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Adaptive multiscale simulation of material failure: applications to molecular-dynamics/continuum coupling, polycrystalline materials and Hydrogen cutting of Silicon wafers Bordas, Stéphane ; Speeches/Talks (2014) Detailed reference viewed: 363 (3 UL)An efficient goal-oriented sampling strategy using reduced basis method for parametrized elastodynamic problems ; ; Bordas, Stéphane et al in Numerical Methods for Partial Differential Equations (2014) In this paper, we study the class of linear elastodynamic problems with a ne parameter dependence using a goal-oriented approach by finite element (FE) and reduced basis (RB) methods. The main ... [more ▼] In this paper, we study the class of linear elastodynamic problems with a ne parameter dependence using a goal-oriented approach by finite element (FE) and reduced basis (RB) methods. The main contribution of this paper is the "goal-oriented" proper orthogonal decomposition (POD)-Greedy sampling strategy within the RB approximation context. The proposed sampling strategy looks for the parameter points such that the output error approximation will be minimized by Greedy iterations. In estimating such output error approximation, the standard POD-Greedy algorithm is invoked to provide enriched RB approximations for the FE outputs. We propose a so-called "cross-validation" process to choose adaptively the dimension of the enriched RB space corresponding with the dimension of the RB space under consideration. Numerical results show that the new goal-oriented POD-Greedy sampling procedure with the cross-validation process improves signi ficantly the space-time output computations in comparison with the ones computed by the standard POD-Greedy algorithm. The method is thus ideally suited for repeated, rapid and reliable evaluations of input-output relationships in the space-time setting. [less ▲] Detailed reference viewed: 264 (3 UL)Quasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation Beex, Lars ; ; et al in Computer Methods in Applied Mechanics & Engineering (2014), 279 The quasicontinuum (QC) method is a multiscale approach that aims to reduce the computational cost of discrete lattice computations. The method incorporates small-scale local lattice phenomena (e.g. a ... [more ▼] The quasicontinuum (QC) method is a multiscale approach that aims to reduce the computational cost of discrete lattice computations. The method incorporates small-scale local lattice phenomena (e.g. a single lattice defect) in macroscale simulations. Since the method works directly and only on the beam lattice, QC frameworks do not require the construction and calibration of an accompanying continuum model (e.g. a cosserat/micropolar description). Furthermore, no coupling procedures are required between the regions of interest in which the beam lattice is fully resolved and coarse domains in which the lattice is effectively homogenized. Hence, the method is relatively straightforward to implement and calibrate. In this contribution, four variants of the QC method are investigated for their use for planar beam lattices which can also experience out-of-plane deformation. The different frameworks are compared to the direct lattice computations for three truly multiscale test cases in which a single lattice defect is present in an otherwise perfectly regular beam lattice. [less ▲] Detailed reference viewed: 378 (13 UL)Nitsche’s method for two and three dimensional NURBS patch coupling ; ; et al in Computational Mechanics (2014), 53(6), 1163-1182 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 ▲] Detailed reference viewed: 738 (16 UL)Efficient modeling of random heterogeneous materials with an uniform probability density function (slides) ; ; et al Scientific Conference (2014) 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 devel- oped 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: 250 (1 UL)Stochastic modelling of clay/epoxy nanocomposites ; ; et al in Composite Structures (2014), 118 This paper presents a numerical investigation of the mechanical properties of exfoliated clay/epoxy nanocomposites. The large scatter in the material properties and distribution of the inclusions and ... [more ▼] This paper presents a numerical investigation of the mechanical properties of exfoliated clay/epoxy nanocomposites. The large scatter in the material properties and distribution of the inclusions and matrix is taken into account by introducing an appropriate stochastic damage modelling at the nano scale. Then, the overall properties of the nanocomposite are upscaled using computational homogenisation. Two mechanical properties are investigated: the random distribution of the homogenised Young’s modulus and the overall loss of stiffness observed in the case of extreme loading. The results obtained in the former case are in good agreement with experimental results from the literature. In the second case, we show that exfoliation does not significantly affect the overall strength of the nanocomposite. [less ▲] Detailed reference viewed: 80 (0 UL)Two- and three-dimensional isogeometric cohesive elements for composite delamination analysis ; ; Bordas, Stéphane in Composites : Part B, Engineering (2014), 60 We propose an automatic numerical method requiring minimal user intervention to simulate delamination in composite structures. We develop isogeometric cohesive elements for two- and three-dimensional ... [more ▼] We propose an automatic numerical method requiring minimal user intervention to simulate delamination in composite structures. We develop isogeometric cohesive elements for two- and three-dimensional delamination by exploiting the knot insertion algorithm directly from CAD data to generate cohesive elements along delamination. A complete computational framework is presented including pre-processing, processing and post-processing. They are explained in detail and implemented in MIGFEM - an open source Matlab Isogemetric Analysis code developed by the authors. The composite laminates are modeled using both NURBS solid and rotation-free shell elements. Several two and three dimensional examples ranging from standard delamination tests (the mixed mode bending test) to the L-shaped specimen with a fillet, three dimensional (3D) double cantilever beam and a 3D singly curved thick-walled laminate are provided. The method proposed provides a bi-directional system in which one can go forward from CAD to analysis and backwards from analysis to CAD. This is believed to facilitate the design of composite structures. © 2013 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 190 (4 UL)Nitsche’s method method for mixed dimensional analysis: conforming and non-conforming continuum-beam and continuum-plate coupling ; ; et al in Computer Methods in Applied Mechanics & Engineering (2014) A Nitche’s method is presented to couple different mechanical models. They include coupling of a solid and a beam and of a solid and a plate. Both conforming and non-conforming formulations are presented ... [more ▼] A Nitche’s method is presented to couple different mechanical models. They include coupling of a solid and a beam and of a solid and a plate. Both conforming and non-conforming formulations are presented. In a non-conforming formulation, the structure domain is overlapped by a refined solid model which is needed to either get more accuracy or to capture highly nonlinear events. Applications can be found in multi-dimensional analyses in which parts of a structure are modeled with solid elements and others are modeled using a coarser model with beam and/or plate elements. Discretisations are performed using both standard Lagrange elements and high order NURBS (Non Uniform Rational Bsplines) based isogeometric elements. We present various examples to demonstrate the performance of the method. [less ▲] Detailed reference viewed: 264 (17 UL)Isogeometric analysis suitable trivariate NURBS representation of composite panels with a new offset algorithm ; ; Bordas, Stéphane et al in Computer-Aided Design (2014), 55 Trivariate NURBS (non-uniform rational B-splines) representation of composite panels which is suitable for three-dimensional isogeometric analysis (IGA) is constructed with a new curve/surface offset ... [more ▼] Trivariate NURBS (non-uniform rational B-splines) representation of composite panels which is suitable for three-dimensional isogeometric analysis (IGA) is constructed with a new curve/surface offset algorithm. The proposed offset algorithm, which is required by IGA, is non-existent in the CAD literature. Using the presented approach, finite element analysis of composite panels can be performed with the only input being the geometry representation of the composite surface. The method proposed provides a bi-directional system in which one can go forward from CAD to analysis and backwards from analysis to CAD. This is believed to facilitate the design of composite structures. Different parts (patches) can be parametrized independently of each other and glued together, in the finite element solver, by a discontinuous Galerkin method. A stress analysis of curved composite panel with stiffeners is provided to demonstrate the proposed framework. © 2014 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 294 (4 UL)Strain smoothing technique in 3D for nearly incompressible neo-Hookean material ; ; et al Report (2014) Detailed reference viewed: 182 (12 UL)IMPROVING THE CONVERGENCE OF BOUNDS FOR EFFECTIVE ELASTIC PARAMETERS OF HETEROGENEOUS MATERIALS ; ; Bordas, Stéphane Scientific Conference (2014) Detailed reference viewed: 224 (0 UL)An integrated design-analysis framework for three dimensional composite panels ; ; Bordas, Stéphane et al in Computer-Aided Design (2014) We present an integrated design-analysis framework for three dimensional composite panels. The main components of the proposed framework consist of (1) a new curve/surface offset algorithm and (2) the ... [more ▼] We present an integrated design-analysis framework for three dimensional composite panels. The main components of the proposed framework consist of (1) a new curve/surface offset algorithm and (2) the isogeometric concept recently emerged in the computational mechanics community. Using the presented approach, finite element analysis of composite panels can be performed with the only input is the geometry representation of the composite surface. In this paper, non-uniform rational B-splines (NURBS) are used to represent the panel surfaces. A stress analysis of curved composite panel with stiffeners is provided to demonstrate the proposed framework. [less ▲] Detailed reference viewed: 276 (6 UL)Gradient Smoothing for Nearly Incompressible Hyperealsticity ; ; et al Poster (2014) Detailed reference viewed: 100 (7 UL)Model order reduction for speeding up computational homogenisation methods of type FE2 ; ; Bordas, Stéphane Presentation (2014) Detailed reference viewed: 103 (2 UL)Gradient Smoothing for Nearly Incompressible Hyperelasticity ; ; et al Poster (2014) Detailed reference viewed: 81 (4 UL)Space-time reduced basis approximation and goal-oriented a posteriori error estimation for wave equation ; ; Bordas, Stéphane in Theory and Application of Model Order Reduction (2013, December) We study numerically the linear second order wave equation with an output quantity of interest which is a linear functional of the field variable using reduced basis approximation methods in the space ... [more ▼] We study numerically the linear second order wave equation with an output quantity of interest which is a linear functional of the field variable using reduced basis approximation methods in the space-time domain. The essential new ingredient is the a posteriori error estimation of the output quantity of interest. The technique, which is based on the well-known dual-weighted residual (DWR) method is deployed within a reduced basis approximation context. First, we introduce the reduced basis recipe - Galerkin projection onto a space spanned by the reduced basis functions which are constructed from the solutions of the governing PDE at several selected points in the parameter space. Second, in order to construct these basis functions we propose a new “goal-oriented” Proper Orthogonal Decomposition (POD)-Greedy sampling procedure, which is based on these new a posteriori error estimations. Finally, this a posteriori error estimation is also used to evaluate approximately the quality of many output computations in the online stage within the reduced basis procedure. [less ▲] Detailed reference viewed: 293 (3 UL)A multiscale partitioned reduced order model applied to damage simulation ; ; Bordas, Stéphane Scientific Conference (2013, July) Simulating fracture in realistic engineering components is computationally expensive. In the context of early-stage design, or reverse engineering, such simulations might need to be performed for a large ... [more ▼] Simulating fracture in realistic engineering components is computationally expensive. In the context of early-stage design, or reverse engineering, such simulations might need to be performed for a large range of material and geometric parameters, which makes the solution to the parametric problem of fracture unaffordable. Model order reduction, such as the proper orthogonal decomposition (POD), is one way to reduce significantly the computational time by reducing the number of spatial unknowns. The solution is searched for in a reduced space spanned by a few well-chosen basis vectors only. In the context of solid mechanics involving structural softening, the strong topological changes in the zone where damage localises are extremely sensitive to variations of the parameters, which requires reduced spaces of prohibitively large dimensions in order to approximate the solution with a sufficiently high degree of accuracy. Introduced in [1], partitioned model order reduction is an alternative to global model order reduction that essentially divides up the problem into smaller regions. Each region can then be tackled using a reduced model of appropriate size, if at all, depending on the local material non-linearities in the region. In the context of multiscale homogenization, simulations of representative volume elements (RVE) have to be performed to obtain the material properties in the different elements of a coarse mesh. When considering a nonlinear material, those multiple RVE simulations can be com- putationally very expensive. They however only differ by the history of boundary conditions applied. This contribution proposes to apply partitioned model order reduction to those RVEs with reduced bases parametrized by the boundary conditions. REFERENCES [1] P. Kerfriden, O. Goury, T. Rabczuk, S. Bordas, A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics, Computer Methods in Applied Mechanics and Engineering, 256:169–188, 2013. [less ▲] Detailed reference viewed: 290 (5 UL)An adaptive multiscale strategy to simulate fracture of composite structures ; ; Bordas, Stéphane Scientific Conference (2013, June 05) Detailed reference viewed: 376 (11 UL)Relaxing the compatibility condition in (extended) finite element methods: applications to fracture and nano-mechanics Bordas, Stéphane ; ; et al in Actes du CSMA, Giens, 2013 (2013, June 01) Recently, novel nite element methods were proposed from the coupling of stabilized conforming nodal integration with the standard nite element method [1]. An overarching theory has been devel- oped in the ... [more ▼] Recently, novel nite element methods were proposed from the coupling of stabilized conforming nodal integration with the standard nite element method [1]. An overarching theory has been devel- oped in the recent paper [2]. The main premise of this theory is the wish to achieve reliable results using lower order elements, i.e. simple meshes (triangles, tetrahedra). SFEM retains the accuracy and inherit the advantages of triangular and tetrahedral meshes to represent complex geometries and can bene t directly from any advance in automatic remeshing. Furthermore, smoothed FEMs are a lot less sensitive to locking (volumetric and shear) as well as mesh distortion (because Jacobians are not required since no isoparametric mapping is used. In this sense, SFEMs are a way to improve the quality of the results obtained by simplex elements, thereby signi cantly reducing the need for human-intervention in the generation of hexahedral meshes. http://csma2013.csma.fr/resumes/r_6ATKU0V3.pdf [less ▲] Detailed reference viewed: 242 (3 UL)A goal-oriented reduced basis method for the wave equation in inverse analysis ; ; Bordas, Stéphane in International Conference on Computational Mechanics CM13 Proceedings (2013, March) In this paper, we extend the reduced-basis methods developed earlier for wave equations to goal-oriented wave equations with a ne parameter dependence. The essential new ingredient is the dual (or adjoint ... [more ▼] In this paper, we extend the reduced-basis methods developed earlier for wave equations to goal-oriented wave equations with a ne parameter dependence. The essential new ingredient is the dual (or adjoint) problem and the use of its solution in a sampling procedure to pick up “goal-orientedly” parameter samples. First, we introduce the reduced-basis recipe — Galerkin projection onto a space YN spanned by the reduced basis functions which are constructed from the solutions of the governing partial di erential equation at several selected points in parameter space. Second, we propose a new “goal-oriented” Proper Orthogonal Decomposition (POD)–Greedy sampling procedure to construct these associated ba-sis functions. Third, based on the assumption of a ne parameter dependence, we use the o ine-online computational procedures developed earlier to split the computational procedure into o ine and online stages. We verify the proposed computational procedure by applying it to a three-dimensional simulation dental implant problem. The good numeri-cal results show that our proposed procedure performs better than the standard POD–Greedy procedure in terms of the accuracy of output functionals. [less ▲] Detailed reference viewed: 259 (3 UL) |
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