References of "Kerfriden, P"
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See detailA fast, certified and "tuning free" two-field reduced basis method for the metamodelling of affinely-parametrised elasticity problems
Hoang, K. C.; Kerfriden, P.; Bordas, Stéphane UL

in Computer Methods in Applied Mechanics & Engineering (2016), 298

This paper proposes a new reduced basis algorithm for the metamodelling of parametrised elliptic problems. The developments rely on the Constitutive Relation Error (CRE), and the construction of separate ... [more ▼]

This paper proposes a new reduced basis algorithm for the metamodelling of parametrised elliptic problems. The developments rely on the Constitutive Relation Error (CRE), and the construction of separate reduced order models for the primal variable (displacement) and flux (stress) fields. A two field greedy sampling strategy is proposed to construct these two fields simultaneously and in an efficient manner: at each iteration, one of the two fields is enriched by increasing the dimension of its reduced space in such a way that the CRE is minimised. This sampling strategy is then used as a basis to construct goal-oriented reduced order modelling. The resulting algorithm is certified and “tuning free”: the only requirement from the engineer is the level of accuracy that is desired for each of the outputs of the surrogate. It is also shown to be significantly more efficient in terms of computational expense than competing methodologies. [less ▲]

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See detailAn efficient goal-oriented sampling strategy using reduced basis method for parametrized elastodynamic problems
Hoang, K. C.; Kerfriden, P.; Khoo, B. C. et al

in Numerical Methods for Partial Differential Equations (2015), 31(2), 575-608

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See detailNumerical analysis of the inclusion-crack interaction by the extended finite element method
Natarajan, S; Kerfriden, P; Mahapatra, D Roy et al

in International Journal for Computational Methods in Engineering Science and Mechanics (2014)

One of the partition of unity methods, the extended finite ele- ment method (XFEM), is applied to study the inclusion-crack in- teractions in an elastic medium. Both the inclusions and the crack are ... [more ▼]

One of the partition of unity methods, the extended finite ele- ment method (XFEM), is applied to study the inclusion-crack in- teractions in an elastic medium. Both the inclusions and the crack are modelled within the XFEM framework. A structured quadri- lateral mesh is used and the influence of crack length, the number of inclusions, and the geometry of the inclusions on the crack tip stress field are numerically studied. The interaction integral for non-homogeneous materials is used to compute the stress intensity factors ahead of the crack tip. The accuracy and flexibility of the XFEM is demonstrated by various numerical examples. [less ▲]

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See detailPOD-based model order reduction for the simulation of strong nonlinear evolutions in structures: Application to damage propagation
Kerfriden, P.; Gosselet, P.; Adhikari, S. et al

in IOP Conference Series: Materials Science and Engineering (2014), 10(1),

In this paper, we develop a bridge between POD-based model order reduction techniques and the classical Newton-Krylov solvers to derive an efficient solution procedure for highly nonlinear problems ... [more ▼]

In this paper, we develop a bridge between POD-based model order reduction techniques and the classical Newton-Krylov solvers to derive an efficient solution procedure for highly nonlinear problems undergoing strong topological changes. [less ▲]

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See detailReal-time simulation of contact and cutting of heterogeneous soft-tissues
Courtecuisse, H.; Allard, J.; Kerfriden, P. et al

in Medical Image Analysis (2014), 18(2), 394-410

This paper presents a numerical method for interactive (real-time) simulations, which considerably improves the accuracy of the response of heterogeneous soft-tissue models undergoing contact, cutting and ... [more ▼]

This paper presents a numerical method for interactive (real-time) simulations, which considerably improves the accuracy of the response of heterogeneous soft-tissue models undergoing contact, cutting and other topological changes. We provide an integrated methodology able to deal both with the ill-conditioning issues associated with material heterogeneities, contact boundary conditions which are one of the main sources of inaccuracies, and cutting which is one of the most challenging issues in interactive simulations. Our approach is based on an implicit time integration of a non-linear finite element model. To enable real-time computations, we propose a new preconditioning technique, based on an asynchronous update at low frequency. The preconditioner is not only used to improve the computation of the deformation of the tissues, but also to simulate the contact response of homogeneous and heterogeneous bodies with the same accuracy. We also address the problem of cutting the heterogeneous structures and propose a method to update the preconditioner according to the topological modifications. Finally, we apply our approach to three challenging demonstrators: (i) a simulation of cataract surgery (ii) a simulation of laparoscopic hepatectomy (iii) a brain tumor surgery. © 2013 Elsevier B.V. [less ▲]

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See detailMesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery
González-Estrada, O. A.; Nadal, E.; Ródenas, J. J. et al

in Computational Mechanics (2013)

Goal-oriented error estimates (GOEE) have become popular tools to quantify and control the local error in quantities of interest (QoI), which are often more pertinent than local errors in energy for ... [more ▼]

Goal-oriented error estimates (GOEE) have become popular tools to quantify and control the local error in quantities of interest (QoI), which are often more pertinent than local errors in energy for design purposes (e.g. the mean stress or mean displacement in a particular area, the stress intensity factor for fracture problems). These GOEE are one of the key unsolved problems of advanced engineering applications in, for example, the aerospace industry. This work presents a simple recovery-based error estimation technique for QoIs whose main characteristic is the use of an enhanced version of the Superconvergent Patch Recovery (SPR) technique previously used for error estimation in the energy norm. This enhanced SPR technique is used to recover both the primal and dual solutions. It provides a nearly statically admissible stress field that results in accurate estimations of the local contributions to the discretisation error in the QoI and, therefore, in an accurate estimation of this magnitude. This approach leads to a technique with a reasonable computational cost that could easily be implemented into already available finite element codes, or as an independent postprocessing tool. © 2013 Springer-Verlag Berlin Heidelberg. [less ▲]

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See detailCutting in real time in corotational elasticity and perspectives on simulating cuts
Courtecuisse, H.; Kerfriden, P.; Bordas, Stéphane UL

Book published by Springer (2013)

We focus here on the simulation of surgical acts of types similar to cutting and needle insertion in soft tissue, in real time (500 Hz), where the scale of the surgical instrument is several orders of ... [more ▼]

We focus here on the simulation of surgical acts of types similar to cutting and needle insertion in soft tissue, in real time (500 Hz), where the scale of the surgical instrument is several orders of magnitude smaller than that of the organ. [less ▲]

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See detailMolecular dynamics/xfem coupling by a three-dimensional extended bridging domain with applications to dynamic brittle fracture
Talebi, H.; Silani, M.; Bordas, Stéphane UL et al

in International Journal for Multiscale Computational Engineering (2013), 11(6), 527-541

We propose a method to couple a three-dimensional continuum domain to a molecular dynamics domain to simulate propagating cracks in dynamics. The continuum domain is treated by an extended finite element ... [more ▼]

We propose a method to couple a three-dimensional continuum domain to a molecular dynamics domain to simulate propagating cracks in dynamics. The continuum domain is treated by an extended finite element method to handle the discontinuities. The coupling is based on the bridging domain method, which blends the continuum and atomistic energies. The Lennard-Jones potential is used to model the interactions in the atomistic domain, and the Cauchy-Born rule is used to compute the material behavior in the continuum domain. To our knowledge, it is the first time that a three dimensional extended bridging domain method is reported. To show the suitability of the proposed method, a threedimensional crack problem with an atomistic region around the crack front is solved. The results show that the method is capable of handling crack propagation and dislocation nucleation. © 2013 by Begell House, Inc. [less ▲]

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See detailA partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics
Kerfriden, P.; Goury, O.; Rabczuk, T. et al

in Computer Methods in Applied Mechanics & Engineering (2013), 256

We propose in this paper a reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order ... [more ▼]

We propose in this paper a reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus the numerical effort where it is most needed: around the zones where damage propagates. No a priori knowledge of the damage pattern is required, the extraction of the corresponding spatial regions being based solely on algebra. The efficiency of the proposed approach is demonstrated numerically with an example relevant to engineering fracture. © 2012 Elsevier B.V. [less ▲]

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See detailStatistical extraction of process zones and representative subspaces in fracture of random composites
Kerfriden, P.; Schmidt, K. M.; Rabczuk, T. et al

in International Journal for Multiscale Computational Engineering (2013), 11(3), 253-287

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly ... [more ▼]

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly approximated in a low-dimensional deterministic space. Such a low-dimensional space is obtained by a spectral analysis performed on precomputed solution samples. A greedy algorithm is proposed to identify both process zone and low-dimensional representative subspace for the solution in the complementary region. In addition to the novelty of the tools proposed in this paper for the analysis of localized phenomena, we show that the reduced space generated by the method is a valid basis for the construction of a reduced-order model. © 2013 by Begell House, Inc. [less ▲]

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See detailA computational library for multiscale modeling of material failure
Talebi, H.; Silani, M.; Bordas, Stéphane UL et al

in Computational Mechanics (2013)

We present an open-source software framework called PERMIX for multiscale modeling and simulation of fracture in solids. The framework is an object oriented open-source effort written primarily in Fortran ... [more ▼]

We present an open-source software framework called PERMIX for multiscale modeling and simulation of fracture in solids. The framework is an object oriented open-source effort written primarily in Fortran 2003 standard with Fortran/C++ interfaces to a number of other libraries such as LAMMPS, ABAQUS, LS-DYNA and GMSH. Fracture on the continuum level is modeled by the extended finite element method (XFEM). Using several novel or state of the art methods, the piece software handles semi-concurrent multiscale methods as well as concurrent multiscale methods for fracture, coupling two continuum domains or atomistic domains to continuum domains, respectively. The efficiency of our open-source software is shown through several simulations including a 3D crack modeling in clay nanocomposites, a semi-concurrent FE-FE coupling, a 3D Arlequin multiscale example and an MD-XFEM coupling for dynamic crack propagation. © 2013 Springer-Verlag Berlin Heidelberg. [less ▲]

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See detailCertification of projection-based reduced order modelling in computational homogenisation by the constitutive relation error
Kerfriden, P.; Ródenas, J. J.; Bordas, Stéphane UL

in International Journal for Numerical Methods in Engineering (2013)

SUMMARY: In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the ... [more ▼]

SUMMARY: In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction of a reduced model for the stress field. Upon ensuring that the reduced stress satisfies the equilibrium in the finite element sense, the desired bounding property is obtained. The lower bound is obtained by defining a hierarchical enriched reduced model for the displacement. We show that the sharpness of both error estimates can be seamlessly controlled by adapting the parameters of the corresponding reduced order model. © 2013 John Wiley & Sons, Ltd. [less ▲]

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See detailExtended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth
Chen, L.; Rabczuk, T.; Bordas, Stéphane UL et al

in Computer Methods in Applied Mechanics & Engineering (2012), 209-212

This paper presents a strain smoothing procedure for the extended finite element method (XFEM). The resulting "edge-based" smoothed extended finite element method (ESm-XFEM) is tailored to linear elastic ... [more ▼]

This paper presents a strain smoothing procedure for the extended finite element method (XFEM). The resulting "edge-based" smoothed extended finite element method (ESm-XFEM) is tailored to linear elastic fracture mechanics and, in this context, to outperform the standard XFEM. In the XFEM, the displacement-based approximation is enriched by the Heaviside and asymptotic crack tip functions using the framework of partition of unity. This eliminates the need for the mesh alignment with the crack and re-meshing, as the crack evolves. Edge-based smoothing (ES) relies on a generalized smoothing operation over smoothing domains associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, "super-convergence" and "ultra-accurate" solutions. The present method takes advantage of both the ES-FEM and the XFEM. Thanks to the use of strain smoothing, the subdivision of elements intersected by discontinuities and of integrating the (singular) derivatives of the approximation functions is suppressed via transforming interior integration into boundary integration. Numerical examples show that the proposed method improves significantly the accuracy of stress intensity factors and achieves a near optimal convergence rate in the energy norm even without geometrical enrichment or blending correction. [less ▲]

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See detailLocal/global model order reduction strategy for the simulation of quasi-brittle fracture
Kerfriden, P.; Passieux, J. C.; Bordas, Stéphane UL

in International Journal for Numerical Methods in Engineering (2012), 89(2), 154-179

This paper proposes a novel technique to reduce the computational burden associated with the simulation of localized failure. The proposed methodology affords the simulation of damage initiation and ... [more ▼]

This paper proposes a novel technique to reduce the computational burden associated with the simulation of localized failure. The proposed methodology affords the simulation of damage initiation and propagation while concentrating the computational effort where it is most needed, that is, in the localization zones. To do so, a local/global technique is devised where the global (slave) problem (far from the zones undergoing severe damage and cracking) is solved for in a reduced space computed by the classical proper orthogonal decomposition while the local (master) degrees of freedom (associated with the part of the structure where most of the damage is taking place) are fully resolved. Both domains are coupled through a local/global technique. This method circumvents the difficulties associated with model order reduction for the simulation of highly nonlinear mechanical failure and offers an alternative or complementary approach to the development of multiscale fracture simulators. © 2011 John Wiley & Sons, Ltd. [less ▲]

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See detailOn the role of enrichment and statistical admissibility of recovered fields in a posteriori error estimation for enriched finite element methods
González-Estrada, O. A.; Ródenas, J. J.; Bordas, Stéphane UL et al

in Engineering Computations (2012), 29(8), 814-841

Purpose - The purpose of this paper is to assess the effect of the statistical admissibility of the recovered solution and the ability of the recovered solution to represent the singular solution; also ... [more ▼]

Purpose - The purpose of this paper is to assess the effect of the statistical admissibility of the recovered solution and the ability of the recovered solution to represent the singular solution; also the accuracy, local and global effectivity of recovery-based error estimators for enriched finite element methods (e.g. the extended finite element method, XFEM). Design/methodology/approach - The authors study the performance of two recovery techniques. The first is a recently developed superconvergent patch recovery procedure with equilibration and enrichment (SPR-CX). The second is known as the extended moving least squares recovery (XMLS), which enriches the recovered solutions but does not enforce equilibrium constraints. Both are extended recovery techniques as the polynomial basis used in the recovery process is enriched with singular terms for a better description of the singular nature of the solution. Findings - Numerical results comparing the convergence and the effectivity index of both techniques with those obtained without the enrichment enhancement clearly show the need for the use of extended recovery techniques in Zienkiewicz-Zhu type error estimators for this class of problems. The results also reveal significant improvements in the effectivities yielded by statistically admissible recovered solutions. Originality/value - The paper shows that both extended recovery procedures and statistical admissibility are key to an accurate assessment of the quality of enriched finite element approximations. © Emerald Group Publishing Limited. [less ▲]

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See detailEquilibrated patch recovery for accurate evaluation of upper error bounds in quantities of interest
González-Estrada, O. A.; Ródenas, J. J.; Nadal, E. et al

in ECCOMAS Thematic Conference - ADMOS 2011: International Conference on Adaptive Modeling and Simulation, An IACM Special Interest Conference (2012)

There is an increasing interest on the use of goal-oriented error estimates which help to measure and control the local error on a linear or non-linear quantity of interest (QoI) that might result ... [more ▼]

There is an increasing interest on the use of goal-oriented error estimates which help to measure and control the local error on a linear or non-linear quantity of interest (QoI) that might result relevant for design purposes (e.g. the mean stress value in a particular area, displacements, the stress intensity factor for fracture problems,⋯). In general, residual-based error estimators have been used to obtain upper and lower bounds of the error in quantities of interest for finite element approximations. In this work, we propose a novel a posteriori recovery technique to obtain an upper error bound of the QoI. We use a recovery procedure based on the superconvergent patch recovery (SPR) technique to obtain nearly statically admissible recovered stress fields for the primal and dual problems. This recovery technique was previously used to obtain upper bounds of the error in energy norm and has been used in this paper to obtain a computable version of the upper bound for the quantity of interest. [less ▲]

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See detailError estimation and error bounding in quantities of interest based on equilibrated recovered displacement fields
Nadal, E.; González-Estrada, O. A.; Ródenas, J. J. et al

in ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers (2012)

Over the last ten years there has been an increase on the use of goal-oriented error estimates aimed to quantify the local error on a (non)linear quantity of interest (QoI) that might result relevant for ... [more ▼]

Over the last ten years there has been an increase on the use of goal-oriented error estimates aimed to quantify the local error on a (non)linear quantity of interest (QoI) that might result relevant for design purposes. Residual-based error estimators have been used recursively to obtain upper and lower bounds of the error in quantities of interest for finite element approximations. In this paper, we present a recovery technique for 2D linear elasticity problems, based on the superconvergent patch recovery (SPR), which provides recovered displacement and stress fields that are then utilised to evaluate practical upper and lower error bounds in QoI. [less ▲]

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See detailEnriched Element Free Galerkin Method for Gradient Elasticity
Natarajan, S; Kerfriden, P; Bordas, Stéphane UL et al

Scientific Conference (2011, June)

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See detailNatural frequencies of cracked isotropic & specially orthotropic plates using the extended finite element method
Natarajan, S; Baiz, P; Mahapatra, D Roy et al

Scientific Conference (2011, April)

In this paper, the linear free flexural vibration of cracked isotropic and specially orthotropic plates is studied using the extended finite element method. The mixed interpolation technique of the well ... [more ▼]

In this paper, the linear free flexural vibration of cracked isotropic and specially orthotropic plates is studied using the extended finite element method. The mixed interpolation technique of the well- established MITC4 [1] quadrilateral finite element with 12 standard degrees of freedom per element is used for this study. The natural frequencies of simply supported square plates are computed as a function of crack length and crack location. [less ▲]

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See detailLinear buckling analysis of cracked plates by SFEM and XFEM
Baiz, P. M.; Natarajan, S.; Bordas, Stéphane UL et al

in Journal of Mechanics of Material and Structures (2011), 6(9-10), 1213-1238

In this paper, the linear buckling problem for isotropic plates is studied using a quadrilateral element with smoothed curvatures and the extended finite element method. First, the curvature at each point ... [more ▼]

In this paper, the linear buckling problem for isotropic plates is studied using a quadrilateral element with smoothed curvatures and the extended finite element method. First, the curvature at each point is obtained by a nonlocal approximation via a smoothing function. This element is later coupled with partition of unity enrichment to simplify the simulation of cracks. The proposed formulation suppresses locking and yields elements which behave very well, even in the thin plate limit. The buckling coefficient and mode shapes of square and rectangular plates are computed as functions of crack length, crack location, and plate thickness. The effects of different boundary conditions are also studied. © 2011 by Mathematical Sciences Publishers. [less ▲]

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