A Stress-Based Gradient Elasticity in the Smoothed Finite Element Framework

Changkye Lee; Sundararajan Natarajan

doi:10.7734/COSEIK.2024.37.3.187

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2024 Vol.37, Issue 3 Preview Page Next Page

Research Paper

A Stress-Based Gradient Elasticity in the Smoothed Finite Element Framework 평활화 유한요소법을 도입한 응력기반 구배 탄성론

30 June 2024. pp. 187-195

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Abstract

This paper presents two-dimensional boundary value problems of the stress-based gradient elasticity within the smoothed finite element method (S-FEM) framework. Gradient elasticity is introduced to address the limitations of classical elasticity, particularly its struggle to capture size-dependent mechanical behavior at the micro/nano scale. The Ru-Aifantis theorem is employed to overcome the challenges of high-order differential equations in gradient elasticity. This theorem effectively splits the original equation into two solvable second-order differential equations, enabling its incorporation into the S-FEM framework. The present method utilizes a staggered scheme to solve the boundary value problems. This approach efficiently separates the calculation of the local displacement field (obtained over each smoothing domain) from the non-local stress field (computed element-wise). A series of numerical tests are conducted to investigate the influence of the internal length scale, a key parameter in gradient elasticity. The results demonstrate the effectiveness of the proposed approach in smoothing stress concentrations typically observed at crack tips and dislocation lines.

Keywords

smoothed finite element method

gradient elasticity

stress concentration

internal length scale

본 논문에서는 평활화 유한요소법(Smoothed finite element method)을 도입한 응력 기반 구배 탄성론(Gradient elasticity)의 2차원 경계치 문제에 대한 연구를 수행하였다. 구배 탄성론은 기존 탄성론에서는 표현할 수 없는 미소규모의 크기 의존적인 기계적 거동을 설명하기 위해 제안되었다. 구배 탄성체론에서 고차 미분 방정식을 두 개의 2차 미분 방정식으로 분할하는 Ru-Aifantis 이론을 사용하기 때문에 평활화 유한요소법에 적용이 가능하게 된다. 본 연구에서 경계치 문제를 해결하기 위해 평활화 유한 요소 프레임워크에 스태거드 방식(Staggered scheme)을 사용하여 국부 변위장과 비국부 응력장을 평활화 영역 및 요소에서 각각 계산하였다. 구배 탄성에서 중요한 변수인 내부 길이 척도의 영향을 측정하기 위해 일련의 수치 예제를 수행하였다. 수치 해석 결과는 제안한 기법이 내부 길이 척도에 따라 균열 선단과 전위 선에 나타나는 응력 집중을 완화할 수 있음을 보여준다.

키워드

평활화 유한요소법

구배 탄성체

응력 집중

내부 길이 척도

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Information

Publisher :Computational Structural Engineering Institute of Korea
Publisher(Ko) :한국전산구조공학회
Journal Title :Journal of the Computational Structural Engineering Institute of Korea
Journal Title(Ko) :한국전산구조공학회 논문집
Volume : 37
No :3
Pages :187-195
Received Date : 2024-05-08
Revised Date : 2024-05-31
Accepted Date : 2024-06-05
DOI :https://doi.org/10.7734/COSEIK.2024.37.3.187

Journal of the Computational Structural Engineering Institute of Korea ISSN:1229-3059(Print) 2287-2302(Online) 한국전산구조공학회 논문집

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