors make use of two- or three-dimensional finite elements analyses which are often time consuming because of the complexity imposed by the requirement of extremely precise description of the reinforcements distribution. A numerical method is presented here that directly uses images of the microstructure - supposed to be periodically repeated - to compute the composite overall properties, as well as the local distribution of stresses and strains, without requiring further geometrical interpretation by the user. The linear elastic problem is examined first. Its analysis is based on the Lippmann-Schwinger’s equation, which is solved iteratively by means of the Green operator of an homogeneous reference medium. Then the method is extended to non-linear problems where the local stress strain relation is given by an incremental relation.
77 citations
TL;DR: A new approach to determine heterogeneous bone tissue material properties for computational models accurately reproduced the experimentally determined apparent modulus and concentrations of stress at locations of failure.
77 citations
TL;DR: A new discontinuous Galerkin method for elliptic problems which is capable of rendering the same set of unknowns in the final system of equations as for the continuous displacement‐based Galerkins method is presented.
Abstract: A new discontinuous Galerkin method for elliptic problems which is capable of rendering the same set of unknowns in the final system of equations as for the continuous displacement-based Galerkin method is presented. Those equations are obtained by the assembly of element matrices whose structure in particular cases is also identical to that of the continuous displacement approach. This makes the present formulation easily implementable within the existing commercial computer codes. The proposed approach is named the embedded discontinuous Galerkin method. It is applicable to any system of linear partial differential equations but it is presented here in the context of linear elasticity. An application of the method to linear shell problems is then outlined and numerical results are presented.
77 citations
TL;DR: In this article, several finite element methods for large deformation elastic problems in the nearly incompressible and purely incompressibly regimes are considered, in particular, the method ability to accurately capture critical loads for the possible occurrence of bifurcation and limit points.
Abstract: Several finite element methods for large deformation elastic problems in the nearly incompressible and purely incompressible regimes are considered. In particular, the method ability to accurately capture critical loads for the possible occurrence of bifurcation and limit points, is investigated. By means of a couple of 2D model problems involving a very simple neo-Hookean constitutive law, it is shown that within the framework of displacement/pressure mixed elements, even schemes that are inf-sup stable for linear elasticity may exhibit problems when used in the finite deformation regime. The roots of such troubles are identified, but a general strategy to cure them is still missing. Furthermore, a comparison with displacement-based elements, especially of high order, is presented.
77 citations