A minimax problem in plasticity theory

1979 ◽  
pp. 319-333 ◽  
Author(s):  
Gilbert Strang
Keyword(s):  
Minimax Problem ◽  
Plasticity Theory

VARIATIONAL MULTISCALE ANALYSIS OF SOLIDS WITH STRAIN GRADIENT PLASTIC EFFECTS USING MESHFREE APPROXIMATION

2005 ◽  
Vol 02 (04) ◽  
pp. 601-626 ◽  
Author(s):  
JEOUNG-HEUM YEON ◽  
SUNG-KIE YOUN
Keyword(s):  
Strain Gradient ◽  
Partition Of Unity ◽  
Meshfree Method ◽  
Internal Variable ◽  
Plasticity Theory ◽  
Fine Scale ◽  
Meshfree Approximation ◽  
Gradient Effect ◽  
Classical Plasticity ◽  
Variational Form

A meshfree multiscale method is presented for efficient analysis of solids with strain gradient plastic effects. In the analysis of strain gradient plastic solids, localization due to increased hardening of strain gradient effect appears. Chen-Wang theory is adopted, as a strain gradient plasticity theory. It represents strain gradient effects as an internal variable and retains the essential structure of classical plasticity theory. In this work, the scale decomposition is carried out based on variational form of the problem. Coarse scale is designed to represent global behavior and fine scale to represent local behavior and gradient effect by using the intrinsic length scale. From the detection of high strain gradient region, fine scale region is adopted. Each scale variable is approximated using meshfree method. Meshfree approximation is well suited for adaptivity. As a method of increasing resolution, partition of unity based extrinsic enrichment is used. Each scale problem is solved iteratively. The proposed method is applied to bending of a thin beam and bimaterial shear layer and micro-indentation problems. Size effects can be effectively captured in the results of the analysis.

A Study of Microindentation Hardness Tests by Mechanism-based Strain Gradient Plasticity

2000 ◽  
Vol 15 (8) ◽  
pp. 1786-1796 ◽  
Author(s):  
Y. Huang ◽  
Z. Xue ◽  
H. Gao ◽  
W. D. Nix ◽  
Z. C. Xia
Keyword(s):  
Strain Gradient ◽  
Size Dependence ◽  
Plasticity Theory ◽  
Strain Gradient Plasticity ◽  
Gradient Plasticity ◽  
Hierarchical Framework ◽  
Microindentation Hardness ◽  
Dislocation Hardening ◽  
Hardness Tests ◽  
Micro Indentation

We recently proposed a theory of mechanism-based strain gradient (MSG) plasticity to account for the size dependence of plastic deformation at micron- and submicronlength scales. The MSG plasticity theory connects micron-scale plasticity to dislocation theories via a multiscale, hierarchical framework linking Taylor's dislocation hardening model to strain gradient plasticity. Here we show that the theory of MSG plasticity, when used to study micro-indentation, indeed reproduces the linear dependence observed in experiments, thus providing an important self-consistent check of the theory. The effects of pileup, sink-in, and the radius of indenter tip have been taken into account in the indentation model. In accomplishing this objective, we have generalized the MSG plasticity theory to include the elastic deformation in the hierarchical framework.

Developing the concept of the strain rate intensity factor in plasticity theory

2003 ◽  
Vol 48 (3) ◽  
pp. 131-133 ◽  
Author(s):  
S. E. Aleksandrov ◽  
R. V. Goldshtein ◽  
E. A. Lyamina
Keyword(s):  
Intensity Factor ◽  
Strain Rate ◽  
Plasticity Theory ◽  
Strain Rate Intensity Factor ◽  
Rate Intensity ◽  
Strain Rate Intensity

Asymmetric crystal plasticity theory for the evolution of polycrystal microstructures

2012 ◽  
Vol 15 (1-2) ◽  
pp. 58-68 ◽  
Author(s):  
Peter V. Trusov ◽  
P. S. Volegov ◽  
A. Yu. Yants
Keyword(s):  
Crystal Plasticity ◽  
Plasticity Theory ◽  
Crystal Plasticity Theory

A Variant of Tchebichef's Minimax Problem

1967 ◽  
Vol 18 (5) ◽  
pp. 925
Author(s):  
R. J. Levit
Keyword(s):  
Minimax Problem
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