scholarly journals Nonlocal multiscale modeling of deformation behavior of polycrystalline copper by second-order homogenization method

2019 ◽  
Vol 92 (9) ◽  
Author(s):  
Makoto Uchida ◽  
Yoshihisa Kaneko
Keyword(s):  
Multiscale Modeling ◽  
Deformation Behavior ◽  
Homogenization Method ◽  
Second Order ◽  
Polycrystalline Copper

Computational Simulation of Micro- to Macroscopic Deformation Behavior of Cavitated Rubber Blended Amorphous Polymer Using Second-Order Homogenization Method

2014 ◽  
Vol 626 ◽  
pp. 74-80 ◽  
Author(s):  
Makoto Uchida ◽  
Naoya Tada
Keyword(s):  
Deformation Behavior ◽  
Volume Fraction ◽  
Amorphous Polymer ◽  
Computational Simulation ◽  
Fem Simulation ◽  
Homogenization Method ◽  
Second Order ◽  
Localized Deformation ◽  
Macroscopic Deformation ◽  
Rate Form

To evaluate the effect of the size of the microstructure on the mechanical property of the cavitated rubber blended (voided) amorphous polymer, the FEM simulation based on the rate form second-order homogenization method, in which rates of the macroscopic strain and strain gradient are given to the microstructure, was performed. Computational simulations of micro-to macroscopic deformation behaviors of amorphous polymers including different sizes and volume fractions of the voids were performed. Non-affine molecular chain network theory was employed to represent the inelastic deformation behavior of the amorphous polymer matrix. With the increase in the volume fraction of the void, decrease and periodical fluctuation of stress and localized deformation in the macroscopic field were observed, and were more emphasized with the increase in the size of the void. These results were closely related to the non-uniform deformation and volume increase of the void in the microscopic field.

scholarly journals A New Estimate for the Homogenization Method for Second-Order Elliptic Problem with Rapidly Oscillating Periodic Coefficients

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Xiong Liu ◽  
Wenming He
Keyword(s):  
Elliptic Problem ◽  
Homogenization Method ◽  
Second Order ◽  
Homogenization Theory ◽  
High Demand ◽  
Periodic Coefficients ◽  
Order Elliptic Problem ◽  
Multiscale Homogenization

In this paper, we will investigate a multiscale homogenization theory for a second-order elliptic problem with rapidly oscillating periodic coefficients of the form ∂ / ∂ x i a i j x / ε , x ∂ u ε x / ∂ x j = f x . Noticing the fact that the classic homogenization theory presented by Oleinik has a high demand for the smoothness of the homogenization solution u 0 , we present a new estimate for the homogenization method under the weaker smoothness that homogenization solution u 0 satisfies than the classical homogenization theory needs.

scholarly journals Multiscale modeling of ice deformation behavior

2014 ◽  
Vol 61 ◽  
pp. 78-108 ◽  
Author(s):  
M. Montagnat ◽  
O. Castelnau ◽  
P.D. Bons ◽  
S.H. Faria ◽  
O. Gagliardini ◽  
...  
Keyword(s):  
Multiscale Modeling ◽  
Deformation Behavior
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