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A model order reduction technique for speeding up computational homogenisation ; ; et al Scientific Conference (2014, July 24) Detailed reference viewed: 256 (5 UL)11th. World Congress on Computational Mechanics (WCCM XI) ; ; et al Scientific Conference (2014, July 23) Detailed reference viewed: 584 (6 UL)Parallel simulations of soft-tissue using an adaptive quadtree/octree implicit boundary finite element method Hale, Jack ; Bordas, Stéphane ; et al in 11th. World Congress on Computational Mechanics (2014, July 23) Octree (3D) and quadtree (2D) representations of computational geometry are particularly well suited to modelling domains that are defined implicitly, such as those generated by image segmentation ... [more ▼] Octree (3D) and quadtree (2D) representations of computational geometry are particularly well suited to modelling domains that are defined implicitly, such as those generated by image segmentation algorithms applied to medical scans [5]. In this work we consider the simulation of soft-tissue which can be modelled with a incompressible hyperelastic constitutive law. We include the effects of both non-linear geometry and material properties in our model. Similarly to Moumnassi et al. [2] we use the implicitly defined level set functions as the basis for a partition of unity enrichment to more accurately represent the domain boundary on the cartesian quadtree/octree mesh. In addition we introduce arbitrary cuts and discontinuities in the domain using ideas from the classical extended finite element method [3]. Because of its hydrated nature soft-tissue is nearly incompressible [1]. We explore the use of a classical two-field displacement-pressure (u-p) mixed approach to deal with the problem of volumetric-locking in the incompressible limit [4]. We exploit the existing parallel capabilities available in the open-souce finite element toolkit deal.ii [6], including the advanced mesh partitioning and balancing recently introduced in the p4est library [7]. The resulting method scales to run over hundreds of cores on the University of Luxembourg HPC platform. [less ▲] Detailed reference viewed: 443 (26 UL)MULTISCALE QUASICONTINUUM APPROACHES FOR DISCRETE MODELS OF FIBROUS MATERIALS SUCH AS ELECTRONIC TEXTILE AND PAPER MATERIALS Beex, Lars ; ; et al Scientific Conference (2014, July 20) Detailed reference viewed: 350 (8 UL)Challenges Ahead For Modelling And Simulation In Mechanics: From Engineering To Medicine ; ; Bordas, Stéphane Scientific Conference (2014, July 01) Detailed reference viewed: 232 (1 UL)Multiscale Quasicontinuum Approaches for Planar Beam Lattices Beex, Lars ; ; Bordas, Stéphane Scientific Conference (2014, July) Detailed reference viewed: 251 (5 UL)Multiscale quasicontinuum approaches for beam lattices Beex, Lars ; ; et al Scientific Conference (2014, July) The quasicontinuum (QC) method was originally developed to reduce the computational efforts of large-scale atomistic (conservative) lattice computations. QC approaches have an intrinsically multiscale ... [more ▼] The quasicontinuum (QC) method was originally developed to reduce the computational efforts of large-scale atomistic (conservative) lattice computations. QC approaches have an intrinsically multiscale character, as they combine fully resolved regions in which discrete lattice events can occur, with coarse-grained regions in which the lattice model is interpolated and integrated (summed in QC terminology). In previous works, virtual-power-based QC approaches were developed for dissipative (i.e. non-conservative) lattice computations which can for instance be used for fibrous materials. The virtual-power-based QC approaches have focused on dissipative spring/truss networks, but numerous fibrous materials can more accurately be described by (planar) beam networks. In this presentation, different QC approaches for planar beam lattices are introduced. In contrast to spring/truss lattices, beam networks include not only displacements but also rotations which need to be incorporated in the QC method, resulting in a mixed formulation. Furthermore, the presentation will show that QC approaches for planar beam lattices require higher-order interpolations to obtain accurate results, which also influences the numerical integration (summation in QC terminology). Results using different interpolations and types of integration will be shown for multiscale examples. [less ▲] Detailed reference viewed: 285 (4 UL)Multiscale quasicontinuum methods for fibrous materials Beex, Lars ; ; et al Scientific Conference (2014, July) The QC method was originally proposed for (conservative) atomistic lattice models and is based on energy-minimization. Lattice models for fibrous materials however, are often non-conservative and energy ... [more ▼] The QC method was originally proposed for (conservative) atomistic lattice models and is based on energy-minimization. Lattice models for fibrous materials however, are often non-conservative and energy-based QC methods can thus not straightforwardly be used. Examples presented here are a lattice model proposed for woven fabrics and a lattice model to describe interfiber bond failure and subsequent frictional fiber slidings. A QC framework is proposed that is based on the virtual-power statement of a non-conservative lattice model. Using the virtual-power statement, dissipative mechanisms can be included in the QC framework while the same summation rules suffice. Its validity is shown for a lattice model with elastoplastic trusses. The virtual-power-based QC method is also adopted to deal with the lattice model for bond failure and subsequent fiber sliding presented. In contrast to elastoplastic interactions that are intrinsically local dissipative mechanisms, bond failure and subsequent fiber sliding entail nonlocal dissipative mechanisms. Therefore, the virtual-power-based QC method is also equipped with a mixed formulation in which not only the displacements are interpolated, but also the internal variables associated with dissipation. [less ▲] Detailed reference viewed: 283 (4 UL)Gradient Smoothing For Nearly Incompressible Hyperelasticity ; ; et al Scientific Conference (2014, July) Detailed reference viewed: 300 (7 UL)Efficient modeling of random heterogeneous materials with an uniform probability density function ; ; Bordas, Stéphane Scientific Conference (2014, July) Homogenised constitutive laws are largely used to predict the behaviour of composite structures. Assessing the validity of such homogenised models can be done by making use of the concept of ``modelling ... [more ▼] Homogenised constitutive laws are largely used to predict the behaviour of composite structures. Assessing the validity of such homogenised models can be done by making use of the concept of ``modelling error''. First, a microscopic ``faithful'' -and potentially intractable- model of the structure is defined. Then, one tries to quantify the effect of the homogenisation procedure on a result that would be obtained by directly using the ``faithful'' model. Such an approach requires (a) the ``faithful'' model to be more representative of the physical phenomena of interest than the homogenised model and (b) a reliable approximation of the result obtained using the "faithful" and intractable model to be available at cheap costs. We focus here on point (b), and more precisely on the extension of the techniques developed in [3][2] to estimate the error due to the homogenisation of linear, spatially random composite materials. Particularly, we will approximate the unknown probability density function by bounding its first moment. In this paper, we will present this idea in more detail, displaying the numerical efficiencies and computational costs related to the error estimation. The fact that the probability density function is uniform is exploited to greatly reduce the computational cost. We will also show some first attempts to correct the homogenised model using non-conforming, weakly intrusive microscopic patches. [less ▲] Detailed reference viewed: 326 (0 UL)A model order reduction approach to construct efficient and reliable virtual charts in computational homogenisation ; ; et al in Proceedings of the 17th U.S. National Congress on Theoretical and Applied Mechanics (2014, June 15) Computational homogenisation is a widely spread technique to calculate the overall properties of a composite material from the knowledge of the constitutive laws of its microscopic constituents [1, 2 ... [more ▼] Computational homogenisation is a widely spread technique to calculate the overall properties of a composite material from the knowledge of the constitutive laws of its microscopic constituents [1, 2]. Indeed, it relies on fewer assumptions than analytical or semi-analytical homogenisation approaches and can be used to coarse-grain a large range of micro-mechanical models. However, this accuracy comes at large computational costs, which prevents computational homogenisation from being used routinely in optimisation, even in the context of linear elastic materials. Indeed, a unit cell problem has to be solved for each microscopic distribution of interest in order to obtain the corresponding homogenised material constants. In the context of nonlinear, time-dependant problem, the computational effort becomes even greater as computational homogenisation requires solving for the time-evolution of the microstructure at every point of the macroscopic domain. In this paper, we propose to address these two issues within the unified framework of projection-based model order reduction (see for instance [3, 4, 5, 6]). The smoothness of the solution of the unit cell problem with respect to parameter or time variations is used to create a reduced order model with very few degrees of freedom, hence reducing the computational burden by orders of magnitude. [1] Tarek J. Zohdi and Peter Wriggers. Introduction to Computational Micromechanics, volume 20 of lecture notes in applied and computational mechanics. Springer, 2005. [2] M.G.D. Geers, V.G. Kouznetsova, and W.A.M. Brekelmans. Multi-scale computational homogenization: Trends and challenges. J. Computational Applied Mathematics, 234(7):2175–2182, 2010. [3] D.B.P. Huynh G. Rozza and A.T. Patera. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations: Application to transport and continuum mechanics. Archives of Computational Methods in Engineering, 15(3):229–275, 2008. [4] D. Amsallem and C. Farhat. An Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity. AIAA Journal, 46(7):1803–1813, 2008. [5] P. Kerfriden, P. Gosselet, S. Adhikari, and S.P.-A. Bordas. Bridging proper orthogonal decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems. Computer Methods in Applied Mechanics and Engineering, 200(5- 8):850–866, 2011. [6] P. Kerfriden, J.-C. Passieux, and S.P.-A. Bordas. Local/global model order reduction strategy for the simulation of quasi-brittle fracture. International Journal for Numerical Methods in Engineering, 89(2):154–179, 2011. [7] M. Barrault, Y. Maday, N.C. Nguyen, and A.T. Patera. An ’empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations. Comptes Rendus de Math´ematiques, 339(9):667–672, 2004. [less ▲] Detailed reference viewed: 319 (6 UL)Direct image-analysis methods for surgical simulation and mixed meshfree methods Hale, Jack ; Bordas, Stéphane ; et al Presentation (2014, May 28) Detailed reference viewed: 117 (11 UL)Reduced order modelling: towards tractable computational homogenisation schemes ; ; et al Presentation (2014, May 15) Towards rationalised computational expense for simulating fracture over multiple scales The project focuses on the numerical simulation of the failure of complex, heterogeneous structures. The simulation ... [more ▼] Towards rationalised computational expense for simulating fracture over multiple scales The project focuses on the numerical simulation of the failure of complex, heterogeneous structures. The simulation of such physical phenomena is of particular interest to practitioners as it enables to limit the number of destructive tests required to design and assess structures, and, ultimately, to decrease the safety factors used in design. In such heterogeneous media, the description of crack or damage initiation and propagation must be done at the scale of the inhomogeneities (e.g. aggregates in a concrete structure) in order for the results to be predictive. If one uses such a fine-scale material model to simulate structures at an engineering scale (e.g. an aircraft composite panel or a concrete beam), very large numerical problems need to be solved. In addition, there is a strong need for engineers to run their models numerous times, for different sets of the design parameters (e.g. loading conditions, geometry or material properties). Tackling such parametric multiscale problems is prohibitively expensive when using brute force parallel computing. However, one can use the fact that solutions to parametric problems usually evolve in a relatively coarse space: solutions to nearby parameter sets are usually close in a certain sense. This idea is classically used in Model Order Reduction, which proposes to reduce the size of the initial problem by several order of magnitude by simply reusing the information generated when solving the initial problem for several different sets of parameters. However, in the case of fracture, the information provided by the initial problem is most of the time insufficient to describe the behaviour of the system for arbitrary parameters. Crack paths, defects, and subsequent ultimate strengths are strongly influenced by an even slight variation in the parameter set. Fortunately, we showed in our previous research that this characteristic only affects a local region surrounding the structural defects, whilst the behaviour far from these regions is remains relatively unchanged for a wide range of parameter values. The proposed project will make use of this observation in a generic way, by coupling Reduced Order Modeling and Domain Decomposition. The structure will be divided in smaller subcomponents, on which Reduced Order Modeling will be applied separately. The consequence will be that the computational efforts will be greatly decreased in the regions that are far away from the damaged zone. Within the process zone itself, the substructuring framework will allow us to automatically switch to classical direct solvers. In this sense, the research aims at rationalising the computational costs associated to the simulation of parametrised multiscale fracture simulations, by concentrating the numerical effort where it is most required and with minimal intervention of the user. [less ▲] Detailed reference viewed: 199 (7 UL)Reducing the Mesh-burden and Computational Expense in Multi-scale Free Boundary Engineering Problems Bordas, Stéphane ; ; Hale, Jack et al Presentation (2014, May 12) We present recent results aiming at affording faster and error-controlled simulations of multi scale phenomena including fracture of heterogeneous materials and cutting of biological tissue. In a second ... [more ▼] We present recent results aiming at affording faster and error-controlled simulations of multi scale phenomena including fracture of heterogeneous materials and cutting of biological tissue. In a second part, we describe methodologies to isolate the user from the burden of mesh generation and regeneration as moving boundaries evolve. Results include advances in implicit boundary finite elements, (enriched) isogeometric boundary elements and extended finite element methods for multi-crack propagation. ABOUT THE PRESENTER In 1999, Stéphane Bordas joined a joint graduate programme of the French Institute of Technology (Ecole Spéciale des Travaux Publics) and the American Northwestern University. In 2003, he graduated in Theoretical and Applied Mechanics with a PhD from Northwestern University. Between 2003 and 2006, he was at the Laboratory of Structural and Continuum Mechanics at the Swiss Federal Institute of Technology in Lausanne, Switzerland. In 2006, he became permanent lecturer at Glasgow University’s Civil Engineering Department. Stéphane joined the Computational Mechanics team at Cardiff University in September 2009, as a Professor in Computational Mechanics and directed the institute of Mechanics and Advanced Materials from October 2010 to November 2013. He is the Editor of the book series “Advances in Applied Mechanics” since July 2013. In November 2013, he joined the University of Luxembourg as a Professor in Computational Mechanics. The main axes of his research team include (1) free boundary problems and problems involving complex geometries, in particular moving boundaries and (2) ‘a posteriori’ discretisation and model error control, rationalisation of the computational expense. Stéphane’s keen interest is to actively participate in innovation, technological transfer as well as software tool generation. This has been done through a number of joint ventures with various industrial partners (Bosch GmbH, Cenaero, inuTech GmbH, Siemens-LMS, Soitec SA) and the release of open-source software. In 2012, Stéphane was awarded an ERC Starting Independent Research Grant (RealTcut), to address the need for surgical simulators with a computational mechanics angle with a focus on the multi-scale simulation of cutting of heterogeneous materials in real-time. [less ▲] Detailed reference viewed: 193 (6 UL)Model and mesh-burden reduction for multiscale fracture: applications to polycrystals, delamination and surgical simulation Bordas, Stéphane ; ; Hale, Jack et al Presentation (2014, April 23) ABSTRACT We present recent results aiming at affording faster and error-controlled simulations of multi scale phenomena including fracture of heterogeneous materials and cutting of biological tissue. In a ... [more ▼] ABSTRACT We present recent results aiming at affording faster and error-controlled simulations of multi scale phenomena including fracture of heterogeneous materials and cutting of biological tissue. In a second part, we describe methodologies to isolate the user from the burden of mesh generation and regeneration as moving boundaries evolve. Results include advances in implicit boundary finite elements, (enriched) isogeometric extended boundary elements/finite element methods for multi-crack propagation and an asynchronous GPU/CPU method for contact and cutting of heterogeneous materials in real-time with applications to surgical simulation. ABOUT THE PRESENTER In 1999, Stéphane Bordas joined a joint graduate programme of the French Institute of Technology (Ecole Spéciale des Travaux Publics) and the American Northwestern University. In 2003, he graduated in Theoretical and Applied Mechanics with a PhD from Northwestern University. Between 2003 and 2006, he was at the Laboratory of Structural and Continuum Mechanics at the Swiss Federal Institute of Technology in Lausanne, Switzerland. In 2006, he became permanent lecturer at Glasgow University’s Civil Engineering Department. Stéphane joined the Computational Mechanics team at Cardiff University in September 2009, as a Professor in Computational Mechanics and directed the institute of Mechanics and Advanced Materials from October 2010 to November 2013. He is the Editor of the book series “Advances in Applied Mechanics” since July 2013. In November 2013, he joined the University of Luxembourg as a Professor in Computational Mechanics. The main axes of his research team include (1) free boundary problems and problems involving complex geometries, in particular moving boundaries and (2) ‘a posteriori’ discretisation and model error control, rationalisation of the computational expense. Stéphane’s keen interest is to actively participate in innovation, technological transfer as well as software tool generation. This has been done through a number of joint ventures with various industrial partners (Bosch GmbH, Cenaero, inuTech GmbH, Siemens-LMS, Soitec SA) and the release of open-source software. In 2012, Stéphane was awarded an ERC Starting Independent Research Grant (RealTcut), to address the need for surgical simulators with a computational mechanics angle with a focus on the multi-scale simulation of cutting of heterogeneous materials in real-time. [less ▲] Detailed reference viewed: 646 (17 UL)From image to analysis: an extended finite element method to simulate the mechanical response of soft-tissue Hale, Jack ; Bordas, Stéphane ; Presentation (2014, April 10) In this seminar we consider the problem of constructing a numerical method particularly well suited to modelling domains described by segmented image data of the human body. Instead of constructing a ... [more ▼] In this seminar we consider the problem of constructing a numerical method particularly well suited to modelling domains described by segmented image data of the human body. Instead of constructing a conforming mesh of the problem domain, we use implicitly defined domains described using the level-set method. We then include information about the implicitly defined domains by enriching the usual finite element basis functions defined on a cartesian quadtree or octree mesh with hanging nodes. This approach introduces significant complexities compared with classical finite element methods. We will discuss difficulties with the treatment of hanging nodes, numerical integration and imposing Dirichlet boundary conditions. We will discuss the possible future of extensions of this work, including cutting of soft tissue, multiscale problems with complex microstructure, and model order reduction problems. [less ▲] Detailed reference viewed: 153 (8 UL)An enriched quadtree/octree implicit boundary finite element method for the simulation of incompressible hyperelastic materials Hale, Jack ; Bordas, Stéphane ; et al Scientific Conference (2014, April 03) Octree (and quadtree) representations of computational geometry are particularly well suited to modelling domains that are defined implicitly, such as those generated by image segmentation algorithms ... [more ▼] Octree (and quadtree) representations of computational geometry are particularly well suited to modelling domains that are defined implicitly, such as those generated by image segmentation algorithms applied to medical scans. In this work we consider the simulation of soft-tissue which can be modelled with a hyperelastic constitutive law. We include the effects of both non-linear geometry and material properties. Similarly to Legrain et al. (10.1002/nme.3070) and Moumnassi et al. (10.1016/j.cma.2010.10.002) we use the implicitly designed level set functions as the basis for a partition of unity enrichment to more accurately represent the domain boundary. Furthermore we use traditional extended finite element (XFEM) ideas to introduce arbitrary cuts and discontinuities in the domain. We explore the use of a two-field u-p mixed approach as well as a smoothed finite element method (SFEM) to deal with the problem of volumetric-locking in the incompressible limit. We will discuss the extension of our method towards both traditional parallel and GPU implementation. We aim to solve extremely large problems as well as produce snapshots to feed into model order reduction methods for real-time surgical simulations. [less ▲] Detailed reference viewed: 391 (26 UL)Summation rules for higher order Quasi-continuum methods ; ; Bordas, Stéphane et al Presentation (2014, April) Detailed reference viewed: 122 (1 UL)Shape sensitivity analysis and optimization using isogeomgetric boundary element methods in two-dimensional linear elasticity ; Bordas, Stéphane ; Report (2014) Detailed reference viewed: 237 (18 UL)Certification of projection-based reduced order modelling in computational homogenisation by the Constitutive Relation Error ; ; Bordas, Stéphane in International Journal for Numerical Methods in Engineering (2014), 97(6), 395-422 In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction ... [more ▼] In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction of a reduced model for the stress field. Upon ensuring that the reduced stress satisfies the equilibrium in the nite element sense, the desired bounding property is obtained. The lower bound is obtained by defining a hierarchical enriched reduced model for the displacement. We show that the sharpness of both error estimates can be seamlessly controlled by adapting the parameters of the corresponding reduced order model. [less ▲] Detailed reference viewed: 330 (8 UL) |
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