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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 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 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 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 detailA new one point quadrature rule over arbitrary star convex polygon/polyhedron
Natarajan, Sundararajan; Francis, Amrita; Atroshchenko, Elena et al

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

The Linear Smoothing (LS) scheme \cite{francisa.ortiz-bernardin2017} ameliorates linear and quadratic approximations over convex polytopes by employing a three-point integration scheme. In this work, we ... [more ▼]

The Linear Smoothing (LS) scheme \cite{francisa.ortiz-bernardin2017} ameliorates linear and quadratic approximations over convex polytopes by employing a three-point integration scheme. In this work, we propose a linearly consistent one point integration scheme which possesses the properties of the LS scheme with three integration points but requires one third of the integration computational time. The essence of the proposed technique is to approximate the strain by the smoothed nodal derivatives that are determined by the discrete form of the divergence theorem. This is done by the Taylor's expansion of the weak form which facilitates the evaluation of the smoothed nodal derivatives acting as stabilization terms. The smoothed nodal derivatives are evaluated only at the centroid of each integration cell. These integration cells are the simplex subcells (triangle/tetrahedron in two and three dimensions) obtained by subdividing the polytope. The salient feature of the proposed technique is that it requires only $n$ integrations for an $n-$ sided polytope as opposed to $3n$ in~\cite{francisa.ortiz-bernardin2017} and $13n$ integration points in the conventional approach. The convergence properties, the accuracy, and the efficacy of the LS with one point integration scheme are discussed by solving few benchmark problems in elastostatics. [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 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 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 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 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 detailA mass conservative Kalman filter algorithm for thermo-computational fluid dynamics
Introini, Carolina; Baroli, Davide UL; Lorenzi, Stefano et al

in Materials (ISSN 1996-1944) (n.d.)

Computational fluid-dynamics (CFD) is of wide relevance in engineering and science, due to its capability of simulating the three-dimensional flow at various scales. However, the suitability of a given ... [more ▼]

Computational fluid-dynamics (CFD) is of wide relevance in engineering and science, due to its capability of simulating the three-dimensional flow at various scales. However, the suitability of a given model depends on the actual scenarios which are encountered in practice. This challenge of model suitability and calibration could be overcome by a dynamic integration of measured data into the simulation. This paradigm is known as data-driven assimilation (DDA). In this paper, the study is devoted to Kalman filtering, a Bayesian approach, applied to Reynolds-Averaged Navier-Stokes (RANS) equations for turbulent flow. The integration of the Kalman estimator into the PISO segregated scheme was recently investigated by (1). In this work, this approach is extended to the PIMPLE segregated method and to the ther- modynamic analysis of turbulent flow, with the addition of a sub-stepping procedure that ensures mass conservation at each time step and the com- patibility among the unknowns involved. The accuracy of the algorithm is verified with respect to the heated lid-driven cavity benchmark, incorporat- ing also temperature observations, comparing the augmented prediction of the Kalman filter with the CFD solution obtained on a very fine grid. [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 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 & 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 ▲]

Detailed reference viewed: 164 (4 UL)