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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.


Papers
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Journal ArticleDOI
TL;DR: In this paper, an accurate and robust stabilization based on the assumed strain method and an operator orthogonal to constant strain fields is presented for an eight-node hexahedral element with uniform reduced integration.

276 citations

Journal ArticleDOI
TL;DR: Combined finite indentation and biaxial stretch may reveal the specific functional form of the constitutive law--a requirement for quantitative estimates of material constants to be extracted from AFM indentation data.
Abstract: Indentation using the atomic force microscope (AFM) has potential to measure detailed micromechanical properties of soft biological samples. However, interpretation of the results is complicated by the tapered shape of the AFM probe tip, and its small size relative to the depth of indentation. Finite element models (FEMs) were used to examine effects of indentation depth, tip geometry, and material nonlinearity and heterogeneity on the finite indentation response. Widely applied infinitesimal strain models agreed with FEM results for linear elastic materials, but yielded substantial errors in the estimated properties for nonlinear elastic materials. By accounting for the indenter geometry to compute an apparent elastic modulus as a function of indentation depth, nonlinearity and heterogeneity of material properties may be identified. Furthermore, combined finite indentation and biaxial stretch may reveal the specific functional form of the constitutive law--a requirement for quantitative estimates of material constants to be extracted from AFM indentation data.

273 citations

Journal ArticleDOI
TL;DR: New finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approxima- tions to both stresses and displacements are constructed.
Abstract: In this paper, we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approxima- tions to both stresses and displacements. The methods are based on a modified form of the Hellinger-Reissner variational principle that only weakly imposes the symmetry condition on the stresses. Although this approach has been previously used by a number of authors, a key new ingredient here is a constructive derivation of the elasticity complex starting from the de Rham complex. By mimicking this construction in the discrete case, we derive new mixed finite elements for elasticity in a systematic manner from known discretizations of the de Rham complex. These elements appear to be simpler than the ones previously derived. For example, we construct stable discretizations which use only piecewise linear elements to approximate the stress field and piecewise constant functions to approximate the displacement field.

273 citations

Journal ArticleDOI
TL;DR: In this paper, the response of rigid and compressible single piles embedded in a homogeneous isotropic linear elastic medium has been obtained by a rigorous analysis based on Mindlin's solutions for a po...
Abstract: Synopsis The response of rigid and compressible single piles embedded in a homogeneous isotropic linear elastic medium has been obtained by a rigorous analysis based on Mindlin's solutions for a po...

272 citations

Journal ArticleDOI
TL;DR: A new deformable model based on non-linear elasticity, anisotropic behavior, and the finite element method is proposed that is valid for large displacements and improves the realism of the deformations and solves the problems related to the shortcomings of linear elasticity.
Abstract: In this paper, we describe the latest developments of the minimally invasive hepatic surgery simulator prototype developed at INRIA. A key problem with such a simulator is the physical modeling of soft tissues. We propose a new deformable model based on non-linear elasticity, anisotropic behavior, and the finite element method. This model is valid for large displacements, which means in particular that it is invariant with respect to rotations. This property improves the realism of the deformations and solves the problems related to the shortcomings of linear elasticity, which is only valid for small displacements. We also address the problem of volume variations by adding to our model incompressibility constraints. Finally, we demonstrate the relevance of this approach for the real-time simulation of laparoscopic surgical gestures on the liver.

269 citations


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