Probing the cross-effect of strains in non-linear elasticity of nearly regular polymer networks by pure shear deformation

2015 ◽  
Vol 142 (17) ◽  
pp. 174908 ◽  
Author(s):  
Takuya Katashima ◽  
Kenji Urayama ◽  
Ung-il Chung ◽  
Takamasa Sakai
Keyword(s):  
Shear Deformation ◽  
Linear Elasticity ◽  
Pure Shear ◽  
Polymer Networks ◽  
Cross Effect ◽  
Non Linear ◽  
The Cross

scholarly journals Asymptotic Behavior of Stable Structures Made of Beams

2021 ◽  
Author(s):  
Georges Griso ◽  
Larysa Khilkova ◽  
Julia Orlik ◽  
Olena Sivak
Keyword(s):  
Asymptotic Behavior ◽  
Cross Section ◽  
Cross Sections ◽  
Linear Elasticity ◽  
Circular Cross Section ◽  
Linear Elasticity Theory ◽  
Linear Elastic ◽  
The Cross ◽  
Small Rotation ◽  
Stable Structures

AbstractIn this paper, we study the asymptotic behavior of an $\varepsilon $ ε -periodic 3D stable structure made of beams of circular cross-section of radius $r$ r when the periodicity parameter $\varepsilon $ ε and the ratio ${r/\varepsilon }$ r / ε simultaneously tend to 0. The analysis is performed within the frame of linear elasticity theory and it is based on the known decomposition of the beam displacements into a beam centerline displacement, a small rotation of the cross-sections and a warping (the deformation of the cross-sections). This decomposition allows to obtain Korn type inequalities. We introduce two unfolding operators, one for the homogenization of the set of beam centerlines and another for the dimension reduction of the beams. The limit homogenized problem is still a linear elastic, second order PDE.

scholarly journals Increase in Total Elongation Caused by Pure Shear Deformation in Ultra-Fine-Grained Cu Processed by Equal-Channel Angular Pressing

Metals ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 654
Author(s):  
Ryosuke Matsutani ◽  
Nobuo Nakada ◽  
Susumu Onaka
Keyword(s):  
Shear Deformation ◽  
Equal Channel Angular Pressing ◽  
Pure Shear ◽  
Three Dimensional ◽  
Tensile Tests ◽  
Total Elongation ◽  
Local Deformation ◽  
Image Correlation ◽  
Fine Grained ◽  
Angular Pressing

Ultra-fine-grained (UFG) Cu shows little total elongation in tensile tests because simple shear deformation is concentrated in narrow regions during the initial stage of plastic deformation. Here, we attempted to improve the total elongation of UFG Cu obtained by equal-channel angular pressing. By making shallow dents on the side surfaces of the plate-like specimens, this induced pure shear deformation and increased their total elongation. During the tensile tests, we observed the overall and local deformation of the dented and undented UFG Cu specimens. Using three-dimensional digital image correlation, we found that the dented specimens showed suppression of thickness reduction and delay in fracture by enhancement of pure shear deformation. However, the dented and undented specimens had the same ultimate tensile strength. These results provide us a new concept to increase total elongation of UFG materials.

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