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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: 644 (30 UL)Biological Tissue Cutting Mechanics and Dynamics Malukhin, Kostyantyn ; Bordas, Stéphane ; Bilger, Alexandre Presentation (2015, April 02) Detailed reference viewed: 127 (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: 209 (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: 236 (4 UL)Error estimation in homogenisation ; ; et al Presentation (2015, January 30) Detailed reference viewed: 124 (3 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: 2373 (200 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: 657 (22 UL)Interfacial shear stress optimization in sandwich beams with polymeric core using non-uniform distribution of reinforcing ingredients ; ; 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 ▲] Detailed reference viewed: 217 (12 UL)Enriched finite elements for branching cracks in deformable porous media ; ; et al in Engineering Analysis with Boundary Elements (2015), 50 In this paper, we propose and verify a numerical approach to simulate fluid flow in deformable porous media without requiring the discretization to conform to the geometry of the sealed fractures ... [more ▼] In this paper, we propose and verify a numerical approach to simulate fluid flow in deformable porous media without requiring the discretization to conform to the geometry of the sealed fractures (possibly intersecting). This approach is based on a fully coupled hydro-mechanical analysis and an extended finite element method (XFEM) to represent discrete fractures. Convergence tests indicate that the proposed scheme is both consistent and stable. The contributions of this paper include: (1) a new junction enrichment to describe intersecting fractures in deformable porous media; (2) the treatment of sealed fractures. We employ the resulting discretization scheme to perform numerical experiments, to illustrate that the inclination angles of the fractures and the penetration ratio of the sealed fractures are two key parameters governing the flow within the fractured porous medium. [less ▲] Detailed reference viewed: 270 (7 UL)Gradient Smoothing in Finite Elasticity: near-incompressibility ; Bordas, Stéphane ; Report (2015) Detailed reference viewed: 139 (9 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: 123 (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: 138 (3 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: 116 (2 UL)Three-Dimensional Crack Propagation with Global Enrichment XFEM and Vector Level Sets ; ; et al Scientific Conference (2015) Detailed reference viewed: 228 (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: 238 (10 UL)Nonlinear FEM code with Finite elasticity lecture note written by L.A. Mihai ; Bordas, Stéphane Learning material (2015) Detailed reference viewed: 395 (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: 391 (12 UL)Error Controlled Adaptive Multiscale Method For Fracture Modelling in Polycrystalline materials ; ; Bordas, Stéphane in Philosophical Magazine (2015) In this paper an adaptive multiscale method is presented in an attempt to address the lack of separation of scales in simulation of fracture. This method is set in the context of FE2 [20] for which ... [more ▼] In this paper an adaptive multiscale method is presented in an attempt to address the lack of separation of scales in simulation of fracture. This method is set in the context of FE2 [20] 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 refinement 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: 531 (15 UL)A staggered cell-centered finite element method for compressible and nearly-incompressible linear elasticity on general meshes ; ; Bordas, Stéphane et al in SIAM Journal on Numerical Analysis (2015), 53(4), 2051-2073 We propose a new numerical method, namely, the staggered cell-centered finite element method for compressible and nearly incompressible linear elasticity problems. By building a dual mesh and its ... [more ▼] We propose a new numerical method, namely, the staggered cell-centered finite element method for compressible and nearly incompressible linear elasticity problems. By building a dual mesh and its triangular submesh, the scheme can be constructed from a general mesh in which the displacement is approximated by piecewise linear (P1) functions on the dual submesh and, in the case of nearly incompressible problems, the pressure is approximated by piecewise constant (P0) functions on the dual mesh. The scheme is cell centered in the sense that the solution can be computed by cell unknowns of the primal mesh (for the displacement) and of the dual mesh (for the pressure). The method is presented within a rigorous theoretical framework to show stability and convergence. In particular, for the nearly incompressible case, stability is proved by using the macroelement technique. Numerical results show that the method, compared with other methods, is effective in terms of accuracy and computational cost. [less ▲] Detailed reference viewed: 138 (2 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: 204 (11 UL) |
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