References of "Bordas, Stéphane 50000969"
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See detailDamage tolerance assessment directly from CAD: (extended) isogeometric boundary element methods (XIGABEM)
Peng, Xuan; Atroshchenko, Elena; Bordas, Stéphane UL

Scientific Conference (2014)

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See detailExplicit finite deformation analysis of isogeometric membranes
Chen, Lei; Nguyen-Thanh, Nhon; Nguyen-Xuan, Hung et al

in Computer Methods in Applied Mechanics and Engineering (2014)

NURBS-based isogeometric analysis was first extended to thin shell/membrane structures which allows for finite membrane stretching as well as large deflection and bending strain. The assumed non-linear ... [more ▼]

NURBS-based isogeometric analysis was first extended to thin shell/membrane structures which allows for finite membrane stretching as well as large deflection and bending strain. The assumed non-linear kinematics employs the Kirchhoff-Love shell theory to describe the mechanical behaviour of thin to ultrathin structures. The displacement fields are interpolated from the displacements of control points only, and no rotational degrees of freedom are used at control points. Due to the high order Ck (k ≥ 1) continuity of NURBS shape functions the Kirchhoff-Love theory can be seamlessly implemented. An explicit time integration scheme is used to compute the transient response of membrane structures to time-domain excitations, and a dynamic relaxation method is employed to obtain steady-state solutions. The versatility and good performance of the present formulation is demonstrated with the aid of a number of test cases, including a square membrane strip under static pressure, the inflation of a spherical shell under internal pressure, the inflation of a square airbag and the inflation of a rubber balloon. The mechanical contribution of the bending stiffness is also evaluated. [less ▲]

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See detailQuasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation
Beex, Lars UL; Kerfriden, Pierre; Rabczuk, Timon et al

in Computer Methods in Applied Mechanics and 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 ▲]

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See detailAn experimental/numerical investigation into the main driving force for crack propagation in uni-directional fibre-reinforced composite laminae
Cahill, L. M. A.; Natarajan, S.; Bordas, Stéphane UL et al

in Composite Structures (2014), 107

This paper presents an enriched finite element method to simulate the growth of cracks in linear elastic, aerospace composite materials. The model and its discretisation are also validated through a ... [more ▼]

This paper presents an enriched finite element method to simulate the growth of cracks in linear elastic, aerospace composite materials. The model and its discretisation are also validated through a complete experimental test series. Stress intensity factors are calculated by means of an interaction integral. To enable this, we propose application of (1) a modified approach to the standard interaction integral for heterogeneous orthotropic materials where material interfaces are present; (2) a modified maximum hoop stress criterion is proposed for obtaining the crack propagation direction at each step, and we show that the “standard” maximum hoop stress criterion which had been frequently used to date in literature, is unable to reproduce experimental results. The influence of crack description, material orientation along with the presence of holes and multi-material structures are investigated. It is found, for aerospace composite materials with View the MathML source ratios of approximately 10, that the material orientation is the driving factor in crack propagation. This is found even for specimens with a material orientation of 90°, which were previously found to cause difficulty in both damage mechanics and discrete crack models e.g. by the extended finite element method (XFEM). The results also show the crack will predominantly propagate along the fibre direction, regardless of the specimen geometry, loading conditions or presence of voids. [less ▲]

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See detailNitsche’s method method for mixed dimensional analysis: conforming and non-conforming continuum-beam and continuum-plate coupling
Nguyen, VP; Kerfriden, Pierre; Claus, SPA et al

in Computer Methods in Applied Mechanics and 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 ▲]

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See detailIsogeometric analysis of functionally graded plates using a refined plate theory
Nguyen-Xuan, H.; Tran, L. V.; Thai, C. H. et al

in Composites. Part B, Engineering (2014), 64

We present in this paper a simple and effective approach that incorporates isogeometric finite element analysis (IGA) with a refined plate theory (RPT) for static, free vibration and buckling analysis of ... [more ▼]

We present in this paper a simple and effective approach that incorporates isogeometric finite element analysis (IGA) with a refined plate theory (RPT) for static, free vibration and buckling analysis of functionally graded material (FGM) plates. A new inverse tangent distributed function through the plate thickness is proposed. The RPT enables us to describe the non-linear distribution of shear stresses through the plate thickness without any requirement of shear correction factors (SCF). IGA utilizes basis functions namely B-splines or non-uniform rational B-splines (NURBS) which reach easily the smoothness of any arbitrary order. It hence satisfies the C1 requirement of the RPT model. The present method approximates the displacement field with four degrees of freedom per each control point allowing an efficient solution process. [less ▲]

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See detailTwo- and three-dimensional isogeometric cohesive elements for composite delamination analysis
Nguyen, Vinh-Phu; Kerfriden, Pierre; Bordas, Stéphane UL

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 ▲]

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See detailNumerical analysis of the inclusion-crack interaction by the extended finite element method
Natarajan, S; Kerfriden, P; Mahapatra, D Roy et al

in International Journal for Computational Methods in Engineering Science and Mechanics (2014)

One of the partition of unity methods, the extended finite ele- ment method (XFEM), is applied to study the inclusion-crack in- teractions in an elastic medium. Both the inclusions and the crack are ... [more ▼]

One of the partition of unity methods, the extended finite ele- ment method (XFEM), is applied to study the inclusion-crack in- teractions in an elastic medium. Both the inclusions and the crack are modelled within the XFEM framework. A structured quadri- lateral mesh is used and the influence of crack length, the number of inclusions, and the geometry of the inclusions on the crack tip stress field are numerically studied. The interaction integral for non-homogeneous materials is used to compute the stress intensity factors ahead of the crack tip. The accuracy and flexibility of the XFEM is demonstrated by various numerical examples. [less ▲]

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See detailAn integrated design-analysis framework for three dimensional composite panels
Nguyen, Vinh-Phu; Kerfriden, Pierre; Bordas, Stéphane UL 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 ▲]

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See detailAnalysis of functionally graded material plates using triangular elements with cell-based smoothed discrete shear gap method
Natarajan, S; Ferreira; Bordas, Stéphane UL et al

in Mathematical Problems in Engineering (2014), Article ID 247932

In this paper, a cell based smoothed finite element method with discrete shear gap technique is employed to study the static bending, free vibration, mechanical and thermal buckling behaviour of ... [more ▼]

In this paper, a cell based smoothed finite element method with discrete shear gap technique is employed to study the static bending, free vibration, mechanical and thermal buckling behaviour of functionally graded material (FGM) plates. The plate kinematics is based on the first order shear deformation theory and the shear locking is suppressed by a discrete shear gap method. The shear correction factors are evaluated by employing the energy equivalence principle. The material property is assumed to be temperature dependent and graded only in the thickness direction. The effective properties are computed by using the Mori-Tanaka homogenization method. The accuracy of the present formulation is validated against available solutions. A systematic parametric study is carried out to examine the influence the gradient index, the plate aspect ratio, skewness of the plate and the boundary conditions on the global response of the FGM plates. The effect of a centrally located circular cutout on the global response is also studied. [less ▲]

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See detailAn extended finite element method (XFEM) for linear elastic fracture with smooth nodal stress
Peng, Xuan; Kulasegaram, Sivakumar; Bordas, Stéphane UL et al

in Engineering Fracture Mechanics (2014)

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See detailModel order reduction for speeding up computational homogenisation methods of type FE2
Goury, Olivier; Kerfriden, Pierre; Bordas, Stéphane UL

Presentation (2014)

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See detailFundamental Solutions and Dual Boundary Element Method for Crack Problems in Plane Cosserat Elasticity
Atroshchenko, Elena; Bordas, Stéphane UL

in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (2014)

In this paper, both singular and hypersingular fundamental solutions of plane Cosserat elasticity are derived and given in a ready-to-use form. The hypersingular fundamental solutions allow to formulate ... [more ▼]

In this paper, both singular and hypersingular fundamental solutions of plane Cosserat elasticity are derived and given in a ready-to-use form. The hypersingular fundamental solutions allow to formulate the analogue of Somigliana stress identity, which can be used to obtain the stress and couple stress fields inside the domain from the boundary values of the displacements, microrotation and stress and couple stress tractions. Using these newly derived fundamental solutions, the boundary integral equations of both types are formulated and solved by the boundary element method. Simultaneous use of both types of the equations (approach known as the dual BEM) allows to treat problems where parts of the boundary are overlapping, such as crack problems, and to do this for general geometry and loading conditions. The high accuracy of the boundary element method for both types of equations is demonstrated for a number of benchmark problems, including a Griffith crack problem and a plate with an edge crack. The detailed comparison of the BEM-results and the analytical solution for a Griffith crack is given, particularly, in terms of stress and couple stress intensity factors, as well as the crack opening displacements and microrotations on the crack faces. A modified method for computing the couple stress intensity factors is also proposed and evaluated. Finally, the asymptotic behavior of the solution to the Cosserat crack problems, in the vicinity of the crack tip is analyzed. [less ▲]

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See detailStrain smoothing technique in 3D for nearly incompressible neo-Hookean material
Lee, Chang-Kye; Mihai, L. Angela; Kerfriden, Pierre et al

Report (2014)

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See detailIMPROVING THE CONVERGENCE OF BOUNDS FOR EFFECTIVE ELASTIC PARAMETERS OF HETEROGENEOUS MATERIALS
Heaney, Claire; Kerfriden, Pierre; Bordas, Stéphane UL

Scientific Conference (2014)

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See detailGlobal energy minimization for multiple fracture growth
Sutula, Danas; Bordas, Stéphane UL

Report (2013)

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See detailSpace-time reduced basis approximation and goal-oriented a posteriori error estimation for wave equation
Hoang, Khac Chi; Kerfriden, Pierre; Bordas, Stéphane UL

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 ▲]

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See detailAdvances in Applied Mechanics
Bordas, Stéphane UL

Book published by Elsevier (2013)

Advances in Applied Mechanics draws together recent significant advances in various topics in applied mechanics. Published since 1948, Advances in Applied Mechanics aims to provide authoritative review ... [more ▼]

Advances in Applied Mechanics draws together recent significant advances in various topics in applied mechanics. Published since 1948, Advances in Applied Mechanics aims to provide authoritative review articles on topics in the mechanical sciences, primarily of interest to scientists and engineers working in the various branches of mechanics, but also of interest to the many who use the results of investigations in mechanics in various application areas, such as aerospace, chemical, civil, environmental, mechanical and nuclear engineering. [less ▲]

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See detailsmooth nodal stress in the XFEM for crack propagation simulations
Peng, Xuan; Bordas, Stéphane UL; Natarajan, Sundararajan

Scientific Conference (2013, September)

In this paper, we present a method to achive smooth nodal stresses in the XFEM without post-processing. This method was developed by borrowing ideas from ``twice interpolating approximations'' (TFEM) [1 ... [more ▼]

In this paper, we present a method to achive smooth nodal stresses in the XFEM without post-processing. This method was developed by borrowing ideas from ``twice interpolating approximations'' (TFEM) [1]. The salient feature of the method is to introduce an ``average'' gradient into the construction of the approximation, resulting in improved solution accuracy, both in the vicinity of the crack tip and in the far field. Due to the high order polynomial basis provided by the interpolants, the new approximation enhances the smoothness of the solution without requiring an increased number of degrees of freedom. This is particularly advantageous for low-order elements and in fracture mechanics, where smooth stresses are important for certain crack propagation criteria, e.g. based on maximum principal stresses. Since the new approach adopts the same mesh discretization, i.e. simplex meshes, it can be easily extended into various problems and is easily implemented. We discuss the increase in the bandwidth which is the major drawback of the present method and can be somewhat alleviated by using an element-by-element solution strategy. Numerical tests show that the new method is as robust as XFEM, considering precision, model size and post-processing time. By comparing in detail the behaviour of the method on crack propagation examples, we can conclude that for two-dimensional problems, the proposed method tends to be an efficient alternative to the classical XFEM [2][3] especially when local, stress-based propagation criteria are used. [less ▲]

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See detailAnalysis using higher-order XFEM: Implicit representation of geometrical features from a given parametric representation
Moumnassi, Mohammed; Bordas, Stéphane UL; Figueredo, Rémi et al

in Mécanique & Industries (2013, August 30)

We present a promising approach to reduce the difficulties associated with meshing complex curved domain boundaries for higher-order finite elements. In this work, higher-order XFEM analyses for strong ... [more ▼]

We present a promising approach to reduce the difficulties associated with meshing complex curved domain boundaries for higher-order finite elements. In this work, higher-order XFEM analyses for strong discontinuity in the case of linear elasticity problems are presented. Curved implicit boundaries are approximated inside an unstructured coarse mesh by using parametric information extracted from the parametric representation (the most common in Computer Aided Design CAD). This approximation provides local graded sub-mesh (GSM) inside boundary elements (i.e. an element split by the curved boundary) which will be used for integration purpose. Sample geometries and numerical experiments illustrate the accuracy and robustness of the proposed approach. [less ▲]

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