An extended polygonal finite element method for large deformation fracture analysis

Huynh, Hai D.; Tran, Phuong; Zhuang, Xiaoying; Nguyen‐Xuan, H.

doi:10.1016/j.engfracmech.2019.01.024

Cited by 21 publications

(8 citation statements)

References 57 publications

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“…The element type used for the numerical models was a two-dimensional quadrilateral four-noded element of size approximately equal to 1.5 mm side length. In the present study, one should avoid using the triangle element because this element provides results with less accuracy than that of a quadrilateral element as recommended in Huynh et al (2019) studies [18].…”

Section: Finite Element Modelling Using Abaqus Software Programmentioning

confidence: 98%

Non-Smooth Behavior of Reinforced Concrete Beam Using Extended Finite Element Method

Abbas

Al-Zuhairi

2019

Civ Eng J

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Flexure members such as reinforced concrete (RC) simply supported beams subjected to two-point loading were analyzed numerically. The Extended Finite Element Method (XFEM) was employed for the treatment the non-smooth h behaviour such as discontinuities and singularities. This method is a powerful technique used for the analysis of the fracture process and crack propagation in concrete. Concrete is a heterogeneous material that consists of coarse aggregate, cement mortar and air voids distributed in the cement paste. Numerical modeling of concrete comprises a two-scale model, using mesoscale and macroscale numerical models. The effectiveness and validity of the Meso-Scale Approach (MSA) in modeling of the reinforced concrete beams with minimum reinforcement was studied. ABAQUS program was utilized for Finite Element (FE) modeling and analysis of the beams. On the other hand, mesoscale modeling of concrete constituents was executed with the aid of ABAQUS PYTHON language and programing using excel sheets. The concrete beams under flexure were experimentally investigated as well as by the numerical analysis. The comparison between experimental and numerical results showed that the mesoscale model gives a better indication for representing the concrete models in the numerical approach and a more appropriate result when compared with the experimental results.

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Section: Finite Element Modelling Using Abaqus Software Programmentioning

confidence: 98%

Non-Smooth Behavior of Reinforced Concrete Beam Using Extended Finite Element Method

Abbas

Al-Zuhairi

2019

Civ Eng J

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“…Due to their advantages such as more flexible in meshing complicated structures, minimizing the number of elements for a given mesh resolution and reducing mesh-distortion sensitivity compared to the standard FEM, the arbitrary polyhedral finite element (pFEM) has attracted huge attention as well as applications in different fields of engineering, e.g. topology optimization, 1 plate structures, [2][3][4] solid mechanics problems, [5][6][7] fluid flow problems, 8 microstructures, [9][10][11][12] and so forth. The development of pFEM in recent years was clearly reviewed in Reference 13.…”

Section: Introductionmentioning

confidence: 99%

A consecutive‐interpolation polyhedral finite element method for solid structures

Nguyen

et al. 2021

Numerical Meth Engineering

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In this paper, we investigate the use of a consecutive-interpolation for polyhedral finite element method (CIPFEM) in the analysis of three-dimensional solid mechanics problems. A displacement-based Galerkin weak form is used, in which the nodal degrees of freedom (DOF) and their derivatives are both considered for the approximation scheme. Based on arbitrary star-convex polyhedral elements using piecewise linear shape function, the present method can have the advantage of being applicable to complicated structures. Nevertheless, the proposed interpolation technique gives higher-order continuity, greater accuracy with the same number of DOFs. The reliability and efficiency of the CIPFEM are proved by comparing the present results with those obtained by the consecutive-interpolation for tetrahedral element (CT4), conventional linear FEM using polyhedral elements (PFEM), and tetrahedral elements (T4) through numerical examples. Cantilever beam, concrete corbel, and complex hollow concrete revetment block are considered to show the excellent performance of the present approach.

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“…The polygonal elements have many potential applications to a large variety of problems, including constitutive modeling in nonlinear analysis of polycrystalline materials, linear elasticity, analysis of cracked structures, vibration analysis, crack propagation, large deformation problems, topology optimization, hyperelastic analysis, contact‐impact problems, adaptive meshing, plate bending problems, analysis of generalized elastic solids, and multimaterial discretization and optimization . There are other recent works on extension of polygonal FEM for topology optimization, nonlinear analysis of plates, laminates and functionally graded plates, and fracture problems …”

Section: Introductionmentioning

confidence: 99%

“…21,22 There are other recent works on extension of polygonal FEM for topology optimization, 15,23 nonlinear analysis of plates, laminates and functionally graded plates, 24 and fracture problems. 25,26 There have been recent works carried out by using the polygonal FEM for analysis of plates and laminates. An assumed strain field resulting in a locking-free element is considered for analysis of plates.…”

Section: Introductionmentioning

confidence: 99%

An n‐sided polygonal finite element for nonlocal nonlinear analysis of plates and laminates

Aurojyoti

Raghu

Rajagopal

et al. 2019

Numerical Meth Engineering

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Summary In this study, a locking‐free n‐sided C1 polygonal finite element is presented for nonlinear analysis of laminated plates. The plate kinematics is based on Reddy's third‐order shear deformation theory (TSDT). The in‐plane displacements are approximated using barycentric form of Lagrange shape functions. The weak‐form Galerkin formulation based on the kinematics of TSDT requires the C1 approximation of the transverse displacement over the polygonal element. This is achieved by embedding the C0 Lagrange interpolants over a cubic Bernstein‐Bezier patch defined over the n‐sided polygonal element. Such an approach ensures the continuity of the derivative field at the inter‐element edges. In addition, Eringen's stress‐gradient nonlocal constitutive equations are used in the present formulation to account for nonlocality. The effect of geometric nonlinearity is taken by considering the von Kármán geometric nonlinearity. Examples are presented to show the effect of nonlocality, geometric nonlinearity, and the lamination scheme on the bending behavior of laminated composite plates. The results are compared with analytical solutions, conventional FEM results, and with those available in the literature. Shear locking is addressed considering reduced integration and consistent interpolation techniques. The patch test is used to check the convergence of the element developed.

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An extended polygonal finite element method for large deformation fracture analysis

Cited by 21 publications

References 57 publications

Non-Smooth Behavior of Reinforced Concrete Beam Using Extended Finite Element Method

Non-Smooth Behavior of Reinforced Concrete Beam Using Extended Finite Element Method

A consecutive‐interpolation polyhedral finite element method for solid structures

An n‐sided polygonal finite element for nonlocal nonlinear analysis of plates and laminates

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