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Variational inequality‐based framework of discontinuous deformation analysis
Author(s) -
Fan Huo,
Zhao Jidong,
Zheng Hong
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5807
Subject(s) - finite element method , variational inequality , robustness (evolution) , mathematics , deformation (meteorology) , composite number , matrix (chemical analysis) , computer science , mathematical optimization , algorithm , structural engineering , materials science , engineering , composite material , gene , biochemistry , chemistry
Summary For modeling discrete particle‐block systems, a new framework of discontinuous deformation analysis is established on the basis of finite‐dimensional variational inequality. The presented method takes into account the contacts, the rolling resistance, and the tensile resistance of cemented interface among particles and blocks using the corresponding variational or quasivariational inequalities. The new formulation avoids using the artificial springs that are usually indispensable in many conventional methods dealing with similar discrete problems and conveniently integrates the rigid circle particles, the nonrigid ring particles, and the arbitrary shape blocks into a uniform framework. The proposed discontinuous deformation analysis approach is further coupled with the finite element method using a node‐based composite contact matrix and several simple transformation matrices to solve practical problems. A particle/block‐based composite contact matrix is constructed to further broaden the application of the proposed method. The accuracy, robustness, and capability of the presented method are demonstrated with examples.