References of "Bordas, Stéphane 50000969"
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See detailRelaxing the compatibility condition in (extended) finite element methods: applications to fracture and nano-mechanics
Bordas, Stéphane UL; Kerfriden, Pierre; Nguyen-Xuan, Hung 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 ▲]

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See detailOptimization of elastic properties and weaving patterns of woven composites
Abu Bakar, Ilyani Akmar; Kramer, Oliver; Bordas, Stéphane UL et al

in Composite Structures (2013), 100

Predictions of geometric characteristics and elastic properties of patterns in woven fabric composites are proposed based on unit cells. This study addresses the optimization of the elastic properties ... [more ▼]

Predictions of geometric characteristics and elastic properties of patterns in woven fabric composites are proposed based on unit cells. This study addresses the optimization of the elastic properties within woven fabric composite unit cells with multiple designs based on periodic boundary conditions and evolutionary algorithms. Furthermore, the study permits a reliable prediction of mechanical behavior of woven fabric composites unit cells in which the weave patterns are the variables. The models are treated as a single-ply for each weave pattern embedded in a matrix pocket. The analyzed weave patterns are created by TexGen, the simulation is done with ABAQUS. At the unit cell level, effective elastic properties of the yarn were estimated from Finite Element (FE) simulations using periodic boundary conditions. An evolutionary algorithm is adopted in optimizing the elastic properties of woven fabric composites with recombination and mutation operators. We present a parameter study to investigate the effect of various geometric parameters. Those parameters include the gap length, the shape of the yarn section, the yarn thickness, the constituent materials, the fiber volume fraction and the elastic properties. By examining this optimized model through the pre-determined parameters as mentioned above, an optimal parameter set for composite's performance can be properly selected. © 2013 Elsevier Ltd. [less ▲]

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See detailSupersonic flutter analysis of functionally graded material plates with cracks
Natarajan, Sundararajan; Manickam, Ganapathi; Bordas, Stéphane UL

in Frontiers in Aerospace Engineering (2013), 2(2), 91--97

In this paper, the flutter behaviour of functionally graded material plates immersed in a supersonic flow is studied. An enriched 4-noded quadrilateral element based on field consistency approach is used ... [more ▼]

In this paper, the flutter behaviour of functionally graded material plates immersed in a supersonic flow is studied. An enriched 4-noded quadrilateral element based on field consistency approach is used for this study. The crack is modelled independent of the underlying mesh using partition of unity method (PUM), the extended finite element method (XFEM). The material properties are assumed to be graded only in the thickness direction and the effective material properties are estimated using the rule of mixtures. The plate kinematics is described based on the first order shear deformation theory (FSDT) and the shear correction factors are evaluated employing the energy equivalence principle. The influence of the crack length, the crack orientation, the flow angle and the gradient index on the aerodynamic pressure and the frequency are numerically studied. The results obtained here reveal that the critical frequency and pressure decrease with increase in crack the length and are minimum when the crack is aligned to the flow angle. [less ▲]

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See detailNURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter
Valizadeh, N; Natarajan, Sundarajan; González-Estrada, Octavio Andrés et al

in Composite Structures (2013), 99

In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material ... [more ▼]

In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material properties are assumed to be graded only in the thickness direction and the effective properties are computed either using the rule of mixtures or by Mori–Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation plate theory (FSDT). The shear correction factors are evaluated employing the energy equivalence principle and a simple modification to the shear correction factor is presented to alleviate shear locking. Static bending, mechanical and thermal buckling, linear free flexural vibration and supersonic flutter analysis of FGM plates are numerically studied. The accuracy of the present formulation is validated against available three-dimensional solutions. A detailed numerical study is carried out to examine the influence of the gradient index, the plate aspect ratio and the plate thickness on the global response of functionally graded material plates. [less ▲]

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See detailStress analysis without meshing: isogeometric boundary element method
Lian, Haojie; Simpson, Robert; Bordas, Stéphane UL

in Proceedings of the ICE - Engineering and Computational Mechanics (2013), 166(2), 8899

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See detailSensitivity Analysis and Shape Optimisation through a T-spline Isogeometric Boundary Element Method
Lian, Haojie; Simpson, Robert; Bordas, Stéphane UL

Scientific Conference (2013, March 25)

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See detailSensitivity Analysis and Shape Optimisation through a T-spline Isogeometric Boundary Element Method
Lian, Haojie; Simpson, Robert; Bordas, Stéphane UL

Scientific Conference (2013, March)

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See detailA goal-oriented reduced basis method for the wave equation in inverse analysis
Hoang, Khac Chi; Kerfriden, Pierre; Bordas, Stéphane UL

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 ▲]

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See detailAn isogeometric boundary element method for elastostatic analysis: 2D implementation aspects
Simpson, Robert; Bordas, Stéphane UL; Lian, Haojie et al

in Computers and Structures (2013), 118

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See detailIsogeometric boundary element analysis using unstructured T-splines
Scott, M. A.; Simpson, R. N.; Evans, J. A. et al

in Computer Methods in Applied Mechanics and Engineering (2013), 254

We couple collocated isogeometric boundary element methods and unstructured analysis-suitable T-spline surfaces for linear elastostatic problems. We extend the definition of analysis-suitable T-splines to ... [more ▼]

We couple collocated isogeometric boundary element methods and unstructured analysis-suitable T-spline surfaces for linear elastostatic problems. We extend the definition of analysis-suitable T-splines to encompass unstructured control grids (unstructured meshes) and develop basis functions which are smooth (rational) polynomials defined in terms of the Bézier extraction framework and which pass standard patch tests. We then develop a collocation procedure which correctly accounts for sharp edges and corners, extraordinary points, and T-junctions. This approach is applied to several three-dimensional problems, including a real-world T-spline model of a propeller. We believe this work clearly illustrates the power of combining new analysis-suitable computer aided design technologies with established analysis methodologies, in this case, the boundary element method. © 2012 Elsevier B.V. [less ▲]

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See detailVibration of functionally graded material plates with cutouts & cracks in thermal environment
Rahimabadi, A. A.; Natarajan, S.; Bordas, Stéphane UL

in Key Engineering Materials (2013), 560

In this paper, the effect of a centrally located cutout (circular and elliptical) and cracks emanating from the cutout on the free flexural vibration behaviour of functionally graded material plates in ... [more ▼]

In this paper, the effect of a centrally located cutout (circular and elliptical) and cracks emanating from the cutout on the free flexural vibration behaviour of functionally graded material plates in thermal environment is studied. The discontinuity surface is represented independent of the mesh by exploiting the partition of unity method framework. A Heaviside function is used to capture the jump in the displacement across the discontinuity surface and asymptotic branch functions are used to capture the singularity around the crack tip. An enriched shear flexible 4-noded quadrilateral element is used for the spatial discretization. The properties are assumed to vary only in the thickness direction. The effective properties of the functionally graded material are estimated using the Mori-Tanaka homogenization scheme and the plate kinematics is based on the first order shear deformation theory. The influence of the plate geometry, the geometry of the cutout, the crack length, the thermal gradient and the boundary conditions on the free flexural vibration is numerically studied. © (2013) Trans Tech Publications, Switzerland. [less ▲]

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See detailDefect engineering of 2D monatomic-layer materials
Peng, Q.; Crean, J.; Dearden, A. K. et al

in Modern Physics Letters B (2013), 27(23),

Atomic-thick monolayer two-dimensional materials present advantageous properties compared to their bulk counterparts. The properties and behavior of these monolayers can be modified by introducing defects ... [more ▼]

Atomic-thick monolayer two-dimensional materials present advantageous properties compared to their bulk counterparts. The properties and behavior of these monolayers can be modified by introducing defects, namely defect engineering. In this paper, we review a group of common two-dimensional crystals, including graphene, graphyne, graphdiyne, graphn-yne, silicene, germanene, hexagonal boron nitride monolayers and MoS2 monolayers, focusing on the effect of the defect engineering on these two-dimensional monolayer materials. Defect engineering leads to the discovery of potentially exotic properties that make the field of two-dimensional crystals fertile for future investigations and emerging technological applications with precisely tailored properties. © World Scientific Publishing Company. [less ▲]

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See detailAn isogeometric boundary element method for elastostatic analysis: 2D implementation aspects
Simpson, R. N.; Bordas, Stéphane UL; Lian, H. et al

in Computers and Structures (2013), 118

The concept of isogeometric analysis, whereby the parametric functions that are used to describe CAD geometry are also used to approximate the unknown fields in a numerical discretisation, has progressed ... [more ▼]

The concept of isogeometric analysis, whereby the parametric functions that are used to describe CAD geometry are also used to approximate the unknown fields in a numerical discretisation, has progressed rapidly in recent years. This paper advances the field further by outlining an isogeometric boundary element Method (IGABEM) that only requires a representation of the geometry of the domain for analysis, fitting neatly with the boundary representation provided completely by CAD. The method circumvents the requirement to generate a boundary mesh representing a significant step in reducing the gap between engineering design and analysis. The current paper focuses on implementation details of 2D IGABEM for elastostatic analysis with particular attention paid towards the differences over conventional boundary element implementations. Examples of Matlab® code are given whenever possible to aid understanding of the techniques used. [less ▲]

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See detailCertification of projection-based reduced order modelling in computational homogenisation by the constitutive relation error
Kerfriden, P.; Ródenas, J. J.; Bordas, Stéphane UL

in International Journal for Numerical Methods in Engineering (2013)

SUMMARY: 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 ... [more ▼]

SUMMARY: 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 finite 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. © 2013 John Wiley & Sons, Ltd. [less ▲]

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See detailEffects of elastic strain energy and interfacial stress on the equilibrium morphology of misfit particles in heterogeneous solids
Zhao, X.; Duddu, R.; Bordas, Stéphane UL et al

in Journal of the Mechanics and Physics of Solids (2013), 61(6), 1433-1445

This paper presents an efficient sharp interface model to study the morphological transformations of misfit particles in phase separated alloys. Both the elastic anisotropy and interfacial energy are ... [more ▼]

This paper presents an efficient sharp interface model to study the morphological transformations of misfit particles in phase separated alloys. Both the elastic anisotropy and interfacial energy are considered. The geometry of the material interface is implicitly described by the level set method so that the complex morphological transformation of microstructures can be accurately captured. A smoothed extended finite element method is adopted to evaluate the elastic field without requiring remeshing. The equilibrium morphologies of particles are shown to depend on the elastic anisotropy, interfacial energy as well as the particle size. Various morphological transformations, such as shape changes from spheres to cuboids, directional aligned platelets and particle splitting, are observed. The simulated results are in good agreement with experimental observations. The proposed model provides a useful tool in understanding the morphological transformation of precipitates, which will facilitate the analysis and design of metallic alloys. © 2013 Elsevier Ltd. [less ▲]

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See detailImplementation of a XFEM toolbox in Diffpack
Hossain, Md Naim; Paladim, Daniel; Vogel, Frank et al

in International Conference on Extended Finite Element Methods - XFEM 2013, September 11 – 13, 2013, Lyon, France (2013)

The Diffpack Development Framework is an object-oriented software environment for the numerical solution of partial differential equations (PDEs). By its design, Diffpack intends to close the gap between ... [more ▼]

The Diffpack Development Framework is an object-oriented software environment for the numerical solution of partial differential equations (PDEs). By its design, Diffpack intends to close the gap between black-box simulation packages and technical computing environments using interpreted computer languages. The framework provides a high degree of modeling flexibility, while still offering the computational efficiency needed for most demanding simulation problems in science and engineering. Technically speaking, Diffpack is a collection of C++ libraries with classes, functions and utility programs. The numerical functionality is embedded in an environment of software engineering tools supporting the management of Diffpack development projects. Diffpack supports a variety of numerical methods with distinct focus on the finite element method (FEM) but has no inherent restrictions on the types of PDEs and therefore applications to be solved. The key point of partition of unity enriched methods such as XFEM and GFEM is to help capture discontinuities and singularities or large gradients in solutions, which are not well resolved by h or prefinement [1]. The general idea is that the mesh need not conform to the moving boundaries so that minimal or no remeshing is required during the analysis. Our main motivation is to provide a generic implementation of enrichment within a flexible C++ environment, namely the Diffpack platform. The work was inspired by some of our earlier work [6,9] and that of other colleagues [5,7,8]. We demonstrate how object-oriented programming is particularly useful for the treatment of data structures and operations associated with XFEM : mesh-geometry interaction, non-standard integration rules, application of boundary conditions, treatment of level set data [2,6]. We detail the implementation of such features and verify and validate their implementation based on [5]. We show results based on unshifted, shifted [1] and study the behaviour of the stable generalized finite element method (SGFEM) to avoid blending effects and help control the conditioning of the system matrix [4]. For integration of elements cut by interface we use an in-house Delaunay Triangulation algorithm proposed by [3,5] and presented in detail in a companion paper. [less ▲]

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See detailAnalysis of composite plates by a unified formulation-cell based smoothed finite element method and field consistent elements
Natarajan, S.; Ferreira, Ana UL; Bordas, Stéphane UL et al

in Composite Structures (2013), 105

In this article, we combine Carrera's Unified Formulation (CUF) [13,7] and cell based smoothed finite element method [28] for studying the static bending and the free vibration of thin and thick laminated ... [more ▼]

In this article, we combine Carrera's Unified Formulation (CUF) [13,7] and cell based smoothed finite element method [28] for studying the static bending and the free vibration of thin and thick laminated plates. A 4-noded quadrilateral element based on the field consistency requirement is used for this study to suppress the shear locking phenomenon. The combination of cell based smoothed finite element method and field consistent approach with CUF allows a very accurate prediction of field variables. The accuracy and efficiency of the proposed approach are demonstrated through numerical experiments. © 2013 Elsevier Ltd. [less ▲]

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See detailCutting in real time in corotational elasticity and perspectives on simulating cuts
Courtecuisse, H.; Kerfriden, P.; Bordas, Stéphane UL

Book published by Springer (2013)

We focus here on the simulation of surgical acts of types similar to cutting and needle insertion in soft tissue, in real time (500 Hz), where the scale of the surgical instrument is several orders of ... [more ▼]

We focus here on the simulation of surgical acts of types similar to cutting and needle insertion in soft tissue, in real time (500 Hz), where the scale of the surgical instrument is several orders of magnitude smaller than that of the organ. [less ▲]

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See detailStatistical extraction of process zones and representative subspaces in fracture of random composites
Kerfriden, P.; Schmidt, K. M.; Rabczuk, T. et al

in International Journal for Multiscale Computational Engineering (2013), 11(3), 253-287

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly ... [more ▼]

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly approximated in a low-dimensional deterministic space. Such a low-dimensional space is obtained by a spectral analysis performed on precomputed solution samples. A greedy algorithm is proposed to identify both process zone and low-dimensional representative subspace for the solution in the complementary region. In addition to the novelty of the tools proposed in this paper for the analysis of localized phenomena, we show that the reduced space generated by the method is a valid basis for the construction of a reduced-order model. © 2013 by Begell House, Inc. [less ▲]

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See detailA hybrid smoothed extended finite element/level set method for modeling equilibrium shapes of nano-inhomogeneities
Zhao, X.; Bordas, Stéphane UL; Qu, J.

in Computational Mechanics (2013)

Interfacial energy plays an important role in equilibrium morphologies of nanosized microstructures of solid materials due to the high interface-to-volume ratio, and can no longer be neglected as it does ... [more ▼]

Interfacial energy plays an important role in equilibrium morphologies of nanosized microstructures of solid materials due to the high interface-to-volume ratio, and can no longer be neglected as it does in conventional mechanics analysis. When designing nanodevices and to understand the behavior of materials at the nano-scale, this interfacial energy must therefore be taken into account. The present work develops an effective numerical approach by means of a hybrid smoothed extended finite element/level set method to model nanoscale inhomogeneities with interfacial energy effect, in which the finite element mesh can be completely independent of the interface geometry. The Gurtin-Murdoch surface elasticity model is used to account for the interface stress effect and the Wachspress interpolants are used for the first time to construct the shape functions in the smoothed extended finite element method. Selected numerical results are presented to study the accuracy and efficiency of the proposed method as well as the equilibrium shapes of misfit particles in elastic solids. The presented results compare very well with those obtained from theoretical solutions and experimental observations, and the computational efficiency of the method is shown to be superior to that of its most advanced competitor. © 2013 Springer-Verlag Berlin Heidelberg. [less ▲]

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