References of "Bordas, Stéphane 50000969"
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See detailLinear smoothing over arbitrary polytopes
Francis, Amrita; Natarajan, Sundararajan; Ortiz-Bernardin, Alejandro et al

Scientific Conference (n.d.)

The conventional constant strain smoothing technique yields less accurate solutions that other techniques such as the conventional polygonal finite element method [1, 2]. In this work, we propose a linear ... [more ▼]

The conventional constant strain smoothing technique yields less accurate solutions that other techniques such as the conventional polygonal finite element method [1, 2]. In this work, we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex poly- topes. The method relies on sub-division of the polytope into simplical subcells; however instead of using a constant smoothing function, we employ a linear smoothing function over each subcell. This gives a new definition for the strain to compute the stiffness matrix. The convergence properties and accuracy of the proposed scheme are discussed by solving few benchmark problems. Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes able to deliver the optimal convergence rate as in traditional quadrilateral and hexahedral finite elements. The accuracy is also improved, and all the methods tested pass the patch test to machine precision. [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 detailLinear smoothed polygonal and polyhedral finite elements
Francis, Amrita; Ortiz-Bernardin, Alejandro; Bordas, Stéphane UL et al

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

It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal ... [more ▼]

It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method. In this work, we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes. The main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain. This new strain is then used in the computation of the stiffness matrix. The convergence properties and accuracy of the proposed scheme are discussed by solving few benchmark problems. Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes to deliver improved accuracy and pass the patch test to machine precision. [less ▲]

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See detailA well-conditioned and optimally convergent XFEM for 3D linear elastic fracture
Agathos, Konstantinos; Chatzi, Eleni; Bordas, Stéphane UL et al

in International Journal for Numerical Methods in Engineering (n.d.)

A variation of the extended finite element method for 3D fracture mechanics is proposed. It utilizes global enrichment and point-wise as well as integral matching of displacements of the standard and ... [more ▼]

A variation of the extended finite element method for 3D fracture mechanics is proposed. It utilizes global enrichment and point-wise as well as integral matching of displacements of the standard and enriched elements in order to achieve higher accuracy, optimal convergence rates and improved conditioning for two and three dimensional crack problems. A bespoke benchmark problem is introduced to determine the method's accuracy in the general 3D case where it is demonstrated that the proposed approach improves the accuracy and reduces the number of iterations required for the iterative solution of the resulting system of equations by 40% for moderately refined meshes and topological enrichment. Moreover, when a fixed enrichment volume is used, the number of iterations required grows at a rate which is reduced by a factor of 2 compared to standard XFEM, diminishing the number of iterations by almost one order of magnitude. [less ▲]

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See detailAn extended finite element method with smooth nodal stress
Peng, Xuan; Kulasegaram, Sivakumar; Bordas, Stéphane UL et al

Report (n.d.)

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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 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 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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