Effects of couple-stresses in linear elasticity

R. D. Mindlin; H. F. Tiersten

doi:10.1007/bf00253946

Effects of Couple-stresses in Linear Elasticity

The Collected Papers of Raymond D. Mindlin Volume I ◽

10.1007/978-1-4613-8865-4_67 ◽

1989 ◽

pp. 539-572

Author(s):

R. D. Mindlin ◽

H. F. Tiersten

Keyword(s):

Linear Elasticity ◽

Couple Stresses

Linear Elasticity with Couple Stresses

Mechanics of Microstructured Solids 2 - Lecture Notes in Applied and Computational Mechanics ◽

10.1007/978-3-642-05171-5_1 ◽

2010 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Manfred Braun

Keyword(s):

Linear Elasticity ◽

Couple Stresses

Effects of couple-stresses in linear elasticity

Wear ◽

10.1016/0043-1648(63)90083-8 ◽

1963 ◽

Vol 6 (3) ◽

pp. 243

Keyword(s):

Linear Elasticity ◽

Couple Stresses

Scale Effects of Copper with Generalized Linear Elasticity in Simple Plane Shearing

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.700.55 ◽

2013 ◽

Vol 700 ◽

pp. 55-58

Author(s):

Zhi Fu ◽

Zhan Fang Liu

Keyword(s):

Linear Elasticity ◽

Scale Effects ◽

Physical And Mechanical Properties ◽

The Finite Element Method ◽

Sharp Drop ◽

Couple Stresses ◽

Effect Of Copper ◽

Copper Structure ◽

Size Scales ◽

Plane Shearing

The total stress consists of the symmetrical stress and asymmetrical stress, and the latter is connected to the couple stresses. A linear constitutive relation is established between the couple stresses and curvature tensor, three material parameters including the rotational modulus are involved in the generalized linear elasticity. A numerical analysis with the finite element method has been accomplished on the scale effect of copper in simple plane shearing. It is shown that a sharp drop of the stress symmetry occurs when the copper structure scale varies from some 1mm to 0.1mm in the example. When we analyze the physical and mechanical properties of cooper structure under micro size scales, the generalized linear elasticity should be used, and the asymmetrical feature of stress tensor must be considered.

Computing cell tractions from particle displacements on silicone rubber substrata

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100168542 ◽

1994 ◽

Vol 52 ◽

pp. 162-163

Author(s):

Tim Oliver ◽

Akira Ishihara ◽

Ken Jacobsen ◽

Micah Dembo

Keyword(s):

Plane Stress ◽

Linear Elasticity ◽

Silicone Rubber ◽

Mathematical Analysis ◽

Elastic Recovery ◽

Video Images ◽

Cell Traction Forces ◽

Latex Beads ◽

Cell Traction ◽

Better Than

In order to better understand the distribution of cell traction forces generated by rapidly locomoting cells, we have applied a mathematical analysis to our modified silicone rubber traction assay, based on the plane stress Green’s function of linear elasticity. To achieve this, we made crosslinked silicone rubber films into which we incorporated many more latex beads than previously possible (Figs. 1 and 6), using a modified airbrush. These films could be deformed by fish keratocytes, were virtually drift-free, and showed better than a 90% elastic recovery to micromanipulation (data not shown). Video images of cells locomoting on these films were recorded. From a pair of images representing the undisturbed and stressed states of the film, we recorded the cell’s outline and the associated displacements of bead centroids using Image-1 (Fig. 1). Next, using our own software, a mesh of quadrilaterals was plotted (Fig. 2) to represent the cell outline and to superimpose on the outline a traction density distribution. The net displacement of each bead in the film was calculated from centroid data and displayed with the mesh outline (Fig. 3).

Toward Endobronchial Intervention: A Pre-Curved Continuum Robot with Large Deflection and Linear Elasticity

10.31256/hsmr2018.7 ◽

2018 ◽

Author(s):

A Gao ◽

◽

N Liu ◽

Guang-Zhong Yang

Keyword(s):

Linear Elasticity ◽

Large Deflection ◽

Continuum Robot

On pure bending in non-linear elasticity: A circular closed-form 2D solution for semi-linear orthotropic material

European Journal of Mechanics - A/Solids ◽

10.1016/j.euromechsol.2021.104289 ◽

2021 ◽

pp. 104289

Author(s):

Gordan Jelenić

Keyword(s):

Closed Form ◽

Linear Elasticity ◽

Orthotropic Material ◽

Pure Bending ◽

Non Linear

Mathematical analysis and simulation of fixed point formulation of Cauchy problem in linear elasticity

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2021.02.020 ◽

2021 ◽

Vol 187 ◽

pp. 231-247

Author(s):

Abdellatif Ellabib ◽

Abdeljalil Nachaoui ◽

Abdessamad Ousaadane

Keyword(s):

Cauchy Problem ◽

Fixed Point ◽

Linear Elasticity ◽

Mathematical Analysis

Locking-Free and Gradient-Robust $${\varvec{H}}({{\,\mathrm{{\text {div}}}\,}})$$-Conforming HDG Methods for Linear Elasticity

Journal of Scientific Computing ◽

10.1007/s10915-020-01396-6 ◽

2021 ◽

Vol 86 (3) ◽

Author(s):

Guosheng Fu ◽

Christoph Lehrenfeld ◽

Alexander Linke ◽

Timo Streckenbach

Keyword(s):

Linear Elasticity

Atomistic-to-continuum description of edge dislocation core: Unification of the Peierls-Nabarro model with linear elasticity

Physical Review Materials ◽

10.1103/physrevmaterials.2.083803 ◽

2018 ◽

Vol 2 (8) ◽

Cited By ~ 9

Author(s):

Max Boleininger ◽

Thomas D. Swinburne ◽

Sergei L. Dudarev

Keyword(s):

Edge Dislocation ◽

Linear Elasticity ◽

Dislocation Core ◽

Continuum Description