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Global Energy Minimization for Multi-crack Growth in Linear Elastic Fracture using the Extended Finite Element Method ; Bordas, Stéphane Presentation (2014, July 24) Detailed reference viewed: 225 (12 UL)A model order reduction technique for speeding up computational homogenisation ; ; et al Scientific Conference (2014, July 24) Detailed reference viewed: 277 (5 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: 479 (26 UL)11th. World Congress on Computational Mechanics (WCCM XI) ; ; et al Scientific Conference (2014, July 23) Detailed reference viewed: 635 (7 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: 376 (8 UL)Global energy minimization for multi-crack growth in linear elastic fracture using the extended finite element method Bordas, Stéphane Scientific Conference (2014, July 20) Detailed reference viewed: 337 (7 UL)Challenges Ahead For Modelling And Simulation In Mechanics: From Engineering To Medicine ; ; Bordas, Stéphane Scientific Conference (2014, July 01) Detailed reference viewed: 256 (1 UL)The codes on three dimensional shape optimisation using IGABEM ; Bordas, Stéphane Learning material (2014) Detailed reference viewed: 190 (2 UL)Sensitivity analysis and shape optimization using isogeomgetric boundary element methods ; ; Bordas, Stéphane Scientific Conference (2014, July) Detailed reference viewed: 363 (7 UL)Multiscale Quasicontinuum Approaches for Planar Beam Lattices Beex, Lars ; ; Bordas, Stéphane Scientific Conference (2014, July) Detailed reference viewed: 272 (5 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: 349 (0 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: 312 (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: 305 (4 UL)Implementation of an isogeometric finite element toolbox in Diffpack ; ; et al Scientific Conference (2014, July) Detailed reference viewed: 837 (13 UL)Crack growth analysis by a NURBS-based isogeometric boundary element metyhod ; ; et al Presentation (2014, July) Detailed reference viewed: 124 (3 UL)Crack growth analysis by a NURBS-based isogeometric boundary element method ; ; et al Scientific Conference (2014, July) Detailed reference viewed: 562 (26 UL)GEOMETRY-INDEPENDENT FIELD APPROXIMATION FOR SPLINE-BASED FINITE ELEMENT METHODS ; ; Bordas, Stéphane in Proceedings of the 11th World Congress in Computational Mechanics (2014, July) We propose a discretization scheme where the spline spaces used for the geometry and the field variables can be chosen independently in spline-based FEM. he method is thus applicable to arbitrary domains ... [more ▼] We propose a discretization scheme where the spline spaces used for the geometry and the field variables can be chosen independently in spline-based FEM. he method is thus applicable to arbitrary domains with spline representation. (2) It is possible to flexibly choose between different spline spaces with different properties to better represent the solution of the PDE, e.g. the continuity of the solution field. (3) Refinement operations by knot insertion and degree elevation are performed directly on the spline space of the solution field, independently of the spline space of the geometry of the domain, i.e. the parameterization of the given geometry is not altered during the refinement process. Hence, the initial design can be optimized in the subsequent shape optimization stage without constraining the geometry discretization space to conform to the field approximation space. [less ▲] Detailed reference viewed: 576 (15 UL)Gradient Smoothing For Nearly Incompressible Hyperelasticity ; ; et al Scientific Conference (2014, July) Detailed reference viewed: 322 (7 UL)Stress analysis, damage tolerance assessment and shape optimisation without meshing Hale, Jack ; Bordas, Stéphane ; et al Poster (2014, June 24) Detailed reference viewed: 122 (3 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: 350 (6 UL) |
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