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 detailThe edge-based strain smoothing method for compressible and nearly incompressible non-linear elasticity for solid mechanics
Lee, Chang-Kye; Mihai, L. Angela; Kerfriden, Pierre et al

E-print/Working paper (in press)

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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 (in press)

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 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 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 detailProbabilistic Deep Learning for Real-Time Large Deformation Simulations
Deshpande, Saurabh UL; Lengiewicz, Jakub UL; Bordas, Stéphane UL

in Computer Methods in Applied Mechanics and Engineering (2022), 398(0045-7825), 115307

For many novel applications, such as patient-specific computer-aided surgery, conventional solution techniques of the underlying nonlinear problems are usually computationally too expensive and are ... [more ▼]

For many novel applications, such as patient-specific computer-aided surgery, conventional solution techniques of the underlying nonlinear problems are usually computationally too expensive and are lacking information about how certain can we be about their predictions. In the present work, we propose a highly efficient deep-learning surrogate framework that is able to accurately predict the response of bodies undergoing large deformations in real-time. The surrogate model has a convolutional neural network architecture, called U-Net, which is trained with force–displacement data obtained with the finite element method. We propose deterministic and probabilistic versions of the framework. The probabilistic framework utilizes the Variational Bayes Inference approach and is able to capture all the uncertainties present in the data as well as in the deep-learning model. Based on several benchmark examples, we show the predictive capabilities of the framework and discuss its possible limitations. [less ▲]

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See detailSOniCS: Interfacing SOFA and FEniCS for advanced constitutive models
Mazier, Arnaud UL; El Hadramy, Sidaty; Brunet, Jean-Nicolas et al

Scientific Conference (2022, August)

The Simulation Open Framework Architecture (SOFA) is a software environment for building simulations with a particular focus on real-time medical applications, e.g. surgery. Its scope is far broader than ... [more ▼]

The Simulation Open Framework Architecture (SOFA) is a software environment for building simulations with a particular focus on real-time medical applications, e.g. surgery. Its scope is far broader than the FEniCS Project, encompassing e.g. rigid body dynamics, interfacing with haptic devices, contact and visualisation. Naturally, it also includes some finite element models of soft tissue mechanics, but these capabilities are currently ‘pre-baked’ and limited to a few simple constitutive models. The goal of this work is to incorporate state-of-the-art code generation tools from the FEniCS Project into SOFA in order to hugely increase SOFA’s capabilities in terms of soft tissue mechanics. To this end we have developed a new SOFA plugin named SOniCS. For adding a new material model in SOniCS, the user describes its strain energy density function using UFL (Unified Form Language) syntax. Then, using FFCx (FEniCSx Form Compiler) we generate the C code associated with the kernels corresponding to the automatically differentiated cell-local residual and stiffness forms. Finally, we assemble these kernels in SOFA into global tensors and solve the resulting non-linear systems of equations. The result is that it is now possible to straightforwardly implement complex material models such as the Holzapfel-Ogden anisotropic model into SOFA, and to use them alongside SOFA’s existing strong feature set in medical simulation. [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 detailTowards real-time patient-specific breast simulations: from full-field information to surrogate model
Mazier, Arnaud UL; Lavigne, Thomas UL; Lengiewicz, Jakub UL et al

Scientific Conference (2022, July)

In breast cancer treatment, surgery is one of the most common practices [DeSantis et al., 2019]. The surgery involves a complex pipeline, principally due to the difference between the imaging and the ... [more ▼]

In breast cancer treatment, surgery is one of the most common practices [DeSantis et al., 2019]. The surgery involves a complex pipeline, principally due to the difference between the imaging and the surgical posture [Mazier et al., 2021]. Indeed, because of the stance difference, the surgeon has to rely on radioactive or invasive markers to predict the tumor position in the surgical setup. Biomechanical simulations could predict such complex tumor displacements but often require patient-specific data (material properties, organs geometries, or loading and boundary conditions). Full-field acquisitions coupled with landmark identifications allow obtaining relative deformation between the different configurations. Having this information and assuming a finite element model, an identification procedure of the model parameters can be carried out. Finally, finding a suitable computational model allowing for a compromise between accuracy and speed, one may consider surrogate models for real-time simulations (20 to 50 FPS). In this work, we obtained the patient-specific geometry through micro-computed tomography in 8 different configurations, including 15 bio-markers. Assessing the displacement of the bio-markers enabled us to infer the relative strains between the different configurations. A heterogeneous neo-Hookean model was assumed for simulating soft tissue behavior. Based on the displacements and the position of the biomarkers, model parameters identification was performed to calibrate the experimental data with the finite element method results. To overcome speed performance issues, Convolutional Neural Network (CNN) trained with a synthetic simulation-based dataset generated by applying different gravity directions is used. Preliminary results show that CNN can predict the displacement of anatomical landmarks to millimetric precision and is 100 times faster than the finite element method, satisfying our real-time objective. Plus, the use of Bayesian inferences involves a longer prediction time but allows a 95% confidence interval of the biomarkers' displacements. For a given precision, contrary to CNNs, optimization methods are computationally expensive and depend on an initialization point. Although CNNs require new training for each patient, optimization algorithms can be applied regardless of the patient's geometry. Through this study, we observed that material properties were playing an essential role but not as much as the anatomical structures e.g. infra-mammary or Copper’s ligaments. [less ▲]

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See detailA CutFEM Method for a Mechanistic Modelling of Astrocytic Metabolism in 3D Physiological Morphologies
Farina, Sofia UL; Voorsluijs, Valerie UL; Claus, Susanne et al

Scientific Conference (2022, June 07)

Investigating neurodegenerative diseases can be done complementary through biological and computational experiments. A good computational approach describing a simplification of the reality and focusing ... [more ▼]

Investigating neurodegenerative diseases can be done complementary through biological and computational experiments. A good computational approach describing a simplification of the reality and focusing only on some features of the problem can help getting insights on the field. The question addressed in our work is the role of astrocytes in neurodegeneration. These cells have two interesting characteristics that we want to investigate in our model: first, their role as metabolic mediator between neurons and blood vessels and second, their peculiar morphology. In fact, metabolic dysfunctions and morphological changes have been noticed in astrocyte affected by neuropathology. Computationally the main difficulty arising from solving a metabolic model into cellular shape comes from the complexity of the domain. The shape of astrocytes are very ramified, with thin branches and sharp edges. As shown in our previous work \cite{Farina}, a \cutfem{} \cite{Burman} approach is a suitable tool to deal with this issue. In our latest work we use real human three-dimensional astrocyte morphologies obtained via microscopy \cite{Salamanca} as domain to solve our system. The performed simulations highlight the effect of morphological changes on the system output. Suggesting that our model can be crucial in understanding the morphological-dependency in neuropathologies and that the spatial component cannot be neglected. [less ▲]

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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 detailReal-time large deformations: A probabilistic deep learning approach
Deshpande, Saurabh UL; Lengiewicz, Jakub UL; Bordas, Stéphane UL

in The 8th European Congress on Computational Methods in Applied Sciences and Engineering (2022, June)

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See detailInverse deformation analysis: an experimental and numerical assessment using the FEniCS Project
Mazier, Arnaud UL; Bilger, Alexandre; Forte, Antonio E. et al

in Engineering with Computers (2022)

In this paper, we develop a framework for solving inverse deformation problems using the FEniCS Project finite-element software. We validate our approach with experimental imaging data acquired from a ... [more ▼]

In this paper, we develop a framework for solving inverse deformation problems using the FEniCS Project finite-element software. We validate our approach with experimental imaging data acquired from a soft silicone beam under gravity. In contrast with inverse iterative algorithms that require multiple solutions of a standard elasticity problem, the proposed method can compute the undeformed configuration by solving only one modified elasticity problem. This modified problem has a complexity comparable to the standard one. The framework is implemented within an open-source pipeline enabling the direct and inverse deformation simulation directly from imaging data. We use the high-level unified form language (UFL) of the FEniCS Project to express the finite-element model in variational form and to automatically derive the consistent Jacobian. Consequently, the design of the pipeline is flexible: for example, it allows the modification of the constitutive models by changing a single line of code. We include a complete working example showing the inverse deformation of a beam deformed by gravity as supplementary material. [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 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 detailMapping of machine learning approaches for description, prediction, and causal inference in the social and health sciences
Leist, Anja UL; Klee, Matthias UL; Kim, Jung Hyun UL et al

in Science Advances (2022), 8

Machine learning (ML) methodology used in the social and health sciences needs to fit the intended research purposes of description, prediction, or causal inference. This paper provides a comprehensive ... [more ▼]

Machine learning (ML) methodology used in the social and health sciences needs to fit the intended research purposes of description, prediction, or causal inference. This paper provides a comprehensive, systematic meta-mapping of research questions in the social and health sciences to appropriate ML approaches by incorporating the necessary requirements to statistical analysis in these disciplines. We map the established classification into description, prediction, counterfactual prediction, and causal structural learning to common research goals, such as estimating prevalence of adverse social or health outcomes, predicting the risk of an event, and identifying risk factors or causes of adverse outcomes, and explain common ML performance metrics. Such mapping may help to fully exploit the benefits of ML while considering domain-specific aspects relevant to the social and health sciences and hopefully contribute to the acceleration of the uptake of ML applications to advance both basic and applied social and health sciences research. [less ▲]

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