On variational formulations with rigid-body constraints for finite elasticity: Applications to 2D and 3D finite element simulations. (December 2016)

• Record Type: Journal Article
• Authors: Chi, Heng; Paulino, Glaucio H.
• Is Part Of: Mechanics research communications. Volume 78:Part B(2016:Dec.)
• Page Start: 15
• Page End: 26
• Publication Date: 2016-12
• Subjects: Variational principles -- Finite elastostatics -- Rigid inclusions -- 3D FEA; Mechanics, Applied -- Periodicals; Mécanique appliquée -- Périodiques; Mechanics, Applied; Periodicals; 530
• DOI: 10.1016/j.mechrescom.2016.03.003
• Languages: English
• ISSNs: 0093-6413

Abstract

Abstract : Highlights: Present a variational formulation with rigid-body constraints for finite elasticity. The 3D FEM of the variational formulation with rigid-body constraints is proposed. The framework is applied to displacement-based and mixed FE with arbitrary order. Present an application in 2D where the rigid inclusion has highly graded edges. Present an application in 3D with complex spatial distribution of rigid inclusions. Abstract: 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.