Multiscale Coarsening for Linear Elasticity by Energy Minimization

2013 ◽  
pp. 21-44 ◽  
Author(s):  
Marco Buck ◽  
Oleg Iliev ◽  
Heiko Andrä
Keyword(s):  
Linear Elasticity ◽  
Energy Minimization

Computing cell tractions from particle displacements on silicone rubber substrata

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).

Comments on the Antonow and interfacial interaction rules

1990 ◽  
Vol 55 (5) ◽  
pp. 1143-1148 ◽  
Author(s):  
Jan Kloubek
Keyword(s):  
Free Energy ◽  
Energy Minimization ◽  
Interfacial Interaction ◽  
Aliphatic Hydrocarbon ◽  
Theoretical Base ◽  
Water Interface ◽  
Free Energy Minimization ◽  
Interaction Rule

Results presented for the aliphatic hydrocarbon-water interface show that the recent hypothesis of the free energy minimization called interfacial interaction rule, which was suggested as a theoretical base of the Antonow rule, cannot be generally valid.

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

2021 ◽  
Vol 187 ◽  
pp. 231-247
Author(s):  
Abdellatif Ellabib ◽  
Abdeljalil Nachaoui ◽  
Abdessamad Ousaadane
Keyword(s):  
Cauchy Problem ◽  
Fixed Point ◽  
Linear Elasticity ◽  
Mathematical Analysis

Mode-wise Voltage-scalable Design with Activation-aware Slack Assignment for Energy Minimization

2021 ◽  
Author(s):  
TaiYu Cheng ◽  
Yukata Masuda ◽  
Jun Nagayama ◽  
Yoichi Momiyama ◽  
Jun Chen ◽  
...  
Keyword(s):  
Energy Minimization ◽  
Scalable Design

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

2021 ◽  
Vol 86 (3) ◽  
Author(s):  
Guosheng Fu ◽  
Christoph Lehrenfeld ◽  
Alexander Linke ◽  
Timo Streckenbach
Keyword(s):  
Linear Elasticity
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