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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 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 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)

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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 detailFrom quantum to continuum mechanics in the delamination of atomically-thin layers from substrates
Hauseux, Paul; Nguyen, Thanh-Tung; Ambrosetti, Alberto et al

in Nature Communications (2020)

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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 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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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 detailFracture mechanism simulation of inhomogeneous anisotropic rocks by extended finite element method
Mohtarami, Ehsan; Baghbanan, Alireza; Hashemolhosseini, Hamid et al

in Theoretical and Applied Fracture Mechanics (2019), 104

The vast majority of rock masses is anisotropic due to factors such as layering, unequal in-situ stresses, joint sets, and discontinuities. Meanwhile, given the frequently asymmetric distribution of pores ... [more ▼]

The vast majority of rock masses is anisotropic due to factors such as layering, unequal in-situ stresses, joint sets, and discontinuities. Meanwhile, given the frequently asymmetric distribution of pores, grain sizes or different mineralogical compounds in different locations, they are often classified as inhomogeneous materials. In such materials, stress intensity factors (SIFs) at the crack tip, which control the initiation of failure, strongly depend on mechanical properties of the material near that area. On the other hand, crack propagation trajectories highly depend on the orthotropic properties of the rock mass. In this study, the SIFs are calculated by means of anisotropic crack tip enrichments and an interaction integral are developed for inhomogeneous materials with the help of the extended finite element method (XFEM). We also use the T-stress within the crack tip fields to develop a new criterion to estimate the crack initiation angles and propagation in rock masses. To verify and validate the proposed approach, the results are compared with experimental test results and those reported in the literature. It is found that the ratio of elastic moduli, shear stiffnesses, and material orientation angles have a significant impact on the SIFs. However, the rate of change in material properties is found to have a moderate effect on these factors and a more pronounced effect on the failure force. The results highlight the potential of the proposed formulation in the estimation of SIFs and crack propagation paths in inhomogeneous anisotropic materials. [less ▲]

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See detailAdaptive equation-free multiscale modeling of metallic lattices with geometrical nonlinearity and variability
Chen, Li UL; Berke, Peter; Beex, Lars UL et al

Scientific Conference (2019, September 12)

An equation-free concurrent multiscale framework is proposed to model 3D metallic lattice structures. The proposed equation-free multiscale method (EFMM) is effectively a generalization of the ... [more ▼]

An equation-free concurrent multiscale framework is proposed to model 3D metallic lattice structures. The proposed equation-free multiscale method (EFMM) is effectively a generalization of the quasicontinuum method [2] and relies on the use of fully-resolved domains (FRD) in which all details of the lattice micro-structure are captured, and of coarse-grained domains (CGD) in which a model reduction is performed by interpolation and summation steps. The particularity of the lattice geometrical description is that cross section variations along the lattice struts (caused by the manufacturing process) are explicitly represented by their discretization in several beam finite elements, both in the FRDs and CGDs. The interpolation step of the EFMM refers to a kinematic approximation of the lattice deformation within CGDs based on the displacement of a reduced number of material points. One of the originalities of this work is the consideration of a separate interpolation of each type of kinematic variables within the CGDs, as a function of the connectivity of the lattice beam nodes (i.e. taking the location of different cross sections into account) and their kinematical pattern. This, together with accounting for geometric nonlinearity, by the development and implementation of a 3D co-rotational beam finite element [1], are innovative contributions. Choosing the appropriate sizes of the FRDs and the CGDs for a lattice to be simulated is a trade-off because larger FRDs prevail the accuracy but compromise the efficiency while larger CGDs do the opposite. Since the required sizes of the FRDs and CGDs are generally not known a priori for specific applications, an adaptive coarse-graining strategy is developed. To be specific, the whole lattice is initially considered as a CGD. Two kinds of error indicator are proposed (e.g. the Zienkiewicz-Zhu error indicator [4, 3] and the error indicator based on the discrepancy of strain energy). The error indicator guides on: 1) introducing more material points and rearranging the interpolation for the CGDs; 2) changing the localization-prone parts of the lattice into FRDs. The adaptive EFMM is applied to metallic BCC lattices with various sizes and loading conditions. By comparing to the results of those of the direct numerical simulation (DNS), it is shown that geometrical non-linearities can be captured at a fraction of the DNS cost. [less ▲]

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See detailEquation-free multiscale modeling of metallic lattices with geometrical and material nonlinearity and variability
Chen, Li UL; Berke, Peter; Beex, Lars UL et al

Scientific Conference (2019, September 05)

An nonlinear equation-free concurrent multiscale numerical framework, being the generalization of the quasicontinuum method [2] is proposed in this contribution to model 3D metallic lattice structures ... [more ▼]

An nonlinear equation-free concurrent multiscale numerical framework, being the generalization of the quasicontinuum method [2] is proposed in this contribution to model 3D metallic lattice structures. The proposed equation-free multiscale method (EFMM) relies on the use of fully-resolved domains (FRD) in which all of the details of the lattice micro-structure are captured, and of coarse-grained domains (CGD) in which a model reduction is performed by interpolation and summation steps. The particularity of the lattice geometry description is that cross section variations along the lattice struts (that are experimentally observed as a result of the manufacturing process) are explicitly represented by their discretization in several beam finite elements, both in the FRDs and CGDs. The interpolation step of the EFMM refers to a kinematic approximation of the lattice deformation within CGDs based on the movement of a reduced number of material points at the CGD corners. One of the originalities of this work is the consideration of a separate interpolation of each type of degrees of freedom within the CGDs, as a function of the connectivity of the lattice beam nodes (i.e. taking the location of different cross sections into account) and their kinematical pattern. This, together with accounting for plasticity, by the development and implementation of a 3D co-rotational beam finite element [1] with embedded plastic hinges [3], are unprecedented and original contributions. The EFMM is applied to metallic BCC lattices with various sizes and loading conditions. By comparing to direct numerical simulation (DNS), it is shown that both material and geometrical non-linearities can be captured at a fraction of the DNS cost (the computational time is reduced by 97.27% while introducing an error of only 3.76%). [less ▲]

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See detailTaylor-Series Expansion Based Numerical Methods: A Primer, Performance Benchmarking and New Approaches for Problems with Non-smooth Solutions
Jacquemin, Thibault Augustin Marie UL; Tomar, Satyendra UL; Agathos, Konstantinos UL et al

in Archives of Computational Methods in Engineering (2019)

We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these ... [more ▼]

We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files including input files, boundary conditions, point distribution and solution fields, so as to facilitate future benchmarking of new methods. We review traditional methods and recent ones which appeared in the last decade. We aim to help newcomers to the field understand the main characteristics of these methods and to provide sufficient information to both simplify implementation and benchmarking of new methods. Some of the examples are chosen within a subset of problems where collocation is traditionally known to perform sub-par, namely when the solution sought is non-smooth, i.e. contains discontinuities, singularities or sharp gradients. For such problems and other simpler ones with smooth solutions, we study in depth the influence of the weight function, correction function, and the number of nodes in a given support. We also propose new stabilization approaches to improve the accuracy of the numerical methods. In particular, we experiment with the use of a Voronoi diagram for weight computation, collocation method stabilization approaches, and support node selection for problems with singular solutions. With an appropriate selection of the above-mentioned parameters, the resulting collocation methods are compared to the moving least-squares method (and variations thereof), the radial basis function finite difference method and the finite element method. Extensive tests involving two and three dimensional problems indicate that the methods perform well in terms of efficiency (accuracy versus computational time), even for non-smooth solutions. [less ▲]

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