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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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01 Jan 1987
TL;DR: In this paper, a linear elasticity and time-dependent elasticity analysis of the human body is presented, followed by a more complex analysis of rigid body motion and deformation.
Abstract: 1 Linear Elasticity.- 1.1 Introduction.- 1.2 Simple analysis.- 1.3 More complex analysis.- 2 Non-Linear And Time-Dependent Elasticity.- 2.1 Introduction.- 2.2 Material properties.- 2.3 Visco-elasticity.- 2.4 Stress waves.- 3 Plasticity.- 3.1 Introduction.- 3.2 Plastic flow.- 3.3 More complex analysis.- 4 Fracture.- 4.1 Introduction.- 4.2 Ductile fracture.- 4.3 Fracture mechanics.- 5 Rigid Body Motion.- 5.1 Introduction.- 5.2 Simple analysis.- 5.3 More detailed analysis.- 6 Undamped Linear Vibrations.- 6.1 Introduction.- 6.2 Linear motion in one dimension.- 6.3 More complex analysis.- 7 Deformable Bodies.- 7.1 Introduction.- 7.2 Linear motion in one dimension.- 7.3 More complex analysis.- 8 Energy Absorbers.- 8.1 Introduction.- 8.2 Isolating mountings.- 8.3 Deforming solids.- 9 Structures.- 9.1 Introduction.- 9.2 Structural components.- 9.3 Structural models.- 10 Impact Injury.- 10.1 Introduction.- 10.2 Whole body behaviour.- 10.3 Specific body components.- 11 Testing.- 11.1 Introduction.- 11.2 Tests of materials.- 11.3 Tests of components and systems.- 11.4 Data retrieval.- References.

84 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigate the numerical response of the linear Cosserat model with conformal curvature and compare it with a conformal model in torsion and highlight its intriguing features.
Abstract: We investigate the numerical response of the linear Cosserat model with conformal curvature. In our simulations we compare the standard Cosserat model with a novel conformal Cosserat model in torsion and highlight its intriguing features. In all cases, free boundary conditions for the microrotations overline A are applied. The size-effect response is markedly changed for the novel curvature expression. Our results suggest that the Cosserat couple modulus µc > 0 remains a true material parameter independent of the sample size which is impossible for stronger, pointwise positive curvature expressions.

84 citations

Journal ArticleDOI
TL;DR: In this paper, the size effect of microtubules (MTs) is studied via modified strain gradient elasticity theory for buckling by using Bernoulli-Euler beam theory.

84 citations

Journal ArticleDOI
TL;DR: In this paper, the authors consider topology optimization of hyperelastic bodies subjected simultaneously to external forces and prescribed non-zero displacements and show that even for gross rotations that are in all practical aspects small (<3 deg), topology optimisation based on a large deformation theory might generate different design concepts compared to what is obtained when small displacement linear elasticity is used.
Abstract: Stiffness topology optimization is usually based on a state problem of linear elasticity, and there seems to be little discussion on what is the limit for such a small rotation-displacement assumption. We show that even for gross rotations that are in all practical aspects small (<3 deg), topology optimization based on a large deformation theory might generate different design concepts compared to what is obtained when small displacement linear elasticity is used. Furthermore, in large rotations, the choice of stiffness objective (potential energy or compliance), can be crucial for the optimal design concept. The paper considers topology optimization of hyperelastic bodies subjected simultaneously to external forces and prescribed non-zero displacements. In that respect it generalizes a recent contribution of ours to large deformations, but we note that the objectives of potential energy and compliance are no longer equivalent in the non-linear case. We use seven different hyperelastic strain energy functions and find that the numerical performance of the Kirchhoff---St.Venant model is in general significantly worse than the performance of the other six models, which are all modifications of this classical law that are equivalent in the limit of infinitesimal strains, but do not contain the well-known collapse in compression. Numerical results are presented for two different problem settings.

84 citations

Journal ArticleDOI
TL;DR: In this article, the 3D Finite Element method is applied to mixed fracture under anti-plane loading of a straight through-the-thickness crack in a linear elastic plate.

83 citations


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