Three-dimensional crack growth with hp-generalized finite element and face offsetting methods

Pereira, J. P.; Duarte, C. Armando; Jiao, Xiangmin

doi:10.1007/s00466-010-0491-3

Cited by 61 publications

(58 citation statements)

References 70 publications

(147 reference statements)

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“…As a consequence, a sufficiently fine mesh must be used around the crack front to achieve acceptable accuracy. In the hp-adaptive GFEM presented in [44][45][46] mesh refinement and enrichment are done in the global discretization of a problem, in the same spirit as in the standard FEM. This offsets some of the attractive features of the G/XFEM and adds computational complexity to their implementation in available FEM software.…”

Section: Introductionmentioning

confidence: 99%

Analysis of three-dimensional fracture mechanics problems: A non-intrusive approach using a generalized finite element method

Gupta

Pereira

Kim

et al. 2012

Engineering Fracture Mechanics

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Kim, D J.; Duarte, C A.; and Eason, T, "Analysis of three-dimensional fracture mechanics problems: A nonintrusive approach using a generalized finite element method" (2012 (structural) and local (crack) scale problems. In the approach presented here, an initial global scale problem is solved by a commercial finite element analysis software, local problems containing 3-D fractures are solved by an hp-adaptive GFEM software and an enriched global scale problem is solved by a combination of the FEM and GFEM softwares. The interactions between the solvers are limited to the exchange of load and solution vectors and does not require the introduction of user subroutines to existing FEM software. As a results, the user can benefit from built-in features of available commercial grade FEM software while adding the benefits of the GFEM for this class of problems. Several threedimensional fracture mechanics problems aimed at investigating the applicability and accuracy of the proposed two-solver methodology are presented.

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Section: Introductionmentioning

confidence: 99%

Analysis of three-dimensional fracture mechanics problems: A non-intrusive approach using a generalized finite element method

Gupta

Pereira

Kim

et al. 2012

Engineering Fracture Mechanics

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“…As a result, each crack propagation step may take several hours even on teraflop computers [60]. This paper presents a generalized FEM for crack growth simulations that combines the concept of global-local enrichments introduced in [13,19] with the hp-GFEM for 3-D propagating fractures presented in [48]. The GFEM with global-local enrichments (GFEM gl ) uses a two-scale decomposition of the solution of a fracture mechanics problema smooth coarse-scale component and a singular fine-scale component.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, the computing power required to solve this class of problems using existing methodologies can be formidable. Representative methods for three-dimensional crack growth simulations include the standard finite element method (FEM) with remeshing [60], the boundary element method (BEM) [11,36], and the extended [1,8,25,38,57,58] or generalized FEM [18,48]. These methods require the solution of the problem from scratch at each step of a crack growth simulation.…”

Section: Introductionmentioning

confidence: 99%

A two-scale approach for the analysis of propagating three-dimensional fractures

2011

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This paper presents a generalized finite element method (GFEM) for crack growth simulations based on a two-scale decomposition of the solution-a smooth coarsescale component and a singular fine-scale component. The smooth component is approximated by discretizations defined on coarse finite element meshes. The fine-scale component is approximated by the solution of local problems defined in neighborhoods of cracks. Boundary conditions for the local problems are provided by the available solution at a crack growth step. The methodology enables accurate modeling of 3-D propagating cracks on meshes with elements that are orders of magnitude larger than those required by the FEM. The coarse-scale mesh remains unchanged during the simulation. This, combined with the hierarchical nature of GFEM shape functions, allows the recycling of the factorization of the global stiffness matrix during a crack growth simulation. Numerical examples demonstrating the approximating properties of the proposed enrichment functions and the computational performance of the methodology are presented.

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“…Several studies have shown that GFEM has been used successfully in linear elastic fracture mechanics (Areias and Belytschko, 2005;Belytschko, 2001;Duarte et al, 2007;Laborde et al, 2005;Pereira et. al., 2010;Stazi et al, 2003;Tabarraei and Sukumar, 2008).…”

Section: Introductionmentioning

confidence: 99%

Comparative Analysis of Ck- and C0-GFEM Applied to Two-dimensional Problems of Confined Plasticity

Freitas

Torres

Mendonça

et al. 2015

Lat. Am. j. solids struct.

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For many practical applications in engineering, a complex structure shows linear elastic behavior over almost all its extension, but exhibits confined plasticity contained in some small critical regions, e.g. stress concentrations in fillets and sharp internal corners. The behavior of C 0 -and C k -GFEM is investigated in this class of problems.The first goal of this study is to verify the actual formulation of the C k -GFEM for two-dimensional elastoplasticity, as a modification of the C 0 -GFEM formulation. The C k -GFEM is based on a set of basis functions with C k continuity over the domain. The approximation functions are constructed from a C k continuous partition of unity, over which polynomial enrichment functions (or any special function) can be applied, in the same fashion as in the usual C 0 -GFEM. In this way, the finite element approximations show continuous responses for both displacements and stresses across inter-element interfaces. An investigation is performed to assess the behavior of higherregularity partitions of unity against conventional C 0 counterparts. The irreversible response and hardening effects of the material is represented by the rate independent J 2 plasticity theory with linear isotropic hardening of material and von Mises yield criteria, being considered only monotonic loading and the kinematics of small displacements and small deformations. The focus herein is to enlighten any possible advantage of smoothness in the presence of plastification phenomena, seeking for improvements in capturing the evolution of the process zone.

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Three-dimensional crack growth with hp-generalized finite element and face offsetting methods

Cited by 61 publications

References 70 publications

Analysis of three-dimensional fracture mechanics problems: A non-intrusive approach using a generalized finite element method

Analysis of three-dimensional fracture mechanics problems: A non-intrusive approach using a generalized finite element method

A two-scale approach for the analysis of propagating three-dimensional fractures

Comparative Analysis of Ck- and C0-GFEM Applied to Two-dimensional Problems of Confined Plasticity

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