References of "Bordas, Stéphane 50000969"
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See detailA smoothed finite element method for shell analysis
Nguyen-Thanh, N.; Rabczuk, T.; Nguyen-Xuan, H. et al

in Computer Methods in Applied Mechanics and Engineering (2008), 198(2), 165-177

A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on ... [more ▼]

A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples. [less ▲]

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See detailA three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics
Rabczuk, Timon; Bordas, Stéphane UL; Zi, Goangseup

in Computational Mechanics (2007), 40(3), 473-495

This paper proposes a three-dimensional meshfree method for arbitrary crack initiation and propagation that ensures crack path continuity for non-linear material models and cohesive laws. The method is ... [more ▼]

This paper proposes a three-dimensional meshfree method for arbitrary crack initiation and propagation that ensures crack path continuity for non-linear material models and cohesive laws. The method is based on a local partition of unity. An extrinsic enrichment of the meshfree shape functions is used with discontinuous and near-front branch functions to close the crack front and improve accuracy. The crack is hereby modeled as a jump in the displacement field. The initiation and propagation of a crack is determined by the loss of hyperbolicity or the loss of material stability criterion. The method is applied to several static, quasi-static and dynamic crack problems. The numerical results very precisely replicate available experimental and analytical results. [less ▲]

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See detailDerivative recovery and a posteriori error estimate for extended finite elements
Bordas, Stéphane UL; Duflot, M.

in Computer Methods in Applied Mechanics and Engineering (2007), 196(35-36), 3381-3399

This paper is the first attempt at error estimation for extended finite elements. The goal of this work is to devise a simple and effective local a posteriori error estimate for partition of unity ... [more ▼]

This paper is the first attempt at error estimation for extended finite elements. The goal of this work is to devise a simple and effective local a posteriori error estimate for partition of unity enriched finite element methods such as the extended finite element method (XFEM). In each element, the local estimator is the L2 norm of the difference between the raw XFEM strain field and an enhanced strain field computed by extended moving least squares (XMLS) derivative recovery obtained from the raw nodal XFEM displacements. The XMLS construction is tailored to the nature of the solution. The technique is applied to linear elastic fracture mechanics, in which near-tip asymptotic functions are added to the MLS basis. The XMLS shape functions are constructed from weight functions following the diffraction criterion to represent the discontinuity. The result is a very smooth enhanced strain solution including the singularity at the crack tip. Results are shown for two- and three-dimensional linear elastic fracture mechanics problems in mode I and mixed mode. The effectivity index of the estimator is close to 1 and improves upon mesh refinement for the studied near-tip problem. It is also shown that for the linear elastic fracture mechanics problems treated, the proposed estimator outperforms one of the superconvergent patch recovery technique of Zienkiewicz and Zhu, which is only C0. Parametric studies of the general performance of the estimator are also carried out. © 2007 Elsevier B.V. All rights reserved. [less ▲]

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See detailA simulation-based design paradigm for complex cast components
Bordas, Stéphane UL; Conley, James. G.; Moran, Brian et al

in Engineering with Computers (2007), 23(1), 25-37

This paper describes and exercises a new design paradigm for cast components. The methodology integrates foundry process simulation, non-destructive evaluation (NDE), stress analysis and damage tolerance ... [more ▼]

This paper describes and exercises a new design paradigm for cast components. The methodology integrates foundry process simulation, non-destructive evaluation (NDE), stress analysis and damage tolerance simulations into the design process. Foundry process simulation is used to predict an array of porosity-related anomalies. The probability of detection of these anomalies is investigated with a radiographic inspection simulation tool (XRSIM). The likelihood that the predicted array of anomalies will lead to a failure is determined by a fatigue crack growth simulation based on the extended finite element method and therefore does not require meshing nor remeshing as the cracks grow. With this approach, the casting modeling provides initial anomaly information, the stress analysis provides a value for the critical size of an anomaly and the NDE assessment provides a detectability measure. The combination of these tools allows for accept/reject criteria to be determined at the early design stage and enables damage tolerant design philosophies. The methodology is applied to the design of a cast monolithic door used on the Boeing 757 aircraft. [less ▲]

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See detailMechanical failure in microstructural heterogeneous materials
Bordas, Stéphane UL; Hoppe, R. H. W.; Petrova, S. I.

in Lecture Notes in Computer Science (2007), 4310 LNCS

Various heterogeneous materials with multiple scales and multiple phases in the microstructure have been produced in the recent years. We consider a mechanical failure due to the initiation and ... [more ▼]

Various heterogeneous materials with multiple scales and multiple phases in the microstructure have been produced in the recent years. We consider a mechanical failure due to the initiation and propagation of cracks in places of high pore density in the microstructures. A multi-scale method based on the asymptotic homogenization theory together with the mesh superposition method (s-version of FEM) is presented for modeling of cracks. The homogenization approach is used on the global domain excluding the vicinity of the crack where the periodicity of the microstructures is lost and this approach fails. The multiple scale method relies on efficient combination of both macroscopic and microscopic models. The mesh superposition method uses two independent (global and local) finite element meshes and the concept of superposing the local mesh onto the global continuous mesh in such a way that both meshes not necessarily coincide. The homogenized material model is considered on the global mesh while the crack is analyzed in the local domain (patch) which allows to have an arbitrary geometry with respect to the underlying global finite elements. Numerical experiments for biomorphic cellular ceramics with porous microstructures produced from natural wood are presented. [less ▲]

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See detailThree-dimensional non-linear fracture mechanics by enriched meshfree methods without asymptotic enrichment
Bordas, Stéphane UL; Zi, G.; Rabczuk, T.

in Proceedings of the IUTAM Symposium on Discretization Methods for Evolving Discontinuities (2007)

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

This paper presents a three-dimensional, extrinsically enriched meshfree method for initiation, 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 fashioned in this work is that only an extrinsic discontinuous enrichment and no near-tip/asymptotic enrichment is required. Instead, a Lagrange multiplier field is added along the crack front to close the crack along the front. This decreases the computational cost and removes difficulties involved with a branch enrichment. Numerical examples treated include the pull-out of a reinforcement bar from a concrete block, and a Taylor bar impact with very large deformation and fragmentation. The results are compared to experimental results, and other simulations from the literature, which shows the robustness and accuracy of the method. © 2007 Springer. [less ▲]

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See detailAn extended finite element library
Bordas, Stéphane UL; Nguyen, P. V.; Dunant, C. et al

in International Journal for Numerical Methods in Engineering (2007), 71(6), 703-732

This paper presents and exercises a general structure for an object-oriented-enriched finite element code. The programming environment provides a robust tool for extended finite element (XFEM ... [more ▼]

This paper presents and exercises a general structure for an object-oriented-enriched finite element code. The programming environment provides a robust tool for extended finite element (XFEM) computations and a modular and extensible system. The programme structure has been designed to meet all natural requirements for modularity, extensibility, and robustness. To facilitate mesh-geometry interactions with hundreds of enrichment items, a mesh generator and mesh database are included. The salient features of the programme are: flexibility in the integration schemes (subtriangles, subquadrilaterals, independent near-tip, and discontinuous quadrature rules); domain integral methods for homogeneous and bi-material interface cracks arbitrarily oriented with respect to the mesh; geometry is described and updated by level sets, vector level sets or a standard method; standard and enriched approximations are independent; enrichment detection schemes: topological, geometrical, narrow-band, etc.; multi-material problem with an arbitrary number of interfaces and slip-interfaces; non-linear material models such as J2 plasticity with linear, isotropic and kinematic hardening. To illustrate the possible applications of our paradigm, we present 2D linear elastic fracture mechanics for hundreds of cracks with local near-tip refinement, and crack propagation in two dimensions as well as complex 3D industrial problems. Copyright © 2007 John Wiley & Sons, Ltd. [less ▲]

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See detailArchitecture tradeoffs of integrating a mesh generator to partition of unity enriched object-oriented finite element software
Dunant, C.; Nguyen, V. P.; Belgasmia, M. et al

in European Journal of Computational Mechanics (2007), 16(2), 237-258

We explore the tradeoffs of using an internal mesher in a XFEM code. We show that it allows an efficient enrichement detection scheme, while retaining the ability to have welladapted meshes. We provide ... [more ▼]

We explore the tradeoffs of using an internal mesher in a XFEM code. We show that it allows an efficient enrichement detection scheme, while retaining the ability to have welladapted meshes. We provide benchmarks highlighting the considerable gains which can be expected from a well designed architecture. The efficiency of the proposed algorithm is shown by solving fracture mechanics problems of densely micro-cracked bodies including adaptive mesh refinement. [less ▲]

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See detailEnriched finite elements and level sets for damage tolerance assessment of complex structures
Bordas, Stéphane UL; Moran, B.

in Engineering Fracture Mechanics (2006), 73(9), 1176-1201

The extended finite element method (X-FEM) has recently emerged as an alternative to meshing/remeshing crack surfaces in computational fracture mechanics thanks to the concept of discontinuous and ... [more ▼]

The extended finite element method (X-FEM) has recently emerged as an alternative to meshing/remeshing crack surfaces in computational fracture mechanics thanks to the concept of discontinuous and asymptotic partition of unity enrichment (PUM) of the standard finite element approximation spaces. Level set methods have been recently coupled with X-FEM to help track the crack geometry as it grows. However, little attention has been devoted to employing the X-FEM in real-world cases. This paper describes how X-FEM coupled with level set methods can be used to solve complex three-dimensional industrial fracture mechanics problems through combination of an object-oriented (C++) research code and a commercial solid modeling/finite element package (EDS-PLM/ I-DEAS®). The paper briefly describes how object-oriented programming shows its advantages to efficiently implement the proposed methodology. Due to enrichment, the latter method allows for multiple crack growth scenarios to be analyzed with a minimal amount of remeshing. Additionally, the whole component contributes to the stiffness during the whole crack growth simulation. The use of level set methods permits the seamless merging of cracks with boundaries. To show the flexibility of the method, the latter is applied to damage tolerance analysis of a complex aircraft component. © 2006 Elsevier Ltd. All rights reserved. [less ▲]

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See detailLinear smoothed extended finite element method
Murugesan; Natarajan, Sundararajan; Gadyam, Palani et al

E-print/Working paper (n.d.)

The extended finite element method (XFEM) was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions. This enables elements to ... [more ▼]

The extended finite element method (XFEM) was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions. This enables elements to be split by a discontinuity, strong or weak and hence requires the integration of discontinuous functions or functions with discontinuous derivatives over elementary volumes. Moreover, in the case of open surfaces and singularities, special, usually non-polynomial functions must also be integrated.A variety of approaches have been proposed to facilitate these special types of numerical integration, which have been shown to have a large impact on the accuracy and convergence of the numerical solution. The smoothed extended finite element method (SmXFEM) [1], for example, makes numerical integration elegant and simple by transforming volume integrals into surface integrals. However, it was reported in [1, 2] that the strain smoothing is inaccurate when non-polynomial functions are in the basis. This is due to the constant smoothing function used over the smoothing domains which destroys the effect of the singularity. In this paper, we investigate the benefits of a recently developed Linear smoothing procedure [3] which provides better approximation to higher order polynomial fields in the basis. Some benchmark problems in the context of linear elastic fracture mechanics (LEFM) are solved to compare the standard XFEM, the constant-smoothed XFEM (Sm-XFEM) and the linear-smoothed XFEM (LSm-XFEM). We observe that the convergence rates of all three methods are the same. The stress intensity factors (SIFs) computed through the proposed LSm-XFEM are however more accurate than that obtained through Sm-XFEM. To conclude, compared to the conventional XFEM, the same order of accuracy is achieved at a relatively low computational effort. [less ▲]

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See detailCoupled Molecular Dynamics and Finite Element Method: simulations of kinetics induced by field mediated interaction
Cascio, Michele; Baroli, Davide UL; Deretzsis, Ioannis et al

in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (n.d.)

A computational approach coupling Molecular Dynamics (MD)-Finite Element Method (FEM) techniques is here proposed for the theoretical study of the dynamics of particles subjected to the electromechanical ... [more ▼]

A computational approach coupling Molecular Dynamics (MD)-Finite Element Method (FEM) techniques is here proposed for the theoretical study of the dynamics of particles subjected to the electromechanical forces. The system consists in spherical particles (modeled as micrometric rigid bodies with proper densities and dielectric functions) suspended in a colloidal solution which flows in a microfluidic channel in the presence of a generic non-uniform variable electric field, generated by electrodes. The particles are subjected to external forces (e.g. drag or gravity) which satisfy the particle-like formulation, typical of the MD approach, and to electromechanical force which in turn needs, during the equation of the motion integration, the self-consistent solutions in three dimensions of correct continuum field equation. In the MD-FEM method used in this work, Finite Element Method is applied to solve the continuum field equation and MD technique is applied to the stepwise explicit integration of equation of the motion. Our work shows the potential of coupled MD-FEM for the study of electromechanical particles and opens the double perspective to use a) MD away from the field of the atomistic simulation and b) the continuum/particle approach to another case where the conventional forces’ evaluation method used in MD is not applicable. [less ▲]

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See detailControlling the Error on Target Motion through Real-time Mesh Adaptation: Applications to Deep Brain Stimulation
Bui, Huu Phuoc UL; Tomar, Satyendra UL; Courtecuisse, Hadrien et al

E-print/Working paper (n.d.)

We present an error-controlled mesh refinement procedure for needle insertion simulation and apply it to the simulation of electrode implantation for deep brain stimulation, including brain shift. Our ... [more ▼]

We present an error-controlled mesh refinement procedure for needle insertion simulation and apply it to the simulation of electrode implantation for deep brain stimulation, including brain shift. Our approach enables to control the error in the computation of the displacement and stress fields around the needle tip and needle shaft by suitably refining the mesh, whilst maintaining a coarser mesh in other parts of the domain. We demonstrate through academic and practical examples that our approach increases the accuracy of the displacement and stress fields around the needle without increasing the computational expense. This enables real-time simulations. The proposed methodology has direct implications to increase the accuracy and control the computational expense of the simulation of percutaneous procedures such as biopsy, brachytherapy, regional anesthesia, or cryotherapy and can be essential to the development of robotic guidance. [less ▲]

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See detailReal-time error controlled adaptive mesh refinement in surgical simulation: Application to needle insertion simulation
Bui, Huu Phuoc; Tomar, Satyendra UL; Courtecuisse, Hadrien et al

in IEEE Transactions on Biomedical Engineering (n.d.)

This paper presents the first real-time discretisation-error-driven adaptive finite element approach for corotational elasticity problems involving strain localisation. We propose a hexahedron-based ... [more ▼]

This paper presents the first real-time discretisation-error-driven adaptive finite element approach for corotational elasticity problems involving strain localisation. We propose a hexahedron-based finite element method combined with local oct-tree $h$-refinement, driven by a posteriori error estimation, for simulating soft tissue deformation. This enables to control the local error and global error level in the mechanical fields during the simulation. The local error level is used to refine the mesh only where it is needed, while maintaining a coarser mesh elsewhere. We investigate the convergence of the algorithm on academic examples, and demonstrate its practical usability on a percutaneous procedure involving needle insertion in a liver. For the latter case, we compare the force displacement curves obtained from the proposed adaptive algorithm with that obtained from a uniform refinement approach. [less ▲]

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See detailSolving the stochastic Burgers equation with a sensitivity derivative-driven Monte Carlo method
Hauseux, Paul UL; Hale, Jack UL; Bordas, Stéphane UL

Software (n.d.)

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See detailBayesian inference for the stochastic identification of elastoplastic material parameters: Introduction, misconceptions and insights
Rappel, Hussein UL; Beex, Lars UL; Hale, Jack UL et al

E-print/Working paper (n.d.)

We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material ... [more ▼]

We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material parameters. For this purpose a single spring is considered, for which the stress-strain curves are artificially created. Besides offering a didactic introduction to BI, this paper proposes an approach to incorporate statistical errors both in the measured stresses, and in the measured strains. It is assumed that the uncertainty is only due to measurement errors and the material is homogeneous. Furthermore, a number of possible misconceptions on BI are highlighted based on the purely elastic case. [less ▲]

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See detailA two-dimensional isogeometric boundary element method for linear elastic fracture: a path towards damage tolerance analysis without meshing
Peng, Xuan; Atroshchenko, Elena; Kulasegaram, Sivakumar et al

Report (n.d.)

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See detailCoarsen Graining: A Renewal Concept of Efficient Adaptivity Techniques for Multiscale Models
Shih-Wei, Yang; Pattabhi Ramaiah, Budarapu; Roy Mahapatra, Debiprasad et al

in Computer Methods in Applied Mechanics and Engineering (n.d.)

This paper presents a multiscale method for the quasi-static crack propagation. The coarse region is modeled by the di erential reproducing kernel particle(DRKP) method. The coupling between the coarse ... [more ▼]

This paper presents a multiscale method for the quasi-static crack propagation. The coarse region is modeled by the di erential reproducing kernel particle(DRKP) method. The coupling between the coarse scale and ne scale is realized through ghost atoms. The ghost atoms positions are interpolated from the coarse scale solution and enforced as boundary conditions on the ne scale. The ne scale region is adaptively enlarged as the crack propagates and the region behind the crack tip is adaptively coarsened. The centro symmetry parameter(CSP) is used to detect the crack tip location. The triangular lattice corresponds to the lattice structure of the (111) plane of an FCC crystal in the ne scale region. The Lennard-Jones potential is used to model the atom-atom interactions. The method is implemented in two dimensions. The results are compared to pure atomistic simulations and show excellent agreement. [less ▲]

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See detailWeakening the tight coupling between geometry and simulation in isogeometric analysis: from sub- and super- geometric analysis to Geometry Independent Field approximaTion (GIFT)
Atroshchenko, Elena; Xu, Gang; Tomar, Satyendra UL et al

E-print/Working paper (n.d.)

This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution ... [more ▼]

This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main advantage of isogeometric analysis, i.e. preserves the original, exact CAD geometry (for example, given by NURBS), but allows pairing it with an approximation space which is more suitable/flexible for analysis, for example, T-splines, LR-splines, (truncated) hierarchical B-splines, and PHT-splines. This generalization offers the advantage of adaptive local refinement without the need to re-parameterize the domain, and therefore without weakening the link with the CAD model. We demonstrate the use of the method with different choices of the geometry and field splines, and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for non-nested spaces. [less ▲]

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See detailMinimum energy multiple crack propagation. Part III: XFEM computer implementation and applications.
Sutula, Danas UL; Bordas, Stéphane UL

in Engineering Fracture Mechanics (n.d.)

The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions. The principle of minimum total energy, i.e. the sum of the potential and ... [more ▼]

The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions. The principle of minimum total energy, i.e. the sum of the potential and fracture energies, which stems directly from the Griffith's theory of cracks, is applied to the problem of arbitrary crack growth in 2D. The proposed formulation enables minimisation of the total energy of the mechanical system with respect to the crack extension directions and crack extension lengths to solve for the evolution of the mechanical system over time. The three parts focus, in turn, on (I) the theory of multiple crack growth including competing cracks, (II) the discrete solution by the extended finite element method using the minimum-energy formulation, and (III) the aspects of computer implementation within the Matlab programming language. The key contributions of Part-III of the three-part paper are as follows: (1) implementation of XFEM in Matlab with emphasis on the design of the code to enable fast and efficient computational times of fracture problems involving multiple cracks and arbitrary crack intersections, (2) verification of the minimum energy criterion and comparison with the maximum tension criterion via multiple benchmark studies, and (3) we propose a numerical improvement to the crack growth direction criterion that gives significant improvements in accuracy and convergence rates of the fracture paths, especially on coarse meshes. The comparisons of the fracture paths obtained by the maximum tension (or maximum hoop-stress) criterion and the energy minimisation approach via a multitude of numerical case studies show that both criteria converge to virtually the same fracture solutions albeit from opposite directions. In other words, it is found that the converged fracture path lies in between those obtained by each criterion on coarser meshes. Thus, a modified crack growth direction criterion is proposed that assumes the average direction of the directions obtained by the maximum tension and the minimum energy criteria. The numerical results show significant improvements in accuracy (especially on coarse discretisations) and convergence rates of the fracture paths. Finally, the open-source Matlab code, documentation, benchmarks and example cases are included as supplementary material. [less ▲]

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