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A fast, certified and "tuning-free" two-field reduced basis method for the metamodelling of parametrised elasticity problems ; ; Bordas, Stéphane 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 ▲] Detailed reference viewed: 397 (12 UL)Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods ; Bordas, Stéphane ; in International Journal for Numerical Methods in Engineering (2015), 104(13), 1173-1199 We show both theoretically and numerically a connection between the smoothed finite element method (SFEM) and the virtual element method and use this approach to derive stable, cheap and optimally ... [more ▼] We show both theoretically and numerically a connection between the smoothed finite element method (SFEM) and the virtual element method and use this approach to derive stable, cheap and optimally convergent polyhedral FEM.We show that the stiffness matrix computed with one subcell SFEM is identical to the consistency term of the virtual element method, irrespective of the topology of the element, as long as the shape functions vary linearly on the boundary. Using this connection, we propose a new stable approach to strain smoothing for polygonal/polyhedral elements where, instead of using sub-triangulations, we are able to use one single polygonal/polyhedral subcell for each element while maintaining stability. For a similar number of degrees of freedom, the proposed approach is more accurate than the conventional SFEM with triangular subcells. The time to compute the stiffness matrix scales with the O.dof s/1:1 in case of the conventional polygonal FEM, while it scales as O.dof s/0:7 in the proposed approach. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. [less ▲] Detailed reference viewed: 125 (2 UL)A meshless adaptive multiscale method for fracture ; ; et al in Computational Materials Science (2015), 96(PB), 382-395 The paper presents a multiscale method for crack propagation. The coarse region is modelled by the differential reproducing kernel particle method. Fracture in the coarse scale region is modelled with the ... [more ▼] The paper presents a multiscale method for crack propagation. The coarse region is modelled by the differential reproducing kernel particle method. Fracture in the coarse scale region is modelled with the Phantom node method. A molecular statics approach is employed in the fine scale where crack propagation is modelled naturally by breaking of bonds. The triangular lattice corresponds to the lattice structure of the (1 1 1) plane of an FCC crystal in the fine scale region. The Lennard-Jones potential is used to model the atom-atom interactions. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively refined and coarsened as the crack propagates. The centro symmetry parameter is used to detect the crack tip location. The method is implemented in two dimensions. The results are compared to pure atomistic simulations and show excellent agreement. [less ▲] Detailed reference viewed: 319 (6 UL)Probabilistic multiconstraints optimization of cooling channels in ceramic matrix composites ; ; Bordas, Stéphane et al in Composites. Part B, Engineering (2015), 81 This paper presents a computational reliable optimization approach for internal cooling channels in Ceramic Matrix Composite (CMC) under thermal and mechanical loadings. The algorithm finds the optimal ... [more ▼] This paper presents a computational reliable optimization approach for internal cooling channels in Ceramic Matrix Composite (CMC) under thermal and mechanical loadings. The algorithm finds the optimal cooling capacity of all channels (which directly minimizes the amount of coolant needed). In the first step, available uncertainties in the constituent material properties, the applied mechanical load, the heat flux and the heat convection coefficient are considered. Using the Reliability Based Design Optimization (RBDO) approach, the probabilistic constraints ensure the failure due to excessive temperature and deflection will not happen. The deterministic constraints restrict the capacity of any arbitrary cooling channel between two extreme limits. A “series system” reliability concept is adopted as a union of mechanical and thermal failure subsets. Having the results of the first step for CMC with uniformly distributed carbon (C-) fibers, the algorithm presents the optimal layout for distribution of the C-fibers inside the ceramic matrix in order to enhance the target reliability of the component. A sequential approach and B-spline finite elements have overcome the cumbersome computational burden. Numerical results demonstrate that if the mechanical loading dominates the thermal loading, C-fibers distribution can play a considerable role towards increasing the reliability of the design. [less ▲] Detailed reference viewed: 126 (4 UL)Stable 3D extended finite elements with higher order enrichment for accurate non planar fracture ; ; Bordas, Stéphane in Computer Methods in Applied Mechanics and Engineering (2015) We present an extended finite element method (XFEM) for 3D nonplanar linear elastic fracture. The new approach not only provides optimal convergence using geometrical enrichment but also enables to ... [more ▼] We present an extended finite element method (XFEM) for 3D nonplanar linear elastic fracture. The new approach not only provides optimal convergence using geometrical enrichment but also enables to contain the increase in conditioning number characteristic of enriched finite element formulations: the number of iterations to convergence of the conjugate gradient solver scales similarly to and converges faster than the topologically-enriched version of the standard XFEM. This has two advantages: (1) the residual can be driven to zero to machine precision for at least 50% fewer iterations than the standard version of XFEM; (2) additional enrichment functions can be added without significant deterioration of the conditioning. Numerical examples also show that our new approach is up to 40% more accurate in terms of stress intensity factors, than the standard XFEM. [less ▲] Detailed reference viewed: 248 (10 UL)Locally equilibrated stress recovery for goal oriented error estimation in the extended finite element method Bordas, Stéphane ; ; et al in Computers and Structures (2015) Goal oriented error estimation and adaptive procedures are essential for the accurate and efficient evaluation of finite element numerical simulations that involve complex domains. By locally improving ... [more ▼] Goal oriented error estimation and adaptive procedures are essential for the accurate and efficient evaluation of finite element numerical simulations that involve complex domains. By locally improving the approximation qual- ity, for example, by using the extended finite element method (XFEM), we can solve expensive problems which could result intractable otherwise. Here, we present an error estimation technique for enriched finite element approxi- mations that is based on an equilibrated recovery technique, which considers the stress intensity factor as the quantity of interest. The locally equilibrated superconvergent patch recovery is used to obtain enhanced stress fields for the primal and dual problems defined to evaluate the error estimate. [less ▲] Detailed reference viewed: 209 (11 UL)Shape optimisation with isogeometric boundary element methods ; Bordas, Stéphane ; Presentation (2014, December) Detailed reference viewed: 135 (3 UL)Isogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates ; Hale, Jack ; 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 ▲] Detailed reference viewed: 487 (27 UL)Advances in Applied Mechanics Bordas, Stéphane 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 ▲] Detailed reference viewed: 1084 (47 UL)Multiscale computational mechanics: industrial applications Bordas, Stéphane ; ; Beex, Lars et al Presentation (2014, November 25) Detailed reference viewed: 189 (7 UL)Multiscale fracture across scales and time Bordas, Stéphane ; 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 ▲] Detailed reference viewed: 426 (14 UL)Multiscale Quasicontinuum Methods for Dissipative Truss Models and Beam Networks Beex, Lars ; ; et al Presentation (2014, November 05) Detailed reference viewed: 138 (4 UL)Cardiff/Luxembourg Computational Mechanics Research Group Bordas, Stéphane ; ; Hale, Jack et al Poster (2014, November) Detailed reference viewed: 185 (7 UL)Discrete Multiscale Modelling and Future Research Plans concerning Metals (presentation) Beex, Lars ; Bordas, Stéphane ; Rappel, Hussein et al Presentation (2014, October 14) Detailed reference viewed: 148 (10 UL)Discrete Multiscale Modelling and Future Research Plans concerning Metals Beex, Lars ; Bordas, Stéphane ; Rappel, Hussein et al Presentation (2014, October 14) Detailed reference viewed: 147 (11 UL)Geometry-Independent Field approximaTion: CAD-Analysis Integration, geometrical exactness and adaptivity ; ; 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 ▲] Detailed reference viewed: 1121 (30 UL)Uncertainty quantification of dry woven fabrics: A sensitivity analysis on material properties ; ; Beex, Lars 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 ▲] Detailed reference viewed: 420 (9 UL)Shape optimisation directly from CAD: an isogeometric boundary element approach ; Bordas, Stéphane ; Report (2014) Detailed reference viewed: 115 (4 UL)Extension of 2D FEniCS implementation of Cosserat non-local elasticity to the 3D case ; Bordas, Stéphane ; Hale, Jack 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 ▲] Detailed reference viewed: 276 (7 UL)Error controlled adaptive multiscale method for fracture in polycrystalline materials ; ; Bordas, Stéphane 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 ▲] Detailed reference viewed: 102 (1 UL) |
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