References of "Bordas, Stéphane 50000969"
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See detailNitsche’s method for two and three dimensional NURBS patch coupling
Nguyen, Vinh-Phu; Kerfriden, Pierre; Brino, Marco et al

in Computational Mechanics (in press)

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 ▲]

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See detailSimple and extensible plate and shell finite element models through automatic code generation tools
Hale, Jack UL; Brunetti, Matteo; Bordas, Stéphane UL et al

in Computers & Structures (in press)

A large number of advanced finite element shell formulations have been developed, but their adoption is hindered by complexities of transforming mathematical formulations into computer code. Furthermore ... [more ▼]

A large number of advanced finite element shell formulations have been developed, but their adoption is hindered by complexities of transforming mathematical formulations into computer code. Furthermore, it is often not straightforward to adapt existing implementations to emerging frontier problems in thin structural mechanics including nonlinear material behaviour, complex microstructures, multi-physical couplings, or active materials. We show that by using a high-level mathematical modelling strategy and automatic code generation tools, a wide range of advanced plate and shell finite element models can be generated easily and efficiently, including: the linear and non-linear geometrically exact Naghdi shell models, the Marguerre-von K ́arm ́an shallow shell model, and the Reissner-Mindlin plate model. To solve shear and membrane-locking issues, we use: a novel re-interpretation of the Mixed Interpolation of Tensorial Component (MITC) procedure as a mixed-hybridisable finite element method, and a high polynomial order Partial Selective Reduced Integration (PSRI) method. The effectiveness of these approaches and the ease of writing solvers is illustrated through a large set of verification tests and demo codes, collected in an open-source library, FEniCS-Shells, that extends the FEniCS Project finite element problem solving environment. [less ▲]

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See detailThe edge-based strain smoothing method for compressible and nearly incompressible non-linear elasticity for solid mechanics
Lee, Chang-Kye; Mihai, L. Angela; Kerfriden, Pierre et al

E-print/Working paper (in press)

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See detailFree boundary problems: numerical methods and data-driven simulations
Bordas, Stéphane UL

Presentation (2018, March 05)

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See detailData-driven modelling and simulation: fracture and medical simulations
Bordas, Stéphane UL

Presentation (2018, February 08)

Predicting failure in aircraft structures – simulating fracture across scales and times You could fly every day of your life in a commercial aircraft for twenty thousand years without suffering a fatal ... [more ▼]

Predicting failure in aircraft structures – simulating fracture across scales and times You could fly every day of your life in a commercial aircraft for twenty thousand years without suffering a fatal accident. This extraordinary level of safety is the product of decades of engineering and materials science research. Simultaneously, engineers have strived to produce lighter and stronger aircraft, with increased range and metals have thus been gradually replaced by lighter advanced composite materials which take up more than half of the structural weight of today's most advanced aircraft. Such progress has been largely enabled by modeling and simulation of materials and structures, which have revolutionized design by enabling engineers to investigate virtually various design strategies. This presentation will focus on the challenges which have been posed, are posed, and will be posed to such modeling and simulation tools in the strive to predict the durability of lighter, stronger, longer-ranging and more reliable aircraft. [less ▲]

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See detailMultiple crack detection in 3D using a stable XFEM and global optimization
Agathos, Konstantinos; Chatzi, Eleni; Bordas, Stéphane UL

in Computational Mechanics (2018)

A numerical scheme is proposed for the detection of multiple cracks in three dimensional (3D) structures. The scheme is based on a variant of the extended finite element method (XFEM) and a hybrid ... [more ▼]

A numerical scheme is proposed for the detection of multiple cracks in three dimensional (3D) structures. The scheme is based on a variant of the extended finite element method (XFEM) and a hybrid optimizer solution. The proposed XFEM variant is particularly well-suited for the simulation of 3D fracture problems, and as such serves as an efficient solution to the so-called forward problem. A set of heuristic optimization algorithms are recombined into a multiscale optimization scheme. The introduced approach proves effective in tackling the complex inverse problem involved, where identification of multiple flaws is sought on the basis of sparse measurements collected near the structural boundary. The potential of the scheme is demonstrated through a set of numerical case studies of varying complexity. [less ▲]

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See detailOn the effect of grains interface parameters on the macroscopic properties of polycrystalline materials
Akbari, Ahmad; Kerfriden, Pierre; Bordas, Stéphane UL

in Computers & Structures (2018), 196

In this paper, the influence of microscopic parameters on the macroscopic behaviour of polycrystalline materials under different loading configuration is investigated. Linear elastic grains with zero ... [more ▼]

In this paper, the influence of microscopic parameters on the macroscopic behaviour of polycrystalline materials under different loading configuration is investigated. Linear elastic grains with zero thickness cohesive interfaces are considered at the microscale with in depth introduction of effective parameters. A multiscale method based on homogenisation technique is employed to bridge the scales. In order to minimize the homogenisation error, a representative volume element (RVE) of the microscopic structure is statistically determined to be used in the numerical analysis. For each loading condition of the RVE, several numerical examinations are conducted to illustrate the relationship between the microscopic parameters. Finally, the effects of microscopic critical fracture energies, maximum tensile and shear strengths of grain interfaces on the mechanical properties, i.e. stress-strain curve and yield surface at the macroscale are discussed in details. It is shown that macroscopic yield surface and stress strain curves can be used to characterise the microscopic properties. [less ▲]

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See detailUsing higher-order adjoints to accelerate the solution of UQ problems with random fields
Hale, Jack UL; Hauseux, Paul UL; Bordas, Stéphane UL

Poster (2018, January 08)

A powerful Monte Carlo variance reduction technique introduced in Cao and Zhang 2004 uses local derivatives to accelerate Monte Carlo estimation. This work aims to: develop a new derivative-driven ... [more ▼]

A powerful Monte Carlo variance reduction technique introduced in Cao and Zhang 2004 uses local derivatives to accelerate Monte Carlo estimation. This work aims to: develop a new derivative-driven estimator that works for SPDEs with uncertain data modelled as Gaussian random fields with Matérn covariance functions (infinite/high-dimensional problems) (Lindgren, Rue, and Lindström, 2011), use second-order derivative (Hessian) information for improved variance reduction over our approach in (Hauseux, Hale, and Bordas, 2017), demonstrate a software framework using FEniCS (Logg and Wells, 2010), dolfin-adjoint (Farrell et al., 2013) and PETSc (Balay et al., 2016) for automatic acceleration of MC estimation for a wide variety of PDEs on HPC architectures. [less ▲]

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See detailWeakening the tight coupling between geometry and simulation in isogeometric analysis: from sub- and super- geometric analysis to Geometry Independent Field approximaTion (GIFT)
Atroshchenko, Elena; Tomar, Satyendra UL; Xu, Gang et al

in International Journal for Numerical Methods in Engineering (2018)

This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution ... [more ▼]

This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main advantage of isogeometric analysis, i.e. preserves the original, exact CAD geometry (for example, given by NURBS), but allows pairing it with an approximation space which is more suitable/flexible for analysis, for example, T-splines, LR-splines, (truncated) hierarchical B-splines, and PHT-splines. This generalization offers the advantage of adaptive local refinement without the need to re-parameterize the domain, and therefore without weakening the link with the CAD model. We demonstrate the use of the method with different choices of the geometry and field splines, and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for non-nested spaces. [less ▲]

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See detailQuantifying the uncertainty in a hyperelastic soft tissue model with stochastic parameters
Hauseux, Paul UL; Hale, Jack UL; Cotin, Stéphane et al

in Applied Mathematical Modelling (2018), 62

We present a simple open-source semi-intrusive computational method to propagate uncertainties through hyperelastic models of soft tissues. The proposed method is up to two orders of magnitude faster than ... [more ▼]

We present a simple open-source semi-intrusive computational method to propagate uncertainties through hyperelastic models of soft tissues. The proposed method is up to two orders of magnitude faster than the standard Monte Carlo method. The material model of interest can be altered by adjusting few lines of (FEniCS) code. The method is able to (1) provide the user with statistical confidence intervals on quantities of practical interest, such as the displacement of a tumour or target site in an organ; (2) quantify the sensitivity of the response of the organ to the associated parameters of the material model. We exercise the approach on the determination of a confidence interval on the motion of a target in the brain. We also show that for the boundary conditions under consideration five parameters of the Ogden-Holzapfel-like model have negligible influence on the displacement of the target zone compared to the three most influential parameters. The benchmark problems and all associated data are made available as supplementary material. [less ▲]

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See detailA volume-averaged nodal projection method for the Reissner-Mindlin plate model
Ortiz-Bernardin, Alejandro; Köbrich, Philip; Hale, Jack UL et al

E-print/Working paper (2018)

We introduce a novel meshfree Galerkin method for the solution of Reissner-Mindlin plate problems that is written in terms of the primitive variables only (i.e., rotations and transverse displacement) and ... [more ▼]

We introduce a novel meshfree Galerkin method for the solution of Reissner-Mindlin plate problems that is written in terms of the primitive variables only (i.e., rotations and transverse displacement) and is devoid of shear-locking. The proposed approach uses linear maximum-entropy approximations and is built variationally on a two-field potential energy functional wherein the shear strain, written in terms of the primitive variables, is computed via a volume-averaged nodal projection operator that is constructed from the Kirchhoff constraint of the three-field mixed weak form. The stability of the method is rendered by adding bubble-like enrichment to the rotation degrees of freedom. Some benchmark problems are presented to demonstrate the accuracy and performance of the proposed method for a wide range of plate thicknesses. [less ▲]

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See detailConstructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization
Xu, Gang; Li, Ming; Mourrain, Bernard et al

in Computer Methods in Applied Mechanics & Engineering (2018), 328

In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries. Instead of the computational domain bounded by four B ... [more ▼]

In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries. Instead of the computational domain bounded by four B-spline curves, planar domains with high genus and more complex boundary curves are considered. Firstly, some pre-processing operations including B´ezier extraction and subdivision are performed on each boundary curve in order to generate a high-quality planar parameterization; then a robust planar domain partition framework is proposed to construct high-quality patch-meshing results with few singularities from the discrete boundary formed by connecting the end points of the resulting boundary segments. After the topology information generation of quadrilateral decomposition, the optimal placement of interior B´ezier curves corresponding to the interior edges of the quadrangulation is constructed by a global optimization method to achieve a patch-partition with high quality. Finally, after the imposition of C1/G1-continuity constraints on the interface of neighboring Bezier patches with respect to each quad in the quadrangulation, the high-quality Bezier patch parameterization is obtained by a local optimization method to achieve uniform and orthogonal iso-parametric structures while keeping the continuity conditions between patches. The efficiency and robustness of the proposed method are demonstrated by several examples which are compared to results obtained by the skeleton-based parameterization approach. [less ▲]

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See detailCalculating the Malliavin derivative of some stochastic mechanics problems
Hauseux, Paul UL; Hale, Jack UL; Bordas, Stéphane UL

in PLoS ONE (2017), 12(12), 0189994

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to ... [more ▼]

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper. [less ▲]

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See detailMicro-structured materials: inhomogeneities and imperfect interfaces in plane micropolar elasticity, a boundary element approach
Atroshchenko, Elena; Hale, Jack UL; Videla, Javier A. et al

in Engineering Analysis with Boundary Elements (2017), 83

In this paper we tackle the simulation of microstructured materials modelled as heterogeneous Cosserat media with both perfect and imperfect interfaces. We formulate a boundary value problem for an ... [more ▼]

In this paper we tackle the simulation of microstructured materials modelled as heterogeneous Cosserat media with both perfect and imperfect interfaces. We formulate a boundary value problem for an inclusion of one plane strain micropolar phase into another micropolar phase and reduce the problem to a system of boundary integral equations, which is subsequently solved by the boundary element method. The inclusion interface condition is assumed to be imperfect, which permits jumps in both displacements/microrotations and tractions/couple tractions, as well as a linear dependence of jumps in displacements/microrotations on continuous across the interface tractions/couple traction (model known in elasticity as homogeneously imperfect interface). These features can be directly incorporated into the boundary element formulation. The BEM-results for a circular inclusion in an in finite plate are shown to be in excellent agreement with the analytical solutions. The BEM-results for inclusions in finite plates are compared with the FEM-results obtained with FEniCS. [less ▲]

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See detailIsogeometric analysis of thin Reissner-Mindlin plates and shells: Locking phenomena and generalized local B-bar method
Hu, Qingyuan UL; Xia, Yang; Natarajan, Sundararajan et al

E-print/Working paper (2017)

We propose a generalized local $\bar{B}$ framework, addressing locking in degenerated Reissner-Mindlin plate and shell formulations in the context of isogeometric analysis. Parasitic strain components are ... [more ▼]

We propose a generalized local $\bar{B}$ framework, addressing locking in degenerated Reissner-Mindlin plate and shell formulations in the context of isogeometric analysis. Parasitic strain components are projected onto the physical space locally, i.e. at the element level, using a least-squares approach. The formulation is general and allows the flexible utilization of basis functions of different order as the projection bases. The present formulation is much cheaper computationally than the global $\bar{B}$ method. Through numerical examples, we show the consistency of the scheme, although the method is not Hu-Washizu variationally consistent. The numerical examples show that the proposed formulation alleviates locking and yields good accuracy for various thicknesses, even for slenderness ratios of $1 \times 10^5$, and has the ability to capture deformations of thin shells using relatively coarse meshes. From the detailed numerical study, it can be opined that the proposed method is less sensitive to locking and mesh distortion. [less ▲]

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See detailBayesian inference to identify parameters in viscoelasticity
Rappel, Hussein UL; Beex, Lars UL; Bordas, Stéphane UL

in Mechanics of Time-Dependent Materials (2017)

This contribution discusses Bayesian inference (BI) as an approach to identify parameters in viscoelasticity. The aims are: (i) to show that the prior has a substantial influence for viscoelasticity, (ii ... [more ▼]

This contribution discusses Bayesian inference (BI) as an approach to identify parameters in viscoelasticity. The aims are: (i) to show that the prior has a substantial influence for viscoelasticity, (ii) to show that this influence decreases for an increasing number of measurements and (iii) to show how different types of experiments influence the identified parameters and their uncertainties. The standard linear solid model is the material description of interest and a relaxation test, a constant strain-rate test and a creep test are the tensile experiments focused on. The experimental data are artificially created, allowing us to make a one-to-one comparison between the input parameters and the identified parameter values. Besides dealing with the aforementioned issues, we believe that this contribution forms a comprehensible start for those interested in applying BI in viscoelasticity. [less ▲]

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