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Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory ; ; et al in Composite Structures (2015), 123 This paper presents a simple and effective formulation based on isogeometric Analysis (IGA) and higher-order shear deformation theory (HSDT) to investigate the static and dynamic vibration behaviour of ... [more ▼] This paper presents a simple and effective formulation based on isogeometric Analysis (IGA) and higher-order shear deformation theory (HSDT) to investigate the static and dynamic vibration behaviour of functionally graded carbon nano-reinforced composite plates. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded through the thickness direction according to several linear distributions of the volume fraction of carbon nanotubes. The governing equation is approximated according to the HSDT model using isogeometric elements based on Non-Uniform Rational B-Spline (NURBS) basis functions. This achieves naturally any desired degree of continuity through the choice of the interpolation order, so that the method easily fulfils the C1-continuity requirement of the HSDT model. The accuracy and reliability of the proposed method is verified by comparing its numerical predictions with those of other available numerical approaches. [less ▲] Detailed reference viewed: 284 (12 UL)Reduced order methods Schenone, Elisa ; Hale, Jack ; Beex, Lars et al Presentation (2015, April 16) Detailed reference viewed: 242 (39 UL)Hybrid mesh/particle meshless method for geological flows with discontinuous transport properties Bourantas, Georgios ; ; et al Scientific Conference (2015, April 12) Geodynamic modeling is an important branch of Earth Sciences. Direct observation of geodynamic processes is limited in both time and space, while on the other hand numerical methods are capable of ... [more ▼] Geodynamic modeling is an important branch of Earth Sciences. Direct observation of geodynamic processes is limited in both time and space, while on the other hand numerical methods are capable of simulating millions of years in a matter of days on a desktop computer. The model equations can be reduced to a set of Partial Differential Equations with possibly discontinuous coefficients, governing mass, momentum and heat transfer over the domain. Some of the major challenges associated with such simulations are (1) geological time scales, which require long (in physical time) simulations using small time steps; (2) the presence of localization zones over which large gradients are present and which are much smaller than the overall physical dimensions of the computational domain and require much more refined discretization than for the rest of the domain, much like in fracture or shear band mechanics. An added difficulty is that such structures in the solution may appear after long periods of stagnant behaviour; (3) the definition of boundary conditions, material parameters and that of a suitable computational domain in terms of size; (4) a posteriori error estimation, sensitivity analysis and discretization adaptivity for the resulting coupled problem, including error propagation between different unknown fields. Consequently, it is arguable that any suitable numerical methods aimed at the solution of such problems on a large scale must be able to (i) provide ease of discretization refinement, including possible partition of unity enrichment; (ii) offer a large stability domain, so that “large” time steps can be chosen; (iii) ease of parallelization and good scalability. Our approach is to rely on “meshless” methods based on a point collocation strategy for the discretization of the set of PDEs. The method is hybrid Eulerian/Lagrangian, which enables to switch easily between stagnant periods and periods of localization. Mass and momentum equations are solved using a meshless point collocation Eulerian method, while energy equation are solved using a set of particles, distributed over the spatial domain, with the solution interpolated back to the Eulerian grid at every time step. This hybrid approach allows for the accurate calculation of fine thermal structures, through the ease of adaptivity offered by the flexibility of the particle method. The approximation space is constructed using the Discretization Correction Particle Strength Exchange (DC PSE) method. The proposed scheme gives the capability of solving flow equations (Stokes flow) in fully irregular geometries while particles, “sprinkled” in the spatial domain, are used to solve convection-diffusion problems avoiding the oscillation produced in the Eulerian approach. The resulting algebraic linear systems were solved using direct solvers. Our hybrid approach can capture sharp variations of stresses and thermal gradients in problems with a strongly variable viscosity and thermal conductivity as demonstrated through various benchmarking test cases such as the development of Rayleigh-Taylor instabilities, viscous heating and flows with non-Newtonian rheology. [less ▲] Detailed reference viewed: 651 (30 UL)Biological Tissue Cutting Mechanics and Dynamics Malukhin, Kostyantyn ; Bordas, Stéphane ; Bilger, Alexandre Presentation (2015, April 02) Detailed reference viewed: 130 (11 UL)Real-time surgical simulation using a lattice-continuum approach ; ; Bordas, Stéphane et al Presentation (2015, February 06) Surgery is a complex practice whose positive outcome relies heavily on the experience of surgeons and therefore involves a number of risks. Computer-based simulation is a strong candidate for surgical ... [more ▼] Surgery is a complex practice whose positive outcome relies heavily on the experience of surgeons and therefore involves a number of risks. Computer-based simulation is a strong candidate for surgical training, guidance and surgical robotics. Cutting, tearing, needle insertion and similar operations which require topological changes, contact, and whose outcome is significantly affected by the microstructure of the material (discontinuities, holes, interfaces) remain some of the most difficult surgical gestures to simulate. One of the difficulties emanates from the requirement to handle propagating discontinuities as well as the micro or meso structure of the material being cut. We are interested in the development of a numerical tool capable of the interactive (50Hz) simulation of surgical cutting using a multi-domain lattice-continuum approach. Around the cutting region, a mesoscopic discrete lattice approach suitable for initiation of cuts and subsequent tears is used. The remaining regions can be modeled by a continuum approach or through model reduction approaches based on pre computations. The algorithms are implemented within the SOFA framework which is targets real-time computations, with an emphasis on medical simulation and the work is being performed in collaboration with the group of Dr Hadrien Courtecuisse and Stéphane Cotin. [less ▲] Detailed reference viewed: 212 (3 UL)Real-time surgical simulation using a lattice-continuum approach ; Bordas, Stéphane Presentation (2015, February) Surgery is a complex practice whose positive outcome relies heavily on the experience of surgeons and therefore involves a number of risks. Computer-based simulation is a strong candidate for surgical ... [more ▼] Surgery is a complex practice whose positive outcome relies heavily on the experience of surgeons and therefore involves a number of risks. Computer-based simulation is a strong candidate for surgical training, guidance and surgical robotics. Cutting, tearing, needle insertion and similar operations which require topological changes, contact, and whose outcome is significantly affected by the microstructure of the material (discontinuities, holes, interfaces) remain some of the most difficult surgical gestures to simulate. One of the difficulties emanates from the requirement to handle propagating discontinuities as well as the micro or meso structure of the material being cut. We are interested in the development of a numerical tool capable of the interactive (50Hz) simulation of surgical cutting using a multi-domain lattice-continuum approach. Around the cutting region, a mesoscopic discrete lattice approach suitable for initiation of cuts and subsequent tears is used. The remaining regions can be modeled by a continuum approach or through model reduction approaches based on pre computations. The algorithms are implemented within the SOFA framework which is targets real-time computations, with an emphasis on medical simulation and the work is being performed in collaboration with the group of Dr Hadrien Courtecuisse and Stéphane Cotin. [less ▲] Detailed reference viewed: 241 (4 UL)Error estimation in homogenisation ; ; et al Presentation (2015, January 30) Detailed reference viewed: 128 (3 UL)Adaptive methods for multiscale fracture Bordas, Stéphane ; ; et al in International Journal of Engineering Science (2015, January 01) Adaptive methods for multiscale fracture In this work, we discuss two classes of methods to reduce the complexity of (multi scale) fracture simulations. In a first part, we discuss algebraic model ... [more ▼] Adaptive methods for multiscale fracture In this work, we discuss two classes of methods to reduce the complexity of (multi scale) fracture simulations. In a first part, we discuss algebraic model reduction. We show that algebraic model reduction such as the proper orthogonal decomposition cannot be used directly because of the lack of corelation introduced by the damage or cracks. We demonstrate the use of proper orthogonal decompositions by subdomains as a candidate to reduce computational expenses in non-linear fracture simulations whilst controlling the error level. We then consider algebraic model reduction, namely the proper orthogonal decomposition(POD) to drastically reduce the computational time associated with computing the response of representative volume elements (RVEs) used in homogenization, e.g. by the FE2 method. The snapshots are obtained by solving the RVE boundary value problem for various loading paths. To speed-up the computations, system approximation through the discrete empirical interpolation (DEIM) is used and allows the evaluation of the internal forces for only a small subset of the elements making the RVE structure. In a second part, we propose an adaptive hybrid multiscale method for modelling fracture in a heterogeneous material that is composed of orthotropic grains with cohesive interfaces between the grains. Instead of a direct solver, FE2 method [1] based on homogenisation is employed in order to compute the effective behaviour of the heterogeneous microscopic material on the coarser scale. At this scale the modelling error due to the homogenisation is still low [3]. The coarse scale is discretized with unstructured triangular finite elements, and adaptive mesh refinement is used to control the discretizsation error. While the mesh refinement keeps the discretisation error with in a certain range, the modelling error increases due to the fact that by refining the coarse elements, the scale separation assumption which is a key issue for homogenisation may no longer be fulfilled [4]. Whereas the modelling error is inversely proportional to the size of the coarse elements, a critical element size can be found that corresponds to the critical value of the modelling error. A critical zone emerges when the size of a coarse element reaches the critical size, or if the underlying representative volume element of the microstructure loses stability due to localisation (lack of scale separation). Thereafter, a zoom-in process is triggered that replaces the corresponding coarse elements of the critical zone with high resolution microscale mesh to which it glues the coarse scale mesh through a strong coupling technique using Lagrange multipliers [5]. The high resolution region can gradually be extended to include the newly emerging critical zones. A local arc-length technique is adopted to trace the highly non-linear curve of the global load-displacement by controlling the opening of microscopic cohesive cracks in the fully resolved regions. The proposed adaptive multiscale method allows us to introduce progressive discrete micro cracks at the macroscale. The unstructured mesh enables us to model problems with non-regular shapes, and the arc-length method, defined over multiple scales, allows the regularisation of softening problems that are treated in quasi-statics. We exercise this method on the simulation of polycrystalline fracture, where each grain is considered orthotropic and compare results to direct numerical simulation. [less ▲] Detailed reference viewed: 660 (22 UL)Computational Mechanics Lab Report 2013-2014 Bordas, Stéphane Report (2015) This is the report of the Computational Mechanics Lab led by Prof. Stéphane Bordas Detailed reference viewed: 2468 (204 UL)Gradient Smoothing in Finite Elasticity: near-incompressibility ; Bordas, Stéphane ; Report (2015) Detailed reference viewed: 142 (10 UL)Equilibrium morphology of misfit particles in elastically stressed solids under chemo-mechanical equilibrium conditions ; Bordas, Stéphane ; in Journal of the Mechanics and Physics of Solids (2015), 81 Detailed reference viewed: 188 (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)An efficient goal-oriented sampling strategy using reduced basis method for parametrized elastodynamic problems ; ; et al in Numerical Methods for Partial Differential Equations (2015), 31(2), 575-608 Detailed reference viewed: 143 (3 UL)Three-Dimensional Crack Propagation with Global Enrichment XFEM and Vector Level Sets ; ; et al Scientific Conference (2015) Detailed reference viewed: 231 (4 UL)Isogeometric Analysis of Laminated Composite Plates Using the Higher-Order Shear Deformation Theory ; ; Bordas, Stéphane et al in Mechanics of Advanced Materials and Structures (2015), 22(6), 451-469 Isogeometric analysis (IGA) aims at simplifying the computer aided design (CAD) and computer aided engineering (CAE) pipeline by using the same functions to describe the geometry (CAD) and the unknown ... [more ▼] Isogeometric analysis (IGA) aims at simplifying the computer aided design (CAD) and computer aided engineering (CAE) pipeline by using the same functions to describe the geometry (CAD) and the unknown fields (Analysis). IGA can be based on a variety of CAD descriptions, the most widely used today being non-uniform rational B-splines (NURBS). In this article, the suitability of NURBS-based isogeometric analysis within a third-order shear deformation theory for the simulation of the static, dynamic, and buckling response of laminated composite plates is investigated. The method employs NURBS basis functions to both represent the geometry (exactly) and the unknown field variables. One of the main advantages of the present method is directly inherited from IGA, that is to easily increase the approximation order. To avoid using a shear correction factor, a third-order shear deformation theory (TSDT) is introduced. It requires C1-continuity of generalized displacements and the NURBS basis functions are well suited for this requirement. Several numerical examples are used to demonstrate the performance of the present method compared with other published ones. [less ▲] Detailed reference viewed: 122 (2 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)Fundamental solutions and dual boundary element methods for fracture in plane Cosserat elasticity ; Bordas, Stéphane in Proceedings of the Royal Society a-Mathematical Physical and Engineering Sciences (2015), 471(2179), 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 equations (approach known as the dual boundary element method (BEM)) allows problems where parts of the boundary are overlapping, such as crack problems, to be treated 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 and an edge 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 and the angular distributions of stresses and couple-stresses around the crack tip. [less ▲] Detailed reference viewed: 120 (2 UL)Nonlinear FEM code with Finite elasticity lecture note written by L.A. Mihai ; Bordas, Stéphane Learning material (2015) Detailed reference viewed: 397 (10 UL)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)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) |
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