References of "Bordas, Stéphane 50000969"
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See detailReal-time Error Control for Surgical Simulation
Bui, Huu Phuoc UL; Tomar, Satyendra UL; Bordas, Stéphane UL

E-print/Working paper (2017)

Real-time simulations are becoming increasingly common for various applications, from geometric design to medical simulation. Two of the main factors concurrently involved in defining the accuracy of ... [more ▼]

Real-time simulations are becoming increasingly common for various applications, from geometric design to medical simulation. Two of the main factors concurrently involved in defining the accuracy of surgical simulations are: the modeling error and the discretization error. Most work in the area has been looking at the above sources of error as a compounded, lumped, overall error. Little or no work has been done to discriminate between modeling error (e.g. needle-tissue interaction, choice of constitutive models) and discretization error (use of approximation methods like FEM). However, it is impossible to validate the complete surgical simulation approach and, more importantly, to understand the sources of error, without evaluating both the discretization error and the modeling error. Our objective is thus to devise a robust and fast approach to measure the discretization error via a posteriori error estimates, which are then used for local remeshing in surgical simulations. To ensure that the approach can be used in clinical practice, the method should be robust enough to deal, as realistically as possible, with the interaction of surgical tools with the organ, and fast enough for real-time simulations. The approach should also lead to an improved convergence so that an economical mesh is obtained at each time step. The final goal is to achieve optimal convergence and the most economical mesh, which will be studied in our future work. [less ▲]

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See detailA linear smoothed higher-order CS-FEM for the analysis of notched laminated composites
Wan, Detao; Hu, Dean; Natarajan, Sundararajan et al

in Engineering Analysis with Boundary Elements (2017), 85

Higher-order elements with highly accurate solutions are attractive for stress analysis and stress concentration problems. However, the distorted eight-node serendipity quadrilateral element is known to ... [more ▼]

Higher-order elements with highly accurate solutions are attractive for stress analysis and stress concentration problems. However, the distorted eight-node serendipity quadrilateral element is known to yield inaccurate re- sults and sub-optimal convergence rate. In this paper, we present a higher order CS-FEM to alleviate the effect of distorted mesh and guarantee the quality of solutions by employing a linear smoothing technique over eight-node quadratic serendipity elements. The modified. strain matrix is computed by the divergence theorem between the nodal shape functions and their derivatives using Taylor’s expansion of the weak form. The proposed method eliminates the need for isoparametric mapping and numerical studies demonstrate that the proposed method is insensitive to mesh distortion. The improved accuracy and superior convergence rates are numerically demon- strated with a few benchmark problems. The analysis of the stress concentration around cutouts also proves that the present method has good performance for the laminated composites. [less ▲]

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See detailA fully smoothed XFEM for analysis of axisymmetric problems with weak discontinuities
Wan, Detao; Hu, Dean; Natarajan, Sundararajan et al

in International Journal for Numerical Methods in Engineering (2017), 110(3), 203-226

In this paper, we propose a fully smoothed extended finite element method (SmXFEM) for axisymmetric problems with weak discontinuities. The salient feature of the proposed approach is that all the terms ... [more ▼]

In this paper, we propose a fully smoothed extended finite element method (SmXFEM) for axisymmetric problems with weak discontinuities. The salient feature of the proposed approach is that all the terms in the stiffness and mass matrixes can be computed by smoothing technique. This is accomplished by combining the Green’s divergence theorem with the evaluation of indefinite integral based on smoothing technique, which is used to transform the domain integral into boundary integral. The proposed technique completely eliminates the need for isoparametric mapping and the computing of Jacobian matrix even for the mass matrix. When employed over the enriched elements, the proposed technique does not require sub-triangulation for the purpose of numerical integration. The accuracy and convergence properties of the proposed technique are demonstrated with a few problems in elastostatics and elastodynamics with weak discontinuities. It can be seen that the proposed technique yields stable and accurate solutions and is less sensitive to mesh distortion. [less ▲]

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See detailA linear smoothed quadratic finite element for the analysis of laminated composite Reissner–Mindlin plates
Wan, Detao; Hu, Dean; Natarajan, Sundararajan et al

in Composite Structures (2017), 180

It is well known that the high-order elements have significantly improved the accuracy of solutions in the traditional finite element analysis, but the performance of high-order elements is restricted by ... [more ▼]

It is well known that the high-order elements have significantly improved the accuracy of solutions in the traditional finite element analysis, but the performance of high-order elements is restricted by the shear-locking and distorted meshes for the plate problems. In this paper, a linear smoothed eight-node Reissner-Mindlin plate element (Q8 plate element) based on the first order shear deformation theory is developed for the static and free vibration analysis of laminated composite plates, the computation of the interior derivatives of shape function and isoparametric mapping can be removed. The strain matrices are modified with a linear smoothing technique by using the divergence theorem between the nodal shape functions and their derivatives in Taylor’s expansion. Moreover, the first order Taylor’s expansion is also employed for the construction of stiffness matrix to satisfy the linear strain distribution. Several numerical examples indicate that the novel Q8 plate element has good performance to alleviate the shear-locking phenomenon and improve the quality of the solutions with distorted meshes. [less ▲]

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See detailAn implicit potential method along with a meshless technique for incompressible fluid flows for regular and irregular geometries in 2D and 3D
Bourantas, Georgios UL; Loukopoulos, V. C.; Chowdhury, H. A. et al

in Engineering Analysis with Boundary Elements (2017), 77

We present the Implicit Potential (IPOT) numerical scheme developed in the framework of meshless point collocation. The proposed scheme is used for the numerical solution of the steady state ... [more ▼]

We present the Implicit Potential (IPOT) numerical scheme developed in the framework of meshless point collocation. The proposed scheme is used for the numerical solution of the steady state, incompressible Navier-Stokes (N-S) equations in their primitive variable (u-v-w-p) formulation. The governing equations are solved in their strong form using either a collocated or a semi-staggered type meshless nodal configuration. The unknown field functions and derivatives are calculated using the Modified Moving Least Squares (MMLS) interpolation method. Both velocity-correction and pressure correction methods applied ensure the incompressibility constraint and mass conservation. The proposed meshless point collocation (MPC) scheme has the following characteristics: (i) it can be applied, in a straightforward manner to: steady, unsteady, internal and external fluid flows in 2D and 3D, (ii) it equally applies to regular an irregular geometries, (iii) a distribution of points is sufficient, no numerical integration in space nor any mesh structure are required, (iv) there is no need for pressure boundary conditions since no pressure constitutive equation is solved, (v) it is quite simple and accurate, (vi) results can be obtained using collocated or semi-staggered nodal distributions, (vii) there is no need to compute the velocity potential nor the unit normal vectors and (viii) there is no need for a curvilinear system of coordinates. Simulations of fluid flow in 2D and 3D for regular and irregular geometries indicate the validity of the proposed methodology. [less ▲]

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See detailError-controlled adaptive extended finite element method for 3D linear elastic crack propagation
Jin, Y.; González-Estrada, O. A.; Pierard, O. et al

in Computer Methods in Applied Mechanics & Engineering (2017), 318

We present a simple error estimation and mesh adaptation approach for 3D linear elastic crack propagation simulations using the eXtended Finite Element Method (X-FEM). A global extended recovery technique ... [more ▼]

We present a simple error estimation and mesh adaptation approach for 3D linear elastic crack propagation simulations using the eXtended Finite Element Method (X-FEM). A global extended recovery technique (Duflot and Bordas, 2008) is used to quantify the interpolation error. Based on this error distribution, four strategies relying on two different mesh optimality criteria are compared. The first aims at homogenizing the error distribution. The second minimizes the total number of elements given a target global error level. We study the behaviour of these criteria in the context of cracks treated by an X-FE approach. In particular, we investigate the convergence rates at the element-level depending its enrichment type. We conclude on the most suitable refinement criterion and propose and verify a strategy for mesh adaptation on 3D damage tolerance assessment problems. [less ▲]

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See detailGuaranteed error bounds in homogenisation: an optimum stochastic approach to preserve the numerical separation of scales
Paladim, Daniel-Alves; de Almeida, José Paulo Baptista; Bordas, Stéphane UL et al

in International Journal for Numerical Methods in Engineering (2017), 110(2), 103132

This paper proposes a new methodology to guarantee the accuracy of the homogenisation schemes that are traditionally employed to approximate the solution of PDEs with random, fast evolving diffusion ... [more ▼]

This paper proposes a new methodology to guarantee the accuracy of the homogenisation schemes that are traditionally employed to approximate the solution of PDEs with random, fast evolving diffusion coefficients. We typically consider linear elliptic diffusion problems in randomly packed particulate composites. Our work extends the pioneering work presented in [26,32] in order to bound the error in the expectation and second moment of quantities of interest, without ever solving the fine-scale, intractable stochastic problem. The most attractive feature of our approach is that the error bounds are computed without any integration of the fine-scale features. Our computations are purely macroscopic, deterministic, and remain tractable even for small scale ratios. The second contribution of the paper is an alternative derivation of modelling error bounds through the Prager-Synge hypercircle theorem. We show that this approach allows us to fully characterise and optimally tighten the interval in which predicted quantities of interest are guaranteed to lie. We interpret our optimum result as an extension of Reuss-Voigt approaches, which are classically used to estimate the homogenised diffusion coefficients of composites, to the estimation of macroscopic engineering quantities of interest. Finally, we make use of these derivations to obtain an efficient procedure for multiscale model verification and adaptation. [less ▲]

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See detailGradient plasticity crack tip characterization by means of the extended finite element method
Martínez-Pañeda, Emilio; Natarajan, Sundar; Bordas, Stéphane UL

in Computational Mechanics (2017)

Strain gradient plasticity theories are being widely used for fracture assessment, as they provide a richer description of crack tip fields by incorporating the influence of geometrically necessary ... [more ▼]

Strain gradient plasticity theories are being widely used for fracture assessment, as they provide a richer description of crack tip fields by incorporating the influence of geometrically necessary dislocations. Characterizing the behavior at the small scales involved in crack tip deformation requires, however, the use of a very refined mesh within microns to the crack. In this work a novel and efficient gradient-enhanced numerical framework is developed by means of the extended finite element method (X-FEM). A mechanism-based gradient plasticity model is employed and the approximation of the displacement field is enriched with the stress singularity of the gradient-dominated solution. Results reveal that the proposed numerical methodology largely outperforms the standard finite element approach. The present work could have important implications on the use of microstructurally-motivated models in large scale applications. The non-linear X-FEM code developed in MATLAB can be downloaded from www.empaneda.com/codes. [less ▲]

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See detailStable 3D XFEM/vector-level sets for non-planar 3D crack propagation and comparison of enrichment schemes
Agathos, Konstantinos UL; Ventura, Giulio; Chatzi, Eleni et al

in International Journal for Numerical Methods in Engineering (2017)

We present a three-dimensional (3D) vector level set method coupled to a recently developed stable extended finite element method (XFEM). We further investigate a new enrichment approach for XFEM adopting ... [more ▼]

We present a three-dimensional (3D) vector level set method coupled to a recently developed stable extended finite element method (XFEM). We further investigate a new enrichment approach for XFEM adopting discontinuous linear enrichment functions in place of the asymptotic near-tip functions. Through the vector level set method, level set values for propagating cracks are obtained via simple geometrical operations, eliminating the need for solution of differential evolution equations. The first XFEM variant ensures optimal convergence rates by means of geometrical enrichment, i.e., the use of enriched elements in a fixed volume around the crack front, without giving rise to conditioning problems. The linear enrichment approach significantly simplifies implementation and reduces the computational cost associated with numerical integration. The two dicretization schemes are tested for different benchmark problems, and their combination to the vector level set method is verified for non-planar crack propagation problems. [less ▲]

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See detailReal-time Error Control for Surgical Simulation
Phuoc Bui, Huu; Tomar, Satyendra; Courtecuisse, Hadrien et al

in IEEE Transactions on Biomedical Engineering (2017)

To present the first real-time a posteriori error-driven adaptive finite element approach for realtime simulation and to demonstrate the method on a needle insertion problem. Methods: We use corotational ... [more ▼]

To present the first real-time a posteriori error-driven adaptive finite element approach for realtime simulation and to demonstrate the method on a needle insertion problem. Methods: We use corotational elasticity and a frictional needle/tissue interaction model. The problem is solved using finite elements within SOFA. The refinement strategy relies upon a hexahedron-based finite element method, combined with a posteriori error estimation driven local h-refinement, for simulating soft tissue deformation. Results: We control the local and global error level in the mechanical fields (e.g. displacement or stresses) during the simulation. We show 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. Conclusions: Error control guarantees that a tolerable error level is not exceeded during the simulations. Local mesh refinement accelerates simulations. Significance: Our work provides a first step to discriminate between discretization error and modeling error by providing a robust quantification of discretization error during simulations. [less ▲]

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See detailNumerical evaluation of buckling behaviour induced by compression on patch-repaired composites
Deng, Jian; Zhou, Guangming; Bordas, Stéphane UL et al

in Composite Structures (2017), 168

A progressive damage model is proposed to predict buckling strengths and failure mechanisms for both symmetric and asymmetric patch repaired carbon-fibre reinforced laminates subjected to compression ... [more ▼]

A progressive damage model is proposed to predict buckling strengths and failure mechanisms for both symmetric and asymmetric patch repaired carbon-fibre reinforced laminates subjected to compression without lateral restrains. Solid and cohesive elements are employed to discretize composite and adhesive layers, respectively. Coupling with three dimensional strain failure criteria, an energy-based crack band model is applied to address the softening behaviour in composites with mesh dependency elimination. Both laminar and laminate scaled failure are addressed. Patch debonding is simulated by the cohesive zone model with a trapezoidal traction–separation law applied for the ductile adhesive. Geometric imperfection is introduced into the nonlinear analysis by the first order linear buckling configuration. Regarding strengths and failure patterns, the simulation demonstrates an accurate and consistent prediction compared with experimental observations. Though shearing is the main contributor to damage initiation in adhesive, stress analysis shows that lateral deformation subsequently reverses the distribution of normal stresses which stimulates patch debonding at one of the repair sides. The influence of patch dimensions on strengths and failure mechanisms can be explained by stress distributions in adhesive and lateral deformation of repairs. Comparison between symmetric and asymmetric regarding strength and failure modes shows that structural asymmetry can intensify lateral flexibility. This resulted in earlier patch debonding and negative effects on strengths. [less ▲]

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See detailProgramming the material point method in Julia
Sinaie, Sina; Nguyen, Viet Ha UL; Nguyen, Chi Thanh et al

in Advances in Engineering Software (2017), 105

This article presents the implementation of the material point method (MPM) using Julia. Julia is an open source, multi-platform, high-level, high-performance dynamic programming language for technical ... [more ▼]

This article presents the implementation of the material point method (MPM) using Julia. Julia is an open source, multi-platform, high-level, high-performance dynamic programming language for technical computing, with syntax that is familiar to Matlab and Python programmers. MPM is a hybrid particle-grid approach that combines the advantages of Eulerian and Lagrangian methods and is suitable for complex solid mechanics problems involving contact, impact and large deformations. We will show that a Julia based MPM code, which is short, compact and readable and uses only Julia built in features, performs much better (with speed up of up to 8) than a similar Matlab based MPM code for large strain solid mechanics simulations. We share our experiences of implementing MPM in Julia and demonstrate that Julia is a very interesting platform for rapid development in the field of scientific computing. [less ▲]

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See detailTrefftz polygonal finite element for linear elasticity: convergence, accuracy, and properties
Hirshikesh; Natarajan, Sundararajan; Ratna Kumar, A. K. et al

in Asia Pacific Journal on Computational Engineering (2017)

In this paper, the accuracy and the convergence properties of Trefftz finite element method over arbitrary polygons are studied. Within this approach, the unknown displacement field within the polygon is ... [more ▼]

In this paper, the accuracy and the convergence properties of Trefftz finite element method over arbitrary polygons are studied. Within this approach, the unknown displacement field within the polygon is represented by the homogeneous solution to the governing differential equations, also called as the T-complete set. While on the boundary of the polygon, a conforming displacement field is independently defined to enforce the continuity of the field variables across the element boundary. An optimal number of T-complete functions are chosen based on the number of nodes of the polygon and the degrees of freedom per node. The stiffness matrix is computed by the hybrid formulation with auxiliary displacement frame. Results from the numerical studies presented for a few benchmark problems in the context of linear elasticity show that the proposed method yields highly accurate results with optimal convergence rates. [less ▲]

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See detailComputational Sciences Year 2016 Activity Report
Bordas, Stéphane UL

Report (2016)

Born from a bottom-up initiative of Mathematics, Computer Science, Physics and Computational Engineering, Computational Sciences (CoSc) have contributed to create at UL a positive and symbiotic research ... [more ▼]

Born from a bottom-up initiative of Mathematics, Computer Science, Physics and Computational Engineering, Computational Sciences (CoSc) have contributed to create at UL a positive and symbiotic research environment relying on a strong fundamental scientific research core. CoSc will continue to rationalize research efforts across a range of strategic innovation domains by centralizing research and development tools and building upon the existing strengths of the Luxembourgish research and socio-economic landscape. [less ▲]

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See detailElastography under uncertainty
Hale, Jack UL; Farrell, Patrick; Bordas, Stéphane UL

Poster (2016, December 12)

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See detailImage to analysis pipeline: single and double balloons kyphoplasty
Baroli, Davide UL; Hauseux, Paul UL; Hale, Jack UL et al

Poster (2016, December 12)

In this work, we present a semi-automatic pipeline from image to simulation of a patient fractured vertebra after the kyphoplastic augmentation with two balloons. In this procedure, the CT-scan medical ... [more ▼]

In this work, we present a semi-automatic pipeline from image to simulation of a patient fractured vertebra after the kyphoplastic augmentation with two balloons. In this procedure, the CT-scan medical image are pre-processed using open-source software Slice3D for segmentation and 3D reconstruction operation. Then, using geometric processing the 3D surface geometry is enhanced to avoid degenerate element and trigging phenomena on vertebra and cement area. We perform a finite element analysis to evaluate the risk of subsequent vertebral fracture. Finally using Monte-Carlo technique, we assess the propagation of uncertainty of material parameter on the evaluation of this risk. Based on the developed semi-automatic pipelines, it is possible to perform a patient-specific simulation that assesses the successful of kyphoplasty operation. [less ▲]

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See detailBayesian inference for parameter identification in computational mechanics
Rappel, Hussein UL; Beex, Lars UL; Hale, Jack UL et al

Poster (2016, December 12)

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See detailReal-time error control for surgical simulation
Bui, Huu Phuoc UL; Tomar, Satyendra UL; Courtecuisse, Hadrien et al

Poster (2016, December 12)

Objective: To present the first real-time a posteriori error-driven adaptive finite element approach for real-time simulation and to demonstrate the method on a needle insertion problem. Methods: We use ... [more ▼]

Objective: To present the first real-time a posteriori error-driven adaptive finite element approach for real-time simulation and to demonstrate the method on a needle insertion problem. Methods: We use corotational elasticity and a frictional needle/tissue interaction model based on friction. The problem is solved using finite elements within SOFA. The refinement strategy relies upon a hexahedron-based finite element method, combined with a posteriori error estimation driven local $h$-refinement, for simulating soft tissue deformation. Results: We control the local and global error level in the mechanical fields (e.g. displacement or stresses) during the simulation. We show 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. Conclusions: Error control guarantees that a tolerable error level is not exceeded during the simulations. Local mesh refinement accelerates simulations. Significance: Our work provides a first step to discriminate between discretization error and modeling error by providing a robust quantification of discretization error during simulations. [less ▲]

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See detailUncertainty quantification for soft tissue biomechanics
Hauseux, Paul UL; Hale, Jack UL; Bordas, Stéphane UL

Poster (2016, December)

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See detailNumerical methods for fracture/cutting of heterogeneous materials
Sutula, Danas UL; Agathos, Konstantinos UL; Ziaei Rad, Vahid UL et al

Presentation (2016, December)

Detailed reference viewed: 170 (15 UL)