References of "Bordas, Stéphane 50000969"
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See detailNitsche’s method for two and three dimensional NURBS patch coupling
Nguyen, Vinh-Phu; Kerfriden, Pierre; Brino, Marco et al

in Computational Mechanics (in press)

We present a Nitche’s method to couple non-conforming two and three-dimensional NURBS (Non Uniform Rational B-splines) patches in the context of isogeometric analysis (IGA). We present results for linear ... [more ▼]

We present a Nitche’s method to couple non-conforming two and three-dimensional NURBS (Non Uniform Rational B-splines) patches in the context of isogeometric analysis (IGA). We present results for linear elastostatics in two and and three-dimensions. The method can deal with surface-surface or volume-volume coupling, and we show how it can be used to handle heterogeneities such as inclusions. We also present preliminary results on modal analysis. This simple coupling method has the potential to increase the applicability of NURBS-based isogeometric analysis for practical applications. [less ▲]

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See detailA refinement indicator for adaptive quasicontinuum approaches for structural lattices
Chen, Li UL; Berke, Peter; Massart, Thierry et al

in International Journal for Numerical Methods in Engineering (in press)

The quasicontinuum method is a concurrent multiscale approach in which lattice models are fully resolved in small regions of interest and coarse-grained elsewhere. Since the method was originally proposed ... [more ▼]

The quasicontinuum method is a concurrent multiscale approach in which lattice models are fully resolved in small regions of interest and coarse-grained elsewhere. Since the method was originally proposed to accelerate atomistic lattice simulations, its refinement criteria – that drive refining coarse-grained regions and/or increasing fully-resolved regions – are generally associated with quantities relevant to the atomistic scale. In this contribution, a new refinement indicator is presented, based on the energies of dedicated cells at coarse-grained domain surfaces. This indicator is incorporated in an adaptive scheme of a generalization of the quasicontinuum method able to consider periodic representative volume elements, like the ones employed in most computational homogenization approaches. However, this indicator can also be used for conventional quasicontinuum frameworks. Illustrative numerical examples of elastic indentation and scratch of different lattices demonstrate the capabilities of the refinement indicator and its impact on adaptive quasicontinuum simulations. [less ▲]

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See detailHierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project
Bulle, Raphaël UL; Hale, Jack UL; Lozinski, Alexei et al

in Computers and Mathematics with Applications (2023), 131

In the seminal paper of Bank and Weiser [Math. Comp., 44 (1985), pp.283-301] a new a posteriori estimator was introduced. This estimator requires the solution of a local Neumann problem on every cell of ... [more ▼]

In the seminal paper of Bank and Weiser [Math. Comp., 44 (1985), pp.283-301] a new a posteriori estimator was introduced. This estimator requires the solution of a local Neumann problem on every cell of the finite element mesh. Despite the promise of Bank-Weiser type estimators, namely locality, computational efficiency, and asymptotic sharpness, they have seen little use in practical computational problems. The focus of this contribution is to describe a novel implementation of hierarchical estimators of the Bank-Weiser type in a modern high-level finite element software with automatic code generation capabilities. We show how to use the estimator to drive (goal-oriented) adaptive mesh refinement and to mixed approximations of the nearly-incompressible elasticity problems. We provide comparisons with various other used estimators. An open-source implementation based on the FEniCS Project finite element software is provided as supplementary material. [less ▲]

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See detailConvolution, aggregation and attention based deep neural networks for accelerating simulations in mechanics
Deshpande, Saurabh UL; Sosa, Raul Ian UL; Bordas, Stéphane UL et al

E-print/Working paper (2022)

Deep learning surrogate models are being increasingly used in accelerating scientific simulations as a replacement for costly conventional numerical techniques. However, their use remains a significant ... [more ▼]

Deep learning surrogate models are being increasingly used in accelerating scientific simulations as a replacement for costly conventional numerical techniques. However, their use remains a significant challenge when dealing with real-world complex examples. In this work, we demonstrate three types of neural network architectures for efficient learning of highly nonlinear deformations of solid bodies. The first two architectures are based on the recently proposed CNN U-NET and MAgNET (graph U-NET) frameworks which have shown promising performance for learning on mesh-based data. The third architecture is Perceiver IO, a very recent architecture that belongs to the family of attention-based neural networks–a class that has revolutionised diverse engineering fields and is still unexplored in computational mechanics. We study and compare the performance of all three networks on two benchmark examples, and show their capabilities to accurately predict the non-linear mechanical responses of soft bodies. [less ▲]

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See detailReal Time Hyper-elastic Simulations with Probabilistic Deep Learning
Deshpande, Saurabh UL; Lengiewicz, Jakub UL; Bordas, Stéphane UL

in 15th World Congress on Computational Mechanics (WCCM-XV) (2022, August)

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See detailImaging-informed BIOmechanical brain tumor forecast MOdelling
Abbad Andaloussi, Meryem UL; Husch, Andreas UL; Urcun, Stephane UL et al

Scientific Conference (2022, June 06)

Grade 3 and 4 Astrocytomas are high grade gliomas (HGG) that usually result from initially less aggressive low grade gliomas (LGG) through malignant transformation (MT). This process has various ... [more ▼]

Grade 3 and 4 Astrocytomas are high grade gliomas (HGG) that usually result from initially less aggressive low grade gliomas (LGG) through malignant transformation (MT). This process has various definitions in the literature, clinical and histopathological, depending on the scale of the study and researchers' interest. We introduce an overview of different aspects of MT: molecular, clinical and the role of the microenvironment in acquiring the malignant phenotype. Furthermore, we introduce a new hypothesis that could explain the spatial progression of low grade astrocytoma (LGA) during MT. The former hypothesis will next be tested on LGA patients through tumor segmentation from Medical Resonance Images (MRI) and a mechanistic growth model. [less ▲]

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See detailAn adaptive multiscale quasicontinuum approach for mechanical simulations of elastoplastic periodic lattices
Chen, Li UL; Berke, Peter; Massart, Thierry et al

in Mechanics Research Communications (2022), 126

The quasicontinuum method is a multiscale method that combines locally supported coarse-grained domains, with small regions in which the microstructural model is fully resolved. This contribution proposes ... [more ▼]

The quasicontinuum method is a multiscale method that combines locally supported coarse-grained domains, with small regions in which the microstructural model is fully resolved. This contribution proposes the first adaptive formulation of the method for microstructural elastoplasticity. The microstructural model uses an elastoplastic beam description. The indicator for refinement is the occurrence of plastic deformation, such that plasticity can only occur in fully resolved regions. An illustrative numerical example of a scratch test of an elastoplastic Kelvin lattice demonstrates the capabilities of the resulting framework. [less ▲]

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See detailAn a posteriori error estimator for the spectral fractional power of the Laplacian
Bulle, Raphaël UL; Barrera, Olga; Bordas, Stéphane UL et al

E-print/Working paper (2022)

We develop a novel a posteriori error estimator for the L2 error committed by the finite ele- ment discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes ... [more ▼]

We develop a novel a posteriori error estimator for the L2 error committed by the finite ele- ment discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi–discretization scheme using a rational approximation which allows to reformulate the fractional problem into a family of non–fractional parametric problems. The estimator involves applying the implicit Bank–Weiser error estimation strategy to each parametric non–fractional problem and reconstructing the fractional error through the same rational approximation used to compute the solution to the original fractional problem. We provide several numerical examples in both two and three-dimensions demonstrating the effectivity of our estimator for varying fractional powers and its ability to drive an adaptive mesh refinement strategy. [less ▲]

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See detailSOniCS: Develop intuition on biomechanical systems through interactive error controlled simulations
Mazier, Arnaud UL; El Hadramy, Sidaty; Brunet, Jean-Nicolas et al

E-print/Working paper (2022)

This new approach allows the user to experiment with model choices easily and quickly without requiring in-depth expertise, as constitutive models can be modified by one line of code only. This ease in ... [more ▼]

This new approach allows the user to experiment with model choices easily and quickly without requiring in-depth expertise, as constitutive models can be modified by one line of code only. This ease in building new models makes SOniCS ideal to develop surrogate, reduced order mod- els and to train machine learning algorithms for uncertainty quantification or to enable patient-specific simulations. SOniCS is thus not only a tool that facilitates the development of surgical training simulations but also, and perhaps more importantly, paves the way to increase the intuition of users or otherwise non-intuitive behaviors of (bio)mechanical systems. The plugin uses new developments of the FEniCSx project enabling au- tomatic generation with FFCx of finite element tensors such as the local residual vector and Jacobian matrix. We validate our approach with nu- merical simulations such as manufactured solutions, cantilever beams, and benchmarks provided by FEBio. We reach machine precision accuracy and demonstrate the use of the plugin for a real-time haptic simulation involv- ing a surgical tool controlled by the user in contact with a hyperelastic liver. We include complete examples showing the use of our plugin for sim- ulations involving Saint Venant-Kirchhoff, Neo-Hookean, Mooney-Rivlin, and Holzapfel Ogden anisotropic models as supplementary material. [less ▲]

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See detailA rigged model of the breast for preoperative surgical planning
Mazier, Arnaud UL; Ribes, Sophie; Gilles, Benjamin et al

in Journal of Biomechanics (2021), 128

In breast surgical practice, drawing is part of the preoperative planning procedure and is essential for a successful operation. In this study, we design a pipeline to assist surgeons with patient ... [more ▼]

In breast surgical practice, drawing is part of the preoperative planning procedure and is essential for a successful operation. In this study, we design a pipeline to assist surgeons with patient-specific breast surgical drawings. We use a deformable torso model containing the surgical patterns to match any breast surface scan. To be compatible with surgical timing, we build an articulated model through a skinning process coupled with shape deformers to enhance a fast registration process. On one hand, the scalable bones of the skinning account for pose and morphological variations of the patients. On the other hand, pre-designed artistic blendshapes create a linear space for guaranteeing anatomical variations. Then, we apply meaningful constraints to the model to find a trade-off between precision and speed. The experiments were conducted on 7 patients, in 2 different poses (prone and supine) with a breast size ranging from 36A and 42C (US/UK bra sizing). The acquisitions were obtained using the depth camera Structure Sensor, and the breast scans were acquired in less than 1 minute. The result is a registration method converging within a few seconds (3 maximum), reaching a Mean Absolute Error of 2.3 mm for mesh registration and 8.0 mm for breast anatomical landmarks. Compared to the existing literature, our model can be personalized and does not require any database. Finally, our registered model can be used to transfer surgical reference patterns onto any patient in any position. [less ▲]

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See detailA hyper-reduction method using adaptivity to cut the assembly costs of reduced order models
Hale, Jack UL; Schenone, Elisa; Baroli, Davide UL et al

in Computer Methods in Applied Mechanics and Engineering (2021), 380

At every iteration or timestep of the online phase of some reduced-order modelling schemes, large linear systems must be assembled and then projected onto a reduced order basis of small dimension. The ... [more ▼]

At every iteration or timestep of the online phase of some reduced-order modelling schemes, large linear systems must be assembled and then projected onto a reduced order basis of small dimension. The projected small linear systems are cheap to solve, but assembly and projection are now the dominant computational cost. In this paper we introduce a new hyper-reduction strategy called reduced assembly (RA) that drastically cuts these costs. RA consists of a triangulation adaptation algorithm that uses a local error indicator to con- struct a reduced assembly triangulation specially suited to the reduced order basis. Crucially, this reduced assembly triangulation has fewer cells than the original one, resulting in lower assembly and projection costs. We demonstrate the efficacy of RA on a Galerkin-POD type reduced order model (RAPOD). We show performance increases of up to five times over the baseline Galerkin-POD method on a non-linear reaction-diffusion problem solved with a semi-implicit time-stepping scheme and up to seven times for a 3D hyperelasticity problem solved with a continuation Newton-Raphson algorithm. The examples are implemented in the DOLFIN finite element solver using PETSc and SLEPc for linear algebra. Full code and data files to produce the results in this paper are provided as supplementary material. [less ▲]

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See detailBubble-Enriched Smoothed Finite Element Methods for Nearly-Incompressible Solids
Lee, Changkye; Natarajan, Sundararajan; Hale, Jack UL et al

in Computer Modeling in Engineering and Sciences (2021), 127(2), 411-436

This work presents a locking-free smoothed finite element method (S-FEM) for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity. The proposed method overcomes ... [more ▼]

This work presents a locking-free smoothed finite element method (S-FEM) for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity. The proposed method overcomes well-known issues of standard finite element methods (FEM) in the incompressible limit: the over-estimation of stiffness and sensitivity to severely distorted meshes. The concepts of cell-based, edge-based and node-based S-FEMs are extended in this paper to three-dimensions. Additionally, a cubic bubble function is utilized to improve accuracy and stability. For the bubble function, an additional displacement degree of freedom is added at the centroid of the element. Several numerical studies are performed demonstrating the stability and validity of the proposed approach. The obtained results are compared with standard FEM and with analytical solutions to show the effectiveness of the method. [less ▲]

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See detailDistributed Prediction of Unsafe Reconfiguration Scenarios of Modular Robotic Programmable Matter
Piranda, Benoit; Chodkiewicz, Paweł; Holobut, Paweł et al

in IEEE Transactions on Robotics (2021), 37(6), 2226-2233

We present a distributed framework for predicting whether a planned reconfiguration step of a modular robot will mechanically overload the structure, causing it to break or lose stability under its own ... [more ▼]

We present a distributed framework for predicting whether a planned reconfiguration step of a modular robot will mechanically overload the structure, causing it to break or lose stability under its own weight. The algorithm is executed by the modular robot itself and based on a distributed iterative solution of mechanical equilibrium equations derived from a simplified model of the robot. The model treats intermodular connections as beams and assumes no-sliding contact between the modules and the ground. We also provide a procedure for simplified instability detection. The algorithm is verified in the Programmable Matter simulator VisibleSim, and in real-life experiments on the modular robotic system Blinky Blocks. © 2004-2012 IEEE. [less ▲]

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See detailDATA DRIVEN SURGICAL SIMULATIONS
Deshpande, Saurabh UL; Bordas, Stéphane UL; Beex, Lars UL et al

Scientific Conference (2020, July)

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See detailIsogeometric analysis of thin Reissner-Mindlin shells: locking phenomena and B-bar method
Hu, Qingyuan; Xia, Yang; Natarajan, Sundararajan et al

in Computational Mechanics (2020), 65(5), 1323-1341

We propose a local type of B-bar formulation, addressing locking in degenerated Reissner–Mindlin shell formulation in the context of isogeometric analysis. Parasitic strain components are projected onto ... [more ▼]

We propose a local type of B-bar formulation, addressing locking in degenerated Reissner–Mindlin shell formulation in the context of isogeometric analysis. Parasitic strain components are projected onto the physical space locally, i.e. at the element level, using a least-squares approach. The formulation allows the flexible utilization of basis functions of different orders as the projection bases. The introduced formulation is much cheaper computationally than the classical $$\bar{B}$$B¯ method. We show the numerical consistency of the scheme through numerical examples, moreover they show that the proposed formulation alleviates locking and yields good accuracy even for slenderness ratios of $$10^5$$105, and has the ability to capture deformations of thin shells using relatively coarse meshes. In addition it can be opined that the proposed method is less sensitive to locking with irregular meshes. [less ▲]

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See detailData Centric Engineering and Data-Driven Modelling - Computational Engineering Lab Report 2019
Bordas, Stéphane UL; Peters, Bernhard UL; Viti, Francesco UL et al

Report (2019)

https://www.cambridge.org/core/journals/data-centric-engineering

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See detailParameter identification problem in bimaterial human skin and sensitivity analysis : Uncertainties in biomechanics of skin
Sutula, Danas; Elouneg, Aflah; Sensale, Marco UL et al

Scientific Conference (2019, December 09)

The proposed paper concerns the prediction of the numerical response of a biomechanical structure submitted to an unknown external loading state. The methodology is based on homogeneous and then ... [more ▼]

The proposed paper concerns the prediction of the numerical response of a biomechanical structure submitted to an unknown external loading state. The methodology is based on homogeneous and then heterogeneous structures such as healthy or pathological cutaneous tissues that can be mechanically tested in vivo under a patchy knowledge of boundary conditions. Experimental data corresponding to the extension of a piece of skin located between two pads with displacement enslavement, represent input data to the numerical model. Data are reaction force on one pad and displacement field between the two pads and all around. The numerical model consists of a representation of the bi-material domain geometry with neo-hookean behaviors. The boundary conditions and loadings of the experimental extension test are imposed. The materials parameters have been identified by inverse method starting from a constrained cost function minimizing the difference between the calculated displacements field and experimental displacements field obtained by digital image correlation and taking into account the reaction force as a constraint. An analysis of the model sensitivity to material parameters is presented. [less ▲]

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See detailMechanical parameters identification of keloid and surrounding healthy skin using Digital Image Correlation measurements in vivo
Elouneg, Aflah; Sutula, Danas; Sensale, Marco UL et al

Scientific Conference (2019, December 09)

The human skin behaves as an elastic membrane initially prestressed but not uniformly. The presence of anatomical sites favorable to the appearance of some tumors, a keloid in our case, while other sites ... [more ▼]

The human skin behaves as an elastic membrane initially prestressed but not uniformly. The presence of anatomical sites favorable to the appearance of some tumors, a keloid in our case, while other sites never develop them attests to the importance of the mechanical environment of the tissue. Thus, a mechanical characterization of the tumored skin is necessary to understand the keloid expansion from a mechanical point of view. Our case study consists in modeling a bi-material structure composed of a keloid skin surrounded by healthy skin located on upper left arm of a young female. From the experimental measurements in vivo, by combining force sensor, displacement sensor and Digital Image Correlation techniques, we perform a mechanical analysis to characterize the mechanical stress fields over the entire area and on the interface ‘healthy skin/keloid skin’. Since the mechanical behavior of the tumorous skin is unknown, many physical models can be implemented and assessed very easily inside the specific digital software to fit with the real data. Once a set of mechanical parameters for both the healthy skin and the keloid skin are identified, the stress fields around the keloid are calculated. Next steps consist in determining matching preferential directions in order to define as precisely as possible the specifications of a device for preventing the growth of keloids. [less ▲]

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