A quadtree-polygon-based scaled boundary finite element method for crack propagation modeling in functionally graded materials

Chen, X.; Luo, Tao; Ooi, Ean Tat; Ooi, Ean Hin; Song, Chongmin

doi:10.1016/j.tafmec.2018.01.008

Cited by 44 publications

(19 citation statements)

References 31 publications

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“…10. The phase field predictions are compared with the results obtained by (a) Kim and Paulino [9], using the maximum energy release rate criterion and a finite element re-meshing algorithm, and (b) Chen et al [38], with the maximum circumferential stress criterion and the scaled boundary finite element method. A similar crack path is predicted in the three cases; the crack deflects towards the hole region, eventually coalescing with the intermediate hole.…”

Section: Complex Crack Patterns In Functionally Graded Solidsmentioning

confidence: 99%

Phase field modelling of crack propagation in functionally graded materials

Hirshikesh

Natarajan

Annabattula

et al. 2019

Composites Part B: Engineering

188

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We present a phase field formulation for fracture in functionally graded materials (FGMs). The model builds upon homogenization theory and accounts for the spatial variation of elastic and fracture properties. Several paradigmatic case studies are addressed to demonstrate the potential of the proposed modelling framework. Specifically, we (i) gain insight into the crack growth resistance of FGMs by conducting numerical experiments over a wide range of material gradation profiles and orientations, (ii) accurately reproduce the crack trajectories observed in graded photodegradable copolymers and glass-filled epoxy FGMs, (iii) benchmark our predictions with results from alternative numerical methodologies, and (iv) model complex crack paths and failure in three dimensional functionally graded solids. The suitability of phase field fracture methods in capturing the crack deflections intrinsic to crack tip mode-mixity due to material gradients is demonstrated. Material gradient profiles that prevent unstable fracture and enhance crack growth resistance are identified: this provides the foundation for the design of fracture resistant FGMs. The finite element code developed can be downloaded from www.empaneda.com/codes.

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Section: Complex Crack Patterns In Functionally Graded Solidsmentioning

confidence: 99%

Phase field modelling of crack propagation in functionally graded materials

Hirshikesh

Natarajan

Annabattula

et al. 2019

Composites Part B: Engineering

188

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“…j (x, y) are C 1 continuous Laplace interpolants. The finite element equations are obtained by substituting the approximations given in Equations (26)-(30) into the weak forms in Equations (21)- (25). The degrees of freedom are shown in Figure 11 for a conforming polygonal element and a nonconforming polygonal element.…”

Section: Finite Element Approximationsmentioning

confidence: 99%

“…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%

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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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“…Several numerical techniques have been proposed in the literature to analyse the fracture processes in orthotropic FGMs [8,[10][11][12][13][14]. The vast majority of the works are based on discrete approaches; for example, the conventional finite element with displacement correlation technique (DCT) [15], the extended finite element method (XFEM) [8,10,11,14], and the scaled boundary finite element method (SBFEM) [12,13]. However, predicting crack initiation and subsequent crack growth requires an ad hoc criterion, with crack trajectories being sensitive to this choice [16].…”

Section: Introductionmentioning

confidence: 99%

Adaptive phase field modelling of crack propagation in orthotropic functionally graded materials

2021

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In this work, we extend the recently proposed adaptive phase field method to model fracture in orthotropic functionally graded materials (FGMs). A recovery type error indicator combined with quadtree decomposition is employed for adaptive mesh refinement. The proposed approach is capable of capturing the fracture process with a localized mesh refinement that provides notable gains in computational efficiency.The implementation is validated against experimental data and other numerical experiments on orthotropic materials with different material orientations. The results reveal an increase in the stiffness and the maximum force with increasing material orientation angle. The study is then extended to the analysis of orthotropic FGMs. It is observed that, if the gradation in fracture properties is neglected, the material gradient plays a secondary role, with the fracture behaviour being dominated by the orthotropy of the material. However, when the toughness increases along the crack propagation path, a substantial gain in fracture resistance is observed.

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A quadtree-polygon-based scaled boundary finite element method for crack propagation modeling in functionally graded materials

Cited by 44 publications

References 31 publications

Phase field modelling of crack propagation in functionally graded materials

Phase field modelling of crack propagation in functionally graded materials

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

Adaptive phase field modelling of crack propagation in orthotropic functionally graded materials

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