References of "Bordas, Stéphane 50000969"
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See detailNumerically determined enrichment functions for the extended finite element method and applications to bi-material anisotropic fracture and polycrystals
Menk, Alexander; Bordas, Stéphane UL

in International Journal for Numerical Methods in Engineering (2010), 83(7), 805-828

Strain singularities appear in many linear elasticity problems. A very fine mesh has to be used in the vicinity of the singularity in order to obtain acceptable numerical solutions with the finite element ... [more ▼]

Strain singularities appear in many linear elasticity problems. A very fine mesh has to be used in the vicinity of the singularity in order to obtain acceptable numerical solutions with the finite element method (FEM). Special enrichment functions describing this singular behavior can be used in the extended finite element method (X-FEM) to circumvent this problem. These functions have to be known in advance, but their analytical form is unknown in many cases. Li et al. described a method to calculate singular strain fields at the tip of a notch numerically. A slight modification of this approach makes it possible to calculate singular fields also in the interior of the structural domain. We will show in numerical experiments that convergence rates can be significantly enhanced by using these approximations in the X-FEM. The convergence rates have been compared with the ones obtained by the FEM. This was done for a series of problems including a polycrystalline structure. [less ▲]

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See detailA simple and robust three-dimensional cracking-particle method without enrichment
Rabczuk, T.; Zi, G.; Bordas, Stéphane UL et al

in Computer Methods in Applied Mechanics and Engineering (2010), 199(37-40), 2437-2455

A new robust and efficient approach for modeling discrete cracks in meshfree methods is described. The method is motivated by the cracking-particle method (Rabczuk T., Belytschko T., International Journal ... [more ▼]

A new robust and efficient approach for modeling discrete cracks in meshfree methods is described. The method is motivated by the cracking-particle method (Rabczuk T., Belytschko T., International Journal for Numerical Methods in Engineering, 2004) where the crack is modeled by a set of cracked segments. However, in contrast to the above mentioned paper, we do not introduce additional unknowns in the variational formulation to capture the displacement discontinuity. Instead, the crack is modeled by splitting particles located on opposite sides of the associated crack segments and we make use of the visibility method in order to describe the crack kinematics. We apply this method to several two- and three-dimensional problems in statics and dynamics and show through several numerical examples that the method does not show any "mesh" orientation bias. © 2010 Elsevier B.V. [less ▲]

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See detailIntegrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework
Natarajan, S.; Roy Mahapatra, D.; Bordas, Stéphane UL

in International Journal for Numerical Methods in Engineering (2010), 83(3), 269-294

Partition of unity methods, such as the extended finite element method, allows discontinuities to be simulated independently of the mesh (Int. J. Numer. Meth. Engng. 1999; 45:601-620). This eliminates the ... [more ▼]

Partition of unity methods, such as the extended finite element method, allows discontinuities to be simulated independently of the mesh (Int. J. Numer. Meth. Engng. 1999; 45:601-620). This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome re-meshing, as the discontinuity evolves. However, to compute the stiffness matrix of the elements intersected by the discontinuity, a subdivision of the elements into quadrature subcells aligned with the discontinuity is commonly adopted. In this paper, we use a simple integration technique, proposed for polygonal domains (Int. J. Numer. Meth. Engng 2009; 80(1):103-134. DOI: 10.1002/nme.2589) to suppress the need for element subdivision. Numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics and a multi-material problem show that the proposed method yields accurate results. Owing to its simplicity, the proposed integration technique can be easily integrated in any existing code. © 2010 John Wiley & Sons, Ltd. [less ▲]

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See detailNumerical integration over arbitrary surfaces in partition of unity finite elements
Natarajan, Sundararajan; dal Pont, Stefano; Hung, Nguyen-Xuan et al

Scientific Conference (2009, September)

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See detailThe smoothed extended finite element method for strong discontinuities
Natarajan, S.; Bordas, Stéphane UL; Rabczuk, Timon

Scientific Conference (2009, June)

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See detailOn the Smoothed eXtended Finite Element Method for Continuum
Natarajan, Sundararajan; Bordas, Stéphane UL; Rabczuk, Timon et al

Scientific Conference (2009, April)

In this paper, we combine the strain smoothing technique proposed by Liu et al [1] coined as the smoothed finite element method (SFEM) to partition of unity methods, namely the extended finite element ... [more ▼]

In this paper, we combine the strain smoothing technique proposed by Liu et al [1] coined as the smoothed finite element method (SFEM) to partition of unity methods, namely the extended finite element method (XFEM) [2] to give birth to the smoothed extended finite element method (SmXFEM) [3]. SmXFEM shares properties both with the SFEM and the XFEM. The proposed method eliminates the need to compute and integrate the derivatives of shape functions (which are singular at the tip for linear elastic fracture mechanics). The need for isoparametric mapping is eliminated because the integration is done along the boundary of the finite element or smoothing cells, which allows elements of arbitrary shape. We present numerical results for various differential equations that have singularity or steep gradient at the boundary. The method is verified on several examples and comparisons are made to the conventional XFEM. [less ▲]

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See detailA novel numerical integration technique over arbitrary polygons
Natarajan, Sundararajan; Mahapatra, D Roy; Bordas, Stéphane UL et al

Scientific Conference (2009, April)

In this paper, a new numerical integration technique [1] on arbitrary polygons is presented. The polygonal do- main is mapped conformally to the unit disk using Schwarz-Christoffel mapping [2] and a ... [more ▼]

In this paper, a new numerical integration technique [1] on arbitrary polygons is presented. The polygonal do- main is mapped conformally to the unit disk using Schwarz-Christoffel mapping [2] and a midpoint quadrature rule defined on the unit circle is used. This method eliminates the need for a two level isoparametric mapping usuall required [3]. Moreover the positivity of the Jacobian is guaranteed. We present numerical results for a few benchmark problems in the context of polygonal finite elements that show the effectiveness of the method. [less ▲]

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See detailAPPLICATION OF EXTENDED ELEMENT-FREE GALERKIN METHOD TO MULTIPLE FLAWS UNDER BRITTLE FRACTURE CONDITIONS
RABCZUK, T.; BEZENSEK, B.; Bordas, Stéphane UL

in PROCEEDINGS OF THE ASME PRESSURE VESSELS AND PIPING CONFERENCE - 2008, VOL 6, PT A AND B (2009)

The extended element-free Galerkin (XEFG) method incorporates cracks through partition of unity enrichment of the standard basis functions. Discontinuous functions are added to capture the jump through ... [more ▼]

The extended element-free Galerkin (XEFG) method incorporates cracks through partition of unity enrichment of the standard basis functions. Discontinuous functions are added to capture the jump through the crack faces and near-front enrichment is added to capture the asymptotic behaviour in the vicinity of the crack fronts. Depending on the material behaviour, these functions can be of various type. The method can treat initiation, growth and coalescence of cracks seamlessly in both linear elastic and non-linear settings. The method is a powerful tool for modelling and studying crack paths, which are a central feature in the assessment of multiple flaws.The method is applied to the problem of multiple non-aligned flaws in a ferritic plate under cleavage failure. Fracture paths from two nonaligned notches in a plate are modelled. Based on the observations of crack paths the critical flaw alignment distance is established for nonaligned through-wall flaws. [less ▲]

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See detailAddressing volumetric locking and instabilities by selective integration in smoothed finite elements
Hung, Nguyen-Xuan; Bordas, Stéphane UL; Hung, Nguyen-Dang

in Communications in Numerical Methods in Engineering (2009), 25(1), 19-34

This paper promotes the development of a novel family of finite elements with smoothed strains, offering remarkable properties. In the smoothed finite element method (FEM), elements are divided into ... [more ▼]

This paper promotes the development of a novel family of finite elements with smoothed strains, offering remarkable properties. In the smoothed finite element method (FEM), elements are divided into subcells. The strain at a point is defined as a weighted average of the standard strain field over a representative domain. This yields superconvergent stresses, both in regular and singular settings, as well as increased accuracy, with slightly lower computational cost than the standard FEM. The one-subcell version that does not exhibit volumetric locking yields more accurate stresses but less accurate displacements and is equivalent to a quasi-equilibrium FEM. It is also subject to instabilities. In the limit where the number of subcells goes to infinity, the standard FEM is recovered, which yields more accurate displacements and less accurate stresses. The specific contribution of this paper is to show that expressing the volumetric part of the strain field using a one-subcell formulation is sufficient to get rid of volumetric locking and increase the displacement accuracy compared with the standard FEM when the single subcell version is used to express both the volumetric and deviatoric parts of the strain. Selective integration also alleviates instabilities associated with the single subcell element, which are due to rank deficiency. Numerical examples on various compressible and incompressible linear elastic test cases show that high accuracy is retained compared with the standard FEM without increasing computational cost. [less ▲]

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See detailInfluence of the microstructure on the stress state of solder joints dusing thermal cycling
Menk, A.; Bordas, Stéphane UL

in Proceedings of 10th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2009 (2009)

The lifetime of a solder joint is mainly determined by its creep behaviour. Creep arises from the stresses inside the solder joints as a consequence of the thermomechanical mismatch of the board and the ... [more ▼]

The lifetime of a solder joint is mainly determined by its creep behaviour. Creep arises from the stresses inside the solder joints as a consequence of the thermomechanical mismatch of the board and the substrate. The stress state is heavily influenced by the anisotropy of tin. To understand the damage process in solder joints, the influence of the anisotropic microstructure must be understood. In this paper the influence of different grain sizes, shapes and orientations on the stress state is evaluated, based on numerical experiments. [less ▲]

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See detailNumerical integration over arbitrary polygonal domains based on Schwarz-Christoffel conformal mapping
Natarajan, S.; Bordas, Stéphane UL; Roy mahapatra, D.

in International Journal for Numerical Methods in Engineering (2009), 80(1), 103-134

This paper presents a new numerical integration technique on arbitrary polygonal domains. The polygonal domain is mapped conformally to the unit disk using Schwarz-Christoffel mapping and a midpoint ... [more ▼]

This paper presents a new numerical integration technique on arbitrary polygonal domains. The polygonal domain is mapped conformally to the unit disk using Schwarz-Christoffel mapping and a midpoint quadrature rule defined on this unit disk is used. This method eliminates the need for a two-level isoparametric mapping usually required. Moreover, the positivity of the Jacobian is guaranteed. Numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results. © 2009 John Wiley & Sons, Ltd. [less ▲]

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See detailMeshless methods: A review and computer implementation aspects
Nguyen, V. P.; Rabczuk, T.; Bordas, Stéphane UL et al

in Mathematics and Computers in Simulation (2008), 79(3), 763-813

The aim of this manuscript is to give a practical overview of meshless methods (for solid mechanics) based on global weak forms through a simple and well-structured MATLAB code, to illustrate our ... [more ▼]

The aim of this manuscript is to give a practical overview of meshless methods (for solid mechanics) based on global weak forms through a simple and well-structured MATLAB code, to illustrate our discourse. The source code is available for download on our website and should help students and researchers get started with some of the basic meshless methods; it includes intrinsic and extrinsic enrichment, point collocation methods, several boundary condition enforcement schemes and corresponding test cases. Several one and two-dimensional examples in elastostatics are given including weak and strong discontinuities and testing different ways of enforcing essential boundary conditions. © 2008 IMACS. [less ▲]

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See detailA combined extended finite element and level set method for biofilm growth
Duddu, Ravindra; Bordas, Stéphane UL; Chopp, David et al

in International Journal for Numerical Methods in Engineering (2008), 74(5), 848-870

This paper presents a computational technique based on the extended finite element method (YFEM) and the level set method for the growth of biofilms. The discontinuous-derivative enrichment of the ... [more ▼]

This paper presents a computational technique based on the extended finite element method (YFEM) and the level set method for the growth of biofilms. The discontinuous-derivative enrichment of the standard finite element approximation eliminates the need for the finite element mesh to coincide with the biofilm-fluid interface and also permits the introduction of the discontinuity in the normal derivative of the substrate concentration field at the biofilm-fluid interface. The XFEM is coupled with a comprehensive level set update scheme with velocity extensions, which makes updating the biofilm interface fast and accurate without need for remeshing. The kinetics of biofilms are briefly given and the non-linear strong and weak forms are presented. The non-linear system of equations is solved using a Newton-Raphson scheme. Example problems including 1D and 2D biofilm growth are presented to illustrate the accuracy and utility of the method. The 1D results we obtain are in excellent agreement with previous 1D results obtained using finite difference methods. Our 2D results that simulate finger formation and finger-tip splitting in biofilms illustrate the robustness of the present computational technique. [less ▲]

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See detailThree-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment
Bordas, Stéphane UL; Rabczuk, Timon; Zi, Goangseup

in Engineering Fracture Mechanics (2008), 75(5), 943-960

This paper presents a three-dimensional, extrinsically enriched meshfree method for initiation, branching, growth and coalescence of an arbitrary number of cracks in non-linear solids including large ... [more ▼]

This paper presents a three-dimensional, extrinsically enriched meshfree method for initiation, branching, growth and coalescence of an arbitrary number of cracks in non-linear solids including large deformations, for statics and dynamics. The novelty of the methodology is that only an extrinsic discontinuous enrichment and no near-tip enrichment is required. Instead, a Lagrange multiplier field is added along the crack front to close the crack. This decreases the computational cost and removes difficulties involved with a branch enrichment. The results are compared to experimental data, and other simulations from the literature to show the robustness and accuracy of the method. [less ▲]

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See detailThe smoothed extended finite element method
Natarajan, S.; Bordas, Stéphane UL; Minh, Q. D. et al

in Proceedings of the 6th International Conference on Engineering Computational Technology (2008)

This paper shows how the strain smoothing technique recently proposed by G.R.Liu [1] coined as smoothed finite element method (SFEM) can be coupled to partition of unity methods, namely extended finite ... [more ▼]

This paper shows how the strain smoothing technique recently proposed by G.R.Liu [1] coined as smoothed finite element method (SFEM) can be coupled to partition of unity methods, namely extended finite element method (XFEM) [2] to give birth to the smoothed extended finite element method (SmXFEM), which shares properties both with the SFEM and the XFEM. The proposed method suppresses the need to compute and integrate the derivatives of shape functions (which are singular at the tip in linear elastic fracture mechanics). Additionally, integration is performed along the boundary of the finite elements or smoothing cells and no isoparametric mapping is required, which allows elements of arbitrary shape. We present numerical results for cracks in linear elastic fracture mechanics problems. The method is verified on several examples and comparisons are made to the conventional XFEM. © 2008 Civil-Comp Press. [less ▲]

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See detailA posteriori error estimation for extended finite elements by an extended global recovery
Duflot, M.; Bordas, Stéphane UL

in International Journal for Numerical Methods in Engineering (2008), 76(8), 1123-1138

This contribution presents an extended global derivative recovery for enriched finite element methods (FEMs), such as the extended FEM along with an associated error indicator. Owing to its simplicity ... [more ▼]

This contribution presents an extended global derivative recovery for enriched finite element methods (FEMs), such as the extended FEM along with an associated error indicator. Owing to its simplicity, the proposed scheme is ideally suited to industrial applications. The procedure is based on global minimization of the L2 norm of the difference between the raw strain field (C-1) and the recovered (C0) strain field. The methodology engineered in this paper extends the ideas of Oden and Brauchli (Int. J. Numer. Meth. Engng 1971; 3) and Hinton and Campbell (Int. J. Numer. Meth. Engng 1974; 8) by enriching the approximation used for the construction of the recovered derivatives (strains) with the gradients of the functions employed to enrich the approximation employed for the primal unknown (displacements). We show linear elastic fracture mechanics examples, both in simple two-dimensional settings, and for a three-dimensional structure. Numerically, we show that the effectivity index of the proposed indicator converges to unity upon mesh refinement. Consequently, the approximate error converges to the exact error, indicating that the error indicator is valid. Additionally, the numerical examples suggest a novel adaptive strategy for enriched approximations in which the dimensions of the enrichment zone are first increased, before standard h- and p-adaptivities are applied; we suggest to coin this methodology e-adaptivity. Copyright © 2008 John Wiley & Sons, Ltd. [less ▲]

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See detailA smoothed finite element method for plate analysis
Nguyen-Xuan, H.; Rabczuk, T.; Bordas, Stéphane UL et al

in Computer Methods in Applied Mechanics and Engineering (2008), 197(13-16), 1184-1203

A quadrilateral element with smoothed curvatures for Mindlin-Reissner plates is proposed. The curvature at each point is obtained by a non-local approximation via a smoothing function. The bending ... [more ▼]

A quadrilateral element with smoothed curvatures for Mindlin-Reissner plates is proposed. The curvature at each point is obtained by a non-local approximation via a smoothing function. The bending stiffness matrix is calculated by a boundary integral along the boundaries of the smoothing elements (smoothing cells). Numerical results show that the proposed element is robust, computational inexpensive and simultaneously very accurate and free of locking, even for very thin plates. The most promising feature of our elements is their insensitivity to mesh distortion. [less ▲]

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See detailA geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures
Rabczuk, Timon; Zi, Goangseup; Bordas, Stéphane UL et al

in Engineering Fracture Mechanics (2008), 75(16), 4740-4758

A three-dimensional meshfree method for modeling arbitrary crack initiation and crack growth in reinforced concrete structure is presented. This meshfree method is based on a partition of unity concept ... [more ▼]

A three-dimensional meshfree method for modeling arbitrary crack initiation and crack growth in reinforced concrete structure is presented. This meshfree method is based on a partition of unity concept and formulated for geometrically non-linear problems. The crack kinematics are obtained by enriching the solution space in order to capture the correct crack kinematics. A cohesive zone model is used after crack initiation. The reinforcement modeled by truss or beam elements is connected by a bond model to the concrete. We applied the method to model the fracture of several reinforced concrete structures and compared the results to experimental data. [less ▲]

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See detailA simple error estimator for extended finite elements
Bordas, Stéphane UL; Duflot, Marc; Le, Phong

in Communications in Numerical Methods in Engineering (2008), 24(11), 961-971

This short communication presents the idea of an a posteriori error estimate for enriched (extended) finite elements (XFEM). The enhanced strain field against which the XFEM strains are compared, is ... [more ▼]

This short communication presents the idea of an a posteriori error estimate for enriched (extended) finite elements (XFEM). The enhanced strain field against which the XFEM strains are compared, is computed through extended moving least-squares smoothing constructed using the diffraction method to preserve the discontinuity. The error estimator is the L2 norm of the difference of the XFEM strain with the enhanced strain. We prove the concept of the proposed method on a 1D example with a singular solution and a 2D fracture mechanics example and conclude with some future work based on our paradigm. [less ▲]

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See detailComparison of recently developed recovery type discretization error estimators for the extended finite element method
Ródenas, J. J.; Duflot, Marc; Bordas, Stéphane UL et al

in Schrefler, B A; Perego, U (Eds.) 8th World Congress on Computational Mechanics (WCCM8). 5th.European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) (2008)

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