Polytopal composite finite elements for modeling concrete fracture based on nonlocal damage models
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ORIGINAL PAPER
Polytopal composite finite elements for modeling concrete fracture based on nonlocal damage models Hai D. Huynh2 · S. Natarajan3 · H. Nguyen-Xuan4,5 · Xiaoying Zhuang1,2 Received: 30 March 2020 / Accepted: 29 July 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The paper presents an assumed strain formulation over polygonal meshes to accurately evaluate the strain fields in nonlocal damage models. An assume strained technique based on the Hu-Washizu variational principle is employed to generate a new strain approximation instead of direct derivation from the basis functions and the displacement fields. The underlying idea embedded in arbitrary finite polygons is named as Polytopal composite finite elements (PCFEM). The PCFEM is accordingly applied within the framework of the nonlocal model of continuum damage mechanics to enhance the description of damage behaviours in which highly localized deformations must be captured accurately. This application is helpful to reduce the meshsensitivity and elaborate the process-zone of damage models. Several numerical examples are designed for various cases of fracture to discuss and validate the computational capability of the present method through comparison with published numerical results and experimental data from the literature. Keywords Nonlocal damage model · Continuum damage mechanics · Fracture · Assumed strain · Polygonal FEM
1 Introduction The recent development of polygonal finite elements has provided an efficient tool for mesh generation and accurate solutions in the engineering simulation. Their applications have been succeeded in various mechanics problems such as analysis of granular materials [1], incompressible fluid flow [2], polycrystalline materials [3], contact models [4], to
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H. Nguyen-Xuan [email protected] Xiaoying Zhuang [email protected]
1
Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai, China
2
Chair of Computational Science and Simulation Technology, Institute of Photonics, Department of Mathematics and Physics, Leibniz University, Hannover, Hannover, Germany
3
Integrated Modelling and Simulation Lab, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India
4
CIRTech Institute, Chi Minh City University of Technology (HUTECH), Ho Chi Minh City, Vietnam
5
Department of Architectural Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Republic of Korea
name a few. As an applicable technique for meshing complicated geometries, several numerical methods, namely the Virtual element methods (VEM) [5–7], the Scaled boundary finite element methods (SBFEM) [8,9], the smoothed finite element method (SFEM) [10] have been developed over such polygonal meshes to deal with challenging issues in solid mechanics. As for the scope of the finite element method (FEM), the performance of polygonal elements with the use of rational basis functions including Wachspress, Laplace, Me
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