Hyperelastic analysis based on a polygonal finite element method

Amirtham, Rajagopal and Kraus, Markus and Steinmann, Paul (2017) Hyperelastic analysis based on a polygonal finite element method. Mechanics of Advanced Materials and Structures. pp. 1-13. ISSN 1537-6494 (In Press)

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In this contribution, we present a novel polygonal finite element method applied to hyperelastic analysis. For generating polygonal meshes in a bounded period of time, we use the adaptive Delaunay tessellation (ADT) proposed by Constantinu et al. [1]. ADT is an unstructured hybrid tessellation of a scattered point set that minimally covers the proximal space around each point. In this work, we have extended the ADT to nonconvex domains using concepts from constrained Delaunay triangulation (CDT). The proposed method is thus based on a constrained adaptive Delaunay tessellation (CADT) for the discretization of domains into polygonal regions. We involve the metric coordinate (Malsch) method for obtaining the interpolation over convex and nonconvex domains. For the numerical integration of the Galerkin weak form, we resort to classical Gaussian quadrature based on triangles. Numerical examples of two-dimensional hyperelasticity are considered to demonstrate the advantages of the polygonal finite element method.

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IITH Creators:
IITH CreatorsORCiD
Amirtham, RajagopalUNSPECIFIED
Item Type: Article
Uncontrolled Keywords: Adaptive Delaunay tessellation; hyperelasticity; polygonal finite element; polygonal interpolant
Subjects: Civil Engineering
Divisions: Department of Civil Engineering
Depositing User: Team Library
Date Deposited: 07 Aug 2017 10:28
Last Modified: 29 Aug 2017 10:20
URI: http://raiith.iith.ac.in/id/eprint/3461
Publisher URL: https://doi.org/10.1080/15376494.2017.1329463
OA policy: http://www.sherpa.ac.uk/romeo/issn/1537-6494/
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