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Modeling and Analysis of Size-Dependent Structural Problems by Using Low-Order Finite Elements with Strain Gradient Plasticity

변형률 구배 소성 저차 유한요소에 의한 크기 의존 구조 문제의 모델링 및 해석

  • 박문식 (한남대학교 기계공학과) ;
  • 서영성 (한남대학교 기계공학과) ;
  • 송승 (한남대학교 기계공학과)
  • Received : 2011.05.03
  • Accepted : 2011.07.18
  • Published : 2011.09.01

Abstract

An elasto-plastic finite element method using the theory of strain gradient plasticity is proposed to evaluate the size dependency of structural plasticity that occurs when the configuration size decreases to micron scale. For this method, we suggest a low-order plane and three-dimensional displacement-based elements, eliminating the need for a high order, many degrees of freedom, a mixed element, or super elements, which have been considered necessary in previous researches. The proposed method can be performed in the framework of nonlinear incremental analysis in which plastic strains are calculated and averaged at nodes. These strains are then interpolated and differentiated for gradient calculation. We adopted a strain-gradient-hardening constitutive equation from the Taylor dislocation model, which requires the plastic strain gradient. The developed finite elements are tested numerically on the basis of typical size-effect problems such as micro-bending, micro-torsion, and micro-voids. With respect to the strain gradient plasticity, i.e., the size effects, the results obtained by using the proposed method, which are simple in their calculation, are in good agreement with the experimental results cited in previously published papers.

Keywords

Strain Gradient Plasticity;Taylor Dislocation Model;Strain Gradient Invariant;Length Parameter;Strain Gradient Hardening;Non-local Constitutive Theory;Averaged at Nodal Plastic Strain

Acknowledgement

Supported by : 한국연구재단

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