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See detailNonlinear FEM code with Finite elasticity lecture note written by L.A. Mihai
Lee, Chang-Kye; Bordas, Stéphane UL

Learning material (2015)

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See detailInterfacial shear stress optimization in sandwich beams with polymeric core using non-uniform distribution of reinforcing ingredients
Ghasemi, Hamid; Kerfriden, Pierre; Muthu, Jacob et al

in Composite Structures (2015)

Core shearing and core/face debonding are two common failure states of sandwich beams which are mainly the result of excessive shear stresses in the core. Generally, the core made of homogeneous Fiber ... [more ▼]

Core shearing and core/face debonding are two common failure states of sandwich beams which are mainly the result of excessive shear stresses in the core. Generally, the core made of homogeneous Fiber Reinforced Polymer (FRP) shows better shear resistance in comparison with that made of pure polymer. Usually, this enhancement is however somewhat limited. This paper proposes a methodology to decrease interfacial stresses by presenting the optimal distribution of reinforcing ingredients in the polymeric matrix. For this purpose, a Non-Uniform Rational Bspline (NURBS) based reinforcement distribution optimizer is developed. This technique aims at the local stress minimization within any arbitrary zone of the design domain. In our methodology, optimization and model analysis (calculation of the objective function and the design constraints) have common data sets. The quadratic NURBS basis functions smoothly define the reinforcement distribution function as a NURBS surface. The core and face sheets are modeled as multi-patches and compatibility in the displacement field is enforced by the penalty method. An adjoint sensitivity method is devised to minimize the objective function within areas of interest defined over arbitrary regions in the design domain. It is also used for efficient updating of design variables through optimization iterations. The method is verified by several examples. [less ▲]

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See detailA fast, certified and "tuning-free" two-field reduced basis method for the metamodelling of parametrised elasticity problems
Hoang, Khac Chi; Kerfriden, Pierre; Bordas, Stéphane UL

in Computer Methods in Applied Mechanics and Engineering (2015)

This paper proposes a new reduced basis algorithm for the metamodelling of parametrised elliptic problems. The developments rely on the Constitutive Relation Error (CRE), and the construction of separate ... [more ▼]

This paper proposes a new reduced basis algorithm for the metamodelling of parametrised elliptic problems. The developments rely on the Constitutive Relation Error (CRE), and the construction of separate reduced order models for the primal variable (displacement) and flux (stress) fields. A two-field Greedy sampling strategy is proposed to construct these two fields simultaneously and efficient manner: at each iteration, one of the two fields is enriched by increasing the dimension of its reduced space in such a way that the CRE is minimised. This sampling strategy is then used as a basis to construct goal-oriented reduced order modelling. The resulting algorithm is certified and "tuning-free": the only requirement from the engineer is the level of accuracy that is desired for each of the outputs of the surrogate. It is also one order of magnitude more efficient in terms of computational expenses than competing methodologies. [less ▲]

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See detailAdvances in Applied Mechanics
Bordas, Stéphane UL

Book published by Elsevier (2014)

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 detailIsogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates
Shuohui, Yin; Hale, Jack UL; Yu, Tiantang et al

in Composite Structures (2014), 118

An effective, simple, robust and locking-free plate formulation is proposed to analyze the static bending, buckling, and free vibration of homogeneous and functionally graded plates. The simple first ... [more ▼]

An effective, simple, robust and locking-free plate formulation is proposed to analyze the static bending, buckling, and free vibration of homogeneous and functionally graded plates. The simple first-order shear deformation theory (S-FSDT), which was recently presented in Thai and Choi (2013) [11], is naturally free from shear-locking and captures the physics of the shear-deformation effect present in the original FSDT, whilst also being less computationally expensive due to having fewer unknowns. The S-FSDT requires C1-continuity that is simple to satisfy with the inherent high-order continuity of the non-uniform rational B-spline (NURBS) basis functions, which we use in the framework of isogeometric analysis (IGA). Numerical examples are solved and the results are compared with reference solutions to confirm the accuracy of the proposed method. Furthermore, the effects of boundary conditions, gradient index, and geometric shape on the mechanical response of functionally graded plates are investigated. [less ▲]

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See detailShape optimisation with isogeometric boundary element methods
Lian, Haojie; Bordas, Stéphane UL; Kerfriden, Pierre

Presentation (2014, December)

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See detailMultiscale computational mechanics: industrial applications
Bordas, Stéphane UL; Kerfriden, Pierre; Beex, Lars UL et al

Presentation (2014, November 25)

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See detailMultiscale fracture across scales and time
Bordas, Stéphane UL; Kerfriden, Pierre

Scientific Conference (2014, November 11)

Multi-scale Computational Mechanics in Aerospace Engineering Flying is today one of the safest ways to spend our time. In the United Kingdom, for example, it is 33,000 times more likely to die from a ... [more ▼]

Multi-scale Computational Mechanics in Aerospace Engineering Flying is today one of the safest ways to spend our time. In the United Kingdom, for example, it is 33,000 times more likely to die from a clinical error than from an air crash. This is probably the consequence of over a century of experience building, starting with the Wright brothers at the beginning of the 20th century to the most recent aerospace developments culminating in technological giants such as the Airbus A380 and the Boeing Dreamliner, through the enlightening catastrophic events of the "Comet Aircraft”, ``Liberty Ships'' and many others. Yet, with the increasing urge to increase flight efficiency, decrease costs and Carbon emissions, airlines have been pushed to drive down the weight of aircraft, whilst guaranteeing their safety. This push for lighter aircraft has progressively seen a reduction in the use of metallic components which have been slowly replaced by composite materials. Such composite materials are made up of two or more phases of which they exploit the mechanical complementarity. For some applications, such as thermal barrier coatings, thermal complementarity is also leveraged. Yet, these novel materials, and especially their failure mechanisms and durability have proven difficult to understand, both through physical and virtual, in silico, experiments. One of the reasons for this is the large ratio between the size of the smallest constituent relevant in the description of failure mechanisms (e.g. 5-10 micron diameter carbon fibres) and the size of the structure (79m wingspan A380). In this presentation, we will briefly review advances in modeling and simulation of failure across the scales. We will discuss non exhaustively some of the recent advances in this field, ranging from adaptive atomistic modeling of fracture to algebraic model reduction methods for severely non-linear problems, including homogenization. We will also discuss the relevance of such simulations in daily engineering practice and claim that devising interactive simula- tors able to let engineers interact with the composite structure of interest and thus develop intuition about these advanced and complex materials. We will conclude by making a parallel between the difficulties encountered in modeling complex aerospace components and those met in personalized medicine, by discussing briefly the concept of Digital Twin. [less ▲]

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See detailMultiscale Quasicontinuum Methods for Dissipative Truss Models and Beam Networks
Beex, Lars UL; Peerlings, Ron; Geers, Marc et al

Presentation (2014, November 05)

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See detailCardiff/Luxembourg Computational Mechanics Research Group
Bordas, Stéphane UL; Kerfriden, Pierre; Hale, Jack UL et al

Poster (2014, November)

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See detailDiscrete Multiscale Modelling and Future Research Plans concerning Metals
Beex, Lars UL; Bordas, Stéphane UL; Rappel, Hussein UL et al

Presentation (2014, October 14)

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See detailGeometry-Independent Field approximaTion: CAD-Analysis Integration, geometrical exactness and adaptivity
Xu, Gang; Atroshchenko, Elena; Ma, Weiyin et al

in Computer Methods in Applied Mechanics and Engineering (2014)

In isogeometric analysis (IGA), the same spline representation is employed for both the geometry of the domain and approximation of the unknown fields over this domain. This identity of the geometry and ... [more ▼]

In isogeometric analysis (IGA), the same spline representation is employed for both the geometry of the domain and approximation of the unknown fields over this domain. This identity of the geometry and field approximation spaces was put forward in the now classic 2005 paper [20] as a key advantage on the way to the integration of Computer Aided Design (CAD) and subsequent analysis in Computer Aided Engineering (CAE). [20] claims indeed that any change to the geometry of the domain is automatically inherited by the approximation of the field variables, without requiring the regeneration of the mesh at each change of the domain geometry. Yet, in Finite Element versions of IGA, a parameterization of the interior of the domain must still be constructed, since CAD only provides information about the boundary. The identity of the boundary and field representation decreases the flexibility in which this parameterization can be generated and somewhat constrains the modeling and simulation process, because an approximation able to represent the domain geometry accurately need not be adequate to also approximate the field variables accurately, in particular when the solution is not smooth. We propose here a new paradigm called Geometry-Independent Field approximaTion (GIFT) where the spline spaces used for the geometry and the field variables can be chosen and adapted independently while preserving geometric exactness and tight CAD integration. GIFT has the following features: (1) It is possible to flexibly choose between different spline spaces with different properties to better represent the solution of the problem, e.g. the continuity of the solution field, boundary layers, singularities, whilst retaining geometrical exactness of the domain boundary. (2) For multi-patch analysis, where the domain is composed of several spline patches, the continuity condition between neighboring patches on the solution field can be automatically guaranteed without additional constraints in the variational form. (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, which makes the method versatile. GIFT with PHT-spline solution spaces and NURBS geometries is used to show the effectiveness of the proposed approach. Keywords : Super-parametric methods, Isogeometric analysis (IGA), Geometry-independent Spline Space, PHT-splines, local refinement, adaptivity [less ▲]

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See detailUncertainty quantification of dry woven fabrics: A sensitivity analysis on material properties
Akmar, Ilyani; Lahmer, Tom; Beex, Lars UL et al

in Composite Structures (2014), 116

Based on sensitivity analysis, we determine the key meso-scale uncertain input variables that influence the macro-scale mechanical response of a dry textile subjected to uni-axial and biaxial deformation ... [more ▼]

Based on sensitivity analysis, we determine the key meso-scale uncertain input variables that influence the macro-scale mechanical response of a dry textile subjected to uni-axial and biaxial deformation. We assume a transversely isotropic fashion at the macro-scale of dry woven fabric. This paper focuses on global sensitivity analysis; i.e. regression- and variance-based methods. The sensitivity of four meso-scale uncertain input parameters on the macro-scale response are investigated; i.e. the yarn height, the yarn spacing, the yarn width and the friction coefficient. The Pearson coefficients are adopted to measure the effect of each uncertain input variable on the structural response. Due to computational effectiveness, the sensitivity analysis is based on response surface models. The Sobol’s variance-based method which consists of first-order and total-effect sensitivity indices are presented. The sensitivity analysis utilizes linear and quadratic correlation matrices, its corresponding correlation coefficients and the coefficients of determination of the response uncertainty criteria. The correlation analysis, the response surface model and Sobol’s indices are presented and compared by means of uncertainty criteria influences on MataBerkait-dry woven fabric material properties. To anticipate, it is observed that the friction coefficient and yarn height are the most influential factors with respect to the specified macro-scale mechanical responses. [less ▲]

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See detailExtension of 2D FEniCS implementation of Cosserat non-local elasticity to the 3D case
Sautot, Camille; Bordas, Stéphane UL; Hale, Jack UL

Report (2014)

The objective of the study is the extension of the existing 2D FEniCS implementation of Cosserat elasticity to the 3D case. The first step is the implementation of a patch-test for a simple problem in ... [more ▼]

The objective of the study is the extension of the existing 2D FEniCS implementation of Cosserat elasticity to the 3D case. The first step is the implementation of a patch-test for a simple problem in classical elasticity as a Timoshenko's beam - this study will show that DOLFIN could offer approximated solutions converging to the analytical solution. The second step is the computation of the stress in a plate with a circular hole. The stress concentration factors around the hole in classical and Cosserat elasticities will be compared, and a convergence study for the Cosserat case will be realised. The third step is the extension to the 3D case with the computation of the stress concentration factor around a spherical cavity in an infinite elastic medium. This computed value will be compare to the analytical solution described by couple-stress theory. [less ▲]

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See detailShape optimisation directly from CAD: an isogeometric boundary element approach
Lian, Haojie; Bordas, Stéphane UL; Kerfriden, Pierre

Report (2014)

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See detailError controlled adaptive multiscale method for fracture in polycrystalline materials
Akbari Rahimabadi, Ahmad; Kerfriden, Pierre; Bordas, Stéphane UL

Report (2014)

A lack of separation of scales is the major hurdle hampering predictive and computationally tractable simulations of fracture over multiple scales. In this thesis an adaptive multiscale method is ... [more ▼]

A lack of separation of scales is the major hurdle hampering predictive and computationally tractable simulations of fracture over multiple scales. In this thesis an adaptive multiscale method is presented in an attempt to address this challenge. This method is set in the context of FE2 Feyel and Chaboche [2000] for which computational homogenisation breaks down upon loss of material stability (softening). The lack of scale separation due to the coalescence of microscopic cracks in a certain zone is tackled by a full discretisation of the microstructure in this zone. Polycrystalline materials are considered with cohesive cracks along the grain boundaries as a model problem. Adaptive mesh re nement of the coarse region and adaptive initiation and growth of fully resolved regions are performed based on discretisation error and homogenisation error criteria, respectively. In order to follow sharp snap-backs in load-displacement paths, a local arc-length technique is developed for the adaptive multiscale method. The results are validated against direct numerical simulation [less ▲]

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See detailA model order reduction technique for speeding up computational homogenisation
Goury, Olivier; Kerfriden, Pierre; Liu, Wing Kam et al

Scientific Conference (2014, July 24)

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See detailParallel simulations of soft-tissue using an adaptive quadtree/octree implicit boundary finite element method
Hale, Jack UL; Bordas, Stéphane UL; Kerfriden, Pierre 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 ▲]

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