A polygonal finite element formulation for modeling nearly incompressible materials

• Published in: Meccanica (Milan) Vol. 55; no. 4; pp. 701 - 723
• Main Author: Jabareen, Mahmood
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.04.2020; Springer Nature B.V
• Subjects: Automotive Engineering; beyond the Finite Elements; Civil Engineering; Classical Mechanics; Computational fluid dynamics; Computational Models for 'Complex' Materials and Structures; Eigenvalues; Finite element method; Locking; Mechanical Engineering; Nonlinear analysis; Patch tests; Physics; Physics and Astronomy; Polygons; Potential energy; Shape functions; Polygonal finite element method; Mixed finite element formulation; Nearly incompressible materials
• ISSN: 0025-6455; 1572-9648
• DOI: 10.1007/s11012-019-01121-0

The objective of the present paper is to develop a finite element formulation for modeling nearly incompressible materials at large strains using polygonal elements. The present finite element formulation is a simplified version of the three-field mixed formulation and, in particular, it reduces the functional of the internal potential energy by expressing the field of the average volume-change in terms of the displacement field, where the latter is discretized using the Wachspress shape functions. The reduced mixed formulation eliminates the volumetric locking in nearly incompressible materials and enhances the computational efficiency as the static condensation is circumvented. A detailed implementation of the finite element formulation is presented in this study. Also, different example problems, including eigenvalue analysis, nonlinear patch test and other benchmark problems are presented for demonstrating the accuracy and the reliability of the developed formulation for polygonal elements.