Three dimensional elements with Lagrange multipliers for the modified couple stress theory

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Three dimensional mixed elements for the modified couple stress theory are proposed. The C-1 continuity for the displacement field, which is required because of the curvature term in the variational form of the theory, is satisfied weakly by introducing a supplementary rotation as an independent variable and constraining the relation between the rotation and the displacement with a Lagrange multiplier vector. An additional constraint about the deviatoric curvature is also considered for three dimensional problems. Weak forms with one constraint and two constraints are derived, and four elements satisfying convergence criteria are developed by applying different approximations to each field of independent variables. The elements pass a C0-1 patch test for three dimensional problems. Numerical examples show that the additional constraint could be considered essential for the three dimensional elements, and one of the elements is recommended for practical applications via the comparison of the performances of the elements. In addition, all the proposed elements can represent the size effect well.
Publisher
SPRINGER
Issue Date
2018-07
Language
English
Article Type
Article
Keywords

STRAIN-GRADIENT ELASTICITY; FINITE-ELEMENT; MODEL; PLASTICITY; MICROSTRUCTURE; FORMULATIONS

Citation

COMPUTATIONAL MECHANICS, v.62, no.1, pp.97 - 110

ISSN
0178-7675
DOI
10.1007/s00466-017-1487-z
URI
http://hdl.handle.net/10203/243681
Appears in Collection
ME-Journal Papers(저널논문)
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