TY - JOUR
T1 - On variational formulations with rigid-body constraints for finite elasticity
T2 - Applications to 2D and 3D finite element simulations
AU - Chi, Heng
AU - Paulino, Glaucio H.
N1 - Funding Information:
We acknowledge the support from the US National Science Foundation (NSF) through Grant CMMI #1624232 (formerly #1437535). The information presented in this paper is the sole opinion of the authors and does not necessarily reflect the views of the sponsoring agency.
Publisher Copyright:
© 2016 Elsevier Ltd
PY - 2016/12/1
Y1 - 2016/12/1
N2 - We investigate a recently proposed variational principle with rigid-body constraints and present an extension of its implementation in three dimensional finite elasticity problems. Through numerical examples, we illustrate that the proposed variational principle with rigid-body constraints is applicable to both single field and mixed finite elements of arbitrary order and geometry, e.g. triangular/tetrahedral and quadrilateral/hexagonal elements, in two and three dimensions. Moreover, we demonstrate that, as compared to the commonly adopted approach of discretizing the rigid domains with standard finite elements, the proposed formulation requires neither discretization nor numerical integration in the interior of each rigid domain. As a comparative result, the variational formulation may reduce the total number of degrees of freedom of the resulting finite element system and provide improved accuracy.
AB - We investigate a recently proposed variational principle with rigid-body constraints and present an extension of its implementation in three dimensional finite elasticity problems. Through numerical examples, we illustrate that the proposed variational principle with rigid-body constraints is applicable to both single field and mixed finite elements of arbitrary order and geometry, e.g. triangular/tetrahedral and quadrilateral/hexagonal elements, in two and three dimensions. Moreover, we demonstrate that, as compared to the commonly adopted approach of discretizing the rigid domains with standard finite elements, the proposed formulation requires neither discretization nor numerical integration in the interior of each rigid domain. As a comparative result, the variational formulation may reduce the total number of degrees of freedom of the resulting finite element system and provide improved accuracy.
KW - 3D FEA
KW - Finite elastostatics
KW - Rigid inclusions
KW - Variational principles
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U2 - 10.1016/j.mechrescom.2016.03.003
DO - 10.1016/j.mechrescom.2016.03.003
M3 - Article
AN - SCOPUS:84979008630
SN - 0093-6413
VL - 78
SP - 15
EP - 26
JO - Mechanics Research Communications
JF - Mechanics Research Communications
ER -