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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 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 detailSimulation of gas-dynamic, pressure surges and adiabatic compression phenomena in geometrically complex respirator oxygen valves
Obeidat, Anas UL; Andreas, Thomas; Bordas, Stéphane UL et al

in Thermal Science and Engineering Progress (2021), 24

Gas-dynamic pressure surges and adiabatic compression phenomena are generally hard to predict numerically. In this contribution, we study the effect of the pressure reserve capacity on the compressible ... [more ▼]

Gas-dynamic pressure surges and adiabatic compression phenomena are generally hard to predict numerically. In this contribution, we study the effect of the pressure reserve capacity on the compressible gas-dynamics pressure surge and adiabatic compression in a fitted respirator oxygen valve geometry. A three-dimensional remeshed smoothed particle hydrodynamics method for the simulation of isotropic turbulence is used, the method is coupled with Brinkman penalisation technique for flow simulation inside the complex valve geometry. Simulations are carried out for three different pressure reserve quantities, to replicate the opening of the valve, two time-based pressure inlet boundary condition functions were simulated along with an impulsively started scenario. A geometrical sensitivity analysis is provided, where the simulation is performed on a modified valve design which exhibits a damping effect on the gas dynamics and flow characteristics, which has a favourable effect on the valve functionality and safety. It is found that the capacity of the pressure reserve has a considerable effect on the simulated flow fields (velocity, temperature), as the temperature could rise 6.0X the reference temperature, and up to 2.7X the reference velocity. The numerical results are compared with a previous study carried out by Rotarex S.A., demonstrating that the remeshed particle-mesh method coupled with Brinkman penalisation provides a good quality simulation and the results are in agreement with the reference solution. [less ▲]

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See detailBayesian model uncertainty quantification for hyperelastic soft tissue models
Zeraatpisheh, Milad UL; Beex, Lars UL; Bordas, Stéphane UL

in Data-Centric Engineering (2021)

Patient-specific surgical simulations require the patient-specific identification of the constitutive parameters. The sparsity of the experimental data and the substantial noise in the data (e.g ... [more ▼]

Patient-specific surgical simulations require the patient-specific identification of the constitutive parameters. The sparsity of the experimental data and the substantial noise in the data (e.g., recovered during surgery) cause considerable uncertainty in the identification. In this exploratory work, parameter uncertainty for incompressible hyperelasticity, often used for soft tissues, is addressed by a probabilistic identification approach based on Bayesian inference. Our study particularly focuses on the uncertainty of the model: we investigate how the identified uncertainties of the constitutive parameters behave when different forms of model uncertainty are considered. The model uncertainty formulations range from uninformative ones to more accurate ones that incorporate more detailed extensions of incompressible hyperelasticity. The study shows that incorporating model uncertainty may improve the results, but this is not guaranteed. [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 detailA cut finite element method for spatially resolved energy metabolism models in complex neuro-cell morphologies with minimal remeshing
Farina, Sofia UL; Claus, Susanne; Hale, Jack UL et al

in Advanced Modeling and Simulation in Engineering Sciences (2021), 8

A thorough understanding of brain metabolism is essential to tackle neurodegenerative diseases. Astrocytes are glial cells which play an important metabolic role by supplying neurons with energy. In ... [more ▼]

A thorough understanding of brain metabolism is essential to tackle neurodegenerative diseases. Astrocytes are glial cells which play an important metabolic role by supplying neurons with energy. In addition, astrocytes provide scaffolding and homeostatic functions to neighboring neurons and contribute to the blood–brain barrier. Recent investigations indicate that the complex morphology of astrocytes impacts upon their function and in particular the efficiency with which these cells metabolize nutrients and provide neurons with energy, but a systematic understanding is still elusive. Modelling and simulation represent an effective framework to address this challenge and to deepen our understanding of brain energy metabolism. This requires solving a set of metabolic partial differential equations on complex domains and remains a challenge. In this paper, we propose, test and verify a simple numerical method to solve a simplified model of metabolic pathways in astrocytes. The method can deal with arbitrarily complex cell morphologies and enables the rapid and simple modification of the model equations by users also without a deep knowledge in the numerical methods involved. The results obtained with the new method (CutFEM) are as accurate as the finite element method (FEM) whilst CutFEM disentangles the cell morphology from its discretisation, enabling us to deal with arbitrarily complex morphologies in two and three dimensions. [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

E-print/Working paper (2021)

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

E-print/Working paper (2021)

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 detailA rigged model of the breast for preoperative surgical planning
Mazier, Arnaud UL; Ribes, Sophie; Testylier, Romain et al

E-print/Working paper (2021)

In breast surgical practice, various scans and medical examinations are performed before surgery. This includes identifying landmarks defining the operating procedure. In most cases, the position of the ... [more ▼]

In breast surgical practice, various scans and medical examinations are performed before surgery. This includes identifying landmarks defining the operating procedure. In most cases, the position of the patient during the scan is vastly different from the one encountered during the operation. We address the challenge of mapping preoperative information to the operating field, with the following constraints: registration has to be done in less than 10 seconds to be compatible with a clinical workflow; the cost of the device must be small and we assume data scarcity, i.e. that our database has twenty scans of patients at most. We build anatomical complexity through a skinning model comprised of scalable bones (to account for pose and morphological variations) and deformable organs (blendshapes, to account for anatomical variations). Similar to animation rigs used in computer graphics, and in contrast to statistical approaches, we manually design a model with some desirable properties, using a reduced number of well-chosen degrees of freedom. Meaningful constraints can be applied to the registration depending on the context, and the trade-off between precision and complexity can be optimized. The result is a surface mesh of the patient obtained in less than 1 minute (scan and reconstruction included) and a registration method that converges within a few seconds (3 maximum), reaching a mean absolute squared error of 2.3 mm for mesh registration and 8.0 mm for anatomical landmarks. The registered model is used to transfer surgical reference patterns on any patient in any position. [less ▲]

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See detailMachine learning in the social and health sciences
Leist, Anja UL; Klee, Matthias UL; Kim, Jung Hyun UL et al

E-print/Working paper (2021)

The uptake of machine learning (ML) approaches in the social and health sciences has been rather slow, and research using ML for social and health research questions remains fragmented. This may be due to ... [more ▼]

The uptake of machine learning (ML) approaches in the social and health sciences has been rather slow, and research using ML for social and health research questions remains fragmented. This may be due to the separate development of research in the computational/data versus social and health sciences as well as a lack of accessible overviews and adequate training in ML techniques for non data science researchers. This paper provides a 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, and causal inference to common research goals, such as estimating prevalence of adverse health or social outcomes, predicting the risk of an event, and identifying risk factors or causes of adverse outcomes. This meta-mapping aims at overcoming disciplinary barriers and starting a fluid dialogue between researchers from the social and health sciences and methodologically trained researchers. Such mapping may also 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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See detailGeneralized quasicontinuum modeling of metallic lattices with geometrical and material nonlinearity and variability
Chen, Li UL; Beex, Lars UL; Berke, Peter et al

in Computer Methods in Applied Mechanics and Engineering (2020), 366(112878),

We propose a generalized quasicontinuum method to model the mechanical response of 3D lattice structures. The method relies on the spatial coupling of fully-resolved domains and coarse-grained domains. In ... [more ▼]

We propose a generalized quasicontinuum method to model the mechanical response of 3D lattice structures. The method relies on the spatial coupling of fully-resolved domains and coarse-grained domains. In the fully-resolved domain, the full micro-structure is taken into account. In the coarse-grained domain, the kinematics of the micro-structure are individually interpolated based on their connectivity. On top of that, the contributions of the microstructure to the governing equations in the coarse-grained domain are sampled using only a few unit cells. In both domains, geometrical and material variability along the strut can be naturally taken into account using a 3D co-rotational beam finite element with embedded plastic hinges. We verify the approach for BCC lattices, demonstrating that the new method can capture both material and geometrical non-linearities of single struts at a fraction of the cost of a direct numerical simulation. [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 detailPractical aspects of the Bank-Weiser estimator implementation and Biomechanics applications.
Bulle, Raphaël UL; Bordas, Stéphane UL; Chouly, Franz et al

Scientific Conference (2020, July)

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See detailInverse simulation for retrieving the undeformed position for hyperelastic materials : application to breast simulations
Mazier, Arnaud UL; Bilger, Alexandre; Forte, Antonio et al

Scientific Conference (2020, July)

The rest position, as well as any associated internal stresses in soft organs, are usually unknown when solving biomechanics problems. In addition, the initial geometry of a specific organ, obtained from ... [more ▼]

The rest position, as well as any associated internal stresses in soft organs, are usually unknown when solving biomechanics problems. In addition, the initial geometry of a specific organ, obtained from medical images, is affected by external forces. An example is breast MRI performed prior to cancer surgery. During the imaging routine, the breast is elongated in prone position in order to better view the tumor. However, during surgery, the patient is in supine position, which causes the breast to rest in a completely different state. To simulate this state from the prone stance, the rest configuration is needed as well as the pre-stress mapping of the organs [1]. To tackle this problem, iterative algorithms have been proposed such as Sellier’s method [2]. In this fixed-point approach, the rest configuration is updated by multiple forward calculations then repeated until the error (between the updated and target configuration) reaches an established threshold. The method presents many benefits e.g. easy implementation and fast convergence. However, convergence issues appear at large deformations induced for instance by hyperelastic material formulations. In this work, we develop a simple formulation and a robust solution procedure for inverse deformation problems in soft-tissue biomechanics using the FEniCS Project finite element solver. In contrast with iterative algorithms, our method can solve with a single simulation the rest position without computing multiple solutions of the forward problem. For a fixed convergence tolerance, our physics-based algorithm is about ten times faster and better handles large deformations than Sellier’s method [2]. Moreover, no additional direct deformation simulations from the rest configuration are required to compute stresses in the organ. The framework is implemented within an open-source pipeline enabling the seamless, fully parallelized, direct and inverse deformation simulation of organs directly from segmented images. The pipeline is also designed to be flexible to user’s needs: for example, it allows the modification of the constitutive models by changing a single line of code. [less ▲]

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See detailAutonomous model-based assessment of mechanical failures of reconfigurable modular robots with a Conjugate Gradient solver
Hołobut, Paweł; Lengiewicz, Jakub UL; Bordas, Stéphane UL

in 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (2020)

Detailed reference viewed: 37 (4 UL)