Unstructured polygonal meshes with adaptive refinement for the numerical simulation of dynamic cohesive fracture

Spring, Daniel; Leon, Sofie E.; Paulino, Gláucio H.

doi:10.1007/s10704-014-9961-5

Cited by 52 publications

(33 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1.1.1 there are a few research groups that successfully applied polytope finite elements to a wide range of problem classes including structural mechanics [4,10,12,22,23], nonlinear analyses [6,[24][25][26][27], optimization [7,[28][29][30][31], crack propagation analysis [11,26,32,33] and fluid flow problems [34]. Noteworthy contributions that have advanced the application of polytope FEMs are discussed in the following paragraph.…”

Section: Applications Of Polygonal Finite Element Methodsmentioning

confidence: 99%

See 1 more Smart Citation

The finite cell method for polygonal meshes: poly-FCM

Duczek

Gabbert

2016

Comput Mech

View full text Add to dashboard Cite

In the current article, we extend the two-dimensional version of the finite cell method (FCM), which has so far only been used for structured quadrilateral meshes, to unstructured polygonal discretizations. Therefore, the adaptive quadtree-based numerical integration technique is reformulated and the notion of generalized barycentric coordinates is introduced. We show that the resulting polygonal (poly-)FCM approach retains the optimal rates of convergence if and only if the geometry of the structure is adequately resolved. The main advantage of the proposed method is that it inherits the ability of polygonal finite elements for local mesh refinement and for the construction of transition elements (e.g. conforming quadtree meshes without hanging nodes). These properties along with the performance of the poly-FCM are illustrated by means of several benchmark problems for both static and dynamic cases.

show abstract

Section: Applications Of Polygonal Finite Element Methodsmentioning

confidence: 99%

“…Eq. (33). After using the affine isoparametric mapping from the reference space ξ to the global coordinate system x the shape functions remain linear on the boundary of a distorted but convex polygon [12].…”

Section: Linear Shape Functionsmentioning

confidence: 99%

The finite cell method for polygonal meshes: poly-FCM

Duczek

Gabbert

2016

Comput Mech

View full text Add to dashboard Cite

show abstract

“…This line of research includes the recent efforts to resolve the issue with the aid of new polyhedral elements , intended for improving accuracy and for enhancing geometric adaptability. Wicke et al .…”

Section: Introductionmentioning

confidence: 99%

“…In addition, quadrature schemes for polygonal and polyhedral elements were developed . Furthermore, the polygonal and polyhedral elements were applied for various practical problems, namely, crack propagation , reinforced composites , structural topology optimization , and so on, and had strong advantages in these fields.…”

Section: Introductionmentioning

confidence: 99%

Polyhedral elements by means of node/edge‐based smoothed finite element method

Lee

Kim

2016

Numerical Meth Engineering

View full text Add to dashboard Cite

Summary The node‐based or edge‐based smoothed finite element method is extended to develop polyhedral elements that are allowed to have an arbitrary number of nodes or faces, and so retain a good geometric adaptability. The strain smoothing technique and implicit shape functions based on the linear point interpolation make the element formulation simple and straightforward. The resulting polyhedral elements are free from the excessive zero‐energy modes and yield a robust solution very much insensitive to mesh distortion. Several numerical examples within the framework of linear elasticity demonstrate the accuracy and convergence behavior. The smoothed finite element method‐based polyhedral elements in general yield solutions of better accuracy and faster convergence rate than those of the conventional finite element methods. Copyright © 2016 John Wiley & Sons, Ltd.

show abstract

“…A number of studies were performed on numerical integration rules of arbitrary polygonal elements by Natarajan et al (2009), Mousavi et al (2010) and . Various implementations of polygonal finite element method have been employed in literature; Ooi et al (2012a, b) proposed the scaled boundary finite element method (SBFEM) within the polygonal finite elements to model the crack propagation; Biabanaki and Khoei (2012) applied the polygonal FEM for modeling arbitrary interfaces in large deformation problems; Biabanaki et al (2014) proposed the technique for contactimpact problems on non-conformal meshes; Spring et al (2014) and Leon et al (2014) applied the polygonal finite elements for dynamic cohesive fracture problems; Gain et al (2014) employed the virtual element method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes; proposed the technique for incompressible fluid flow problems; Khoei et al (2015) applied the method to model the large sliding contact using various polygonal shape functions; Chi et al (2015) employed the polygonal finite elements to model finite elasticity problems.…”

mentioning

confidence: 99%

A polygonal finite element method for modeling crack propagation with minimum remeshing

2015

View full text Add to dashboard Cite

In this paper, a polygonal finite element method is presented for crack growth simulation with minimum remeshing. A local polygonal mesh strategy is performed employing polygonal finite element method to model the crack propagation. In order to model the singular crack tip fields, the convex and concave polygonal elements are modified based on the singular quarter point isoparametric concept that improves the accuracy of the stress intensity factors. Numerical simulations are performed to demonstrate the efficiency of various polygonal shape functions, including the Wachspress, metric, Laplace and mean value shape functions, in modeling the crack tip fields. Eventually, analogy of the results with the existing numerical and experimental data is carried out depicting accuracy of the propounded technique.

show abstract

Unstructured polygonal meshes with adaptive refinement for the numerical simulation of dynamic cohesive fracture

Cited by 52 publications

References 50 publications

The finite cell method for polygonal meshes: poly-FCM

The finite cell method for polygonal meshes: poly-FCM

Polyhedral elements by means of node/edge‐based smoothed finite element method

A polygonal finite element method for modeling crack propagation with minimum remeshing

Contact Info

Product

Resources

About