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Generalizing the isogeometric concept: weakening the tight coupling between geometry and simulation in IGA Bordas, Stéphane ; Tomar, Satyendra ; et al Scientific Conference (2016, May 30) In the standard paradigm of isogeometric analysis [2, 1], the geometry and the simulation spaces are tightly integrated, i.e. the non-uniform rational B-splines (NURBS) space, which is used for the ... [more ▼] In the standard paradigm of isogeometric analysis [2, 1], the geometry and the simulation spaces are tightly integrated, i.e. the non-uniform rational B-splines (NURBS) space, which is used for the geometry representation of the domain, is also employed for the numerical solution of the problem over the domain. However, in certain situations, such as, when the geometry of the domain can be represented by low order NURBS but the numerical solution can be obtained with improved accuracy by using NURBS of order higher than that required for the geometry; or in the shape and topology optimization where the constraint of using the same space for the geometry and the numerical solution is not favorable, this tight coupling is disadvantageous. Therefore, we study the effect of decoupling the spaces for the geometry representation and the numerical solution, though still using the prevalent functions in CAD/CAGD. To begin with, we perform the patch tests on various combinations of polynomial degree, geometry type, and various cases of varying degrees and control variables between the geometry and the numerical solution. This shows that certain cases, perhaps intuitive, should be avoided in practice because patch test fails. The above-mentioned situations are further explored with some numerical examples, which shows that weakening the tight coupling between geometry and simulation offers more flexibility in choosing the numerical solution spaces. [less ▲] Detailed reference viewed: 120 (3 UL)Computational mechanics of interfaces Bordas, Stéphane Presentation (2016, May 22) The course will present an overview of recent developments, which will enable students to make informed choices in terms of discretization and model selection in solving numerical problems in mechanics ... [more ▼] The course will present an overview of recent developments, which will enable students to make informed choices in terms of discretization and model selection in solving numerical problems in mechanics. We will cover discretization strategies ranging from the standard finite element method, the smoothed finite element method, the extended finite element method, polygonal and virtual element methods, meshfree methods. The applications range between fracture of heterogeneous materials and biomedical simulations. The intended learning outcomes of the course are such that the students will be: - able to critically assess discretization schemes in mechanics - able to implement simple error estimators for finite element methods - familiar with basic multi-scale methods for fracture and their limitations - able to follow basic literature in model error and model selection, in particular based on Bayesian inference Course participants will learn these topics through lectures and hands-on numerical experiments. [less ▲] Detailed reference viewed: 349 (16 UL)Propagating uncertainty using FE advanced Monte-Carlo methods: application to non- linear hyperelastic models Hauseux, Paul ; Hale, Jack ; Bordas, Stéphane Presentation (2016, May 09) Detailed reference viewed: 133 (12 UL)Large-deformation lattice model for dry-woven fabrics including contact Magliulo, Marco ; Beex, Lars ; Zilian, Andreas et al Speeches/Talks (2016) Short Presentation on the Quasi-continuum method Detailed reference viewed: 249 (32 UL)Bayesian inference for material parameter identification Rappel, Hussein ; Beex, Lars ; Hale, Jack et al Report (2016) Detailed reference viewed: 112 (13 UL)Reduced order method for patient specific application: biomechanics of brain in presence of tumor Baroli, Davide ; Beex, Lars ; Bordas, Stéphane Speeches/Talks (2016) Detailed reference viewed: 146 (13 UL)3D Crack Detection Using an XFEM Variant and Global Optimization Algorithms Agathos, Konstantinos ; ; Bordas, Stéphane Scientific Conference (2016, May) Detailed reference viewed: 164 (10 UL)Propagating uncertainty through a non-linear hyperelastic model using advanced Monte-Carlo methods Hauseux, Paul ; Hale, Jack ; Bordas, Stéphane Scientific Conference (2016, May) Detailed reference viewed: 200 (20 UL)3D fatigue fracture modeling by isogeometric boundary element methods ; ; et al Scientific Conference (2016, April 01) Detailed reference viewed: 120 (1 UL)Error estimation and space-time adaptivity for the isogeometric analysis of transient structural dynamics ; ; Bordas, Stéphane et al Scientific Conference (2016, April 01) This paper presents a new adaptive scheme for the error-controlled simulation of transient dynamics problem. We rely on spline bases for the higher-order spatial description of our kinematic fields. Local ... [more ▼] This paper presents a new adaptive scheme for the error-controlled simulation of transient dynamics problem. We rely on spline bases for the higher-order spatial description of our kinematic fields. Local adaptivity is performed by employing a hierarchical T-mesh technology, in combination with geometry independent field approximation. The Newmark algorithm is chosen to solve the semidiscrete equation of motion. We will present some simple local error estimates to drive the adaptivity, and show how we can ensure that the mechanical energy of conservative systems is preserved during the refinement process. [less ▲] Detailed reference viewed: 93 (4 UL)Automatised selection of load paths to construct reduced-order models in computational damage micromechanics: from dissipation-driven random selection to Bayesian optimization ; ; Bordas, Stéphane et al in Computational Mechanics (2016) In this paper, we present new reliable model order reduction strategies for computational micromechanics. The difficulties rely mainly upon the high dimensionality of the parameter space represented by ... [more ▼] In this paper, we present new reliable model order reduction strategies for computational micromechanics. The difficulties rely mainly upon the high dimensionality of the parameter space represented by any load path applied onto the representative volume element. We take special care of the challenge of selecting an exhaustive snapshot set. This is treated by first using a random sampling of energy dissipating load paths and then in a more advanced way using Bayesian optimization associated with an interlocked division of the parameter space. Results show that we can insure the selection of an exhaustive snapshot set from which a reliable reduced-order model can be built. [less ▲] Detailed reference viewed: 275 (31 UL)Bayesian statistical inference on the material parameters of a hyperelastic body Hale, Jack ; ; Bordas, Stéphane in Proceedings of the ACME-UK 2016 24th Conference on Computational Mechanics (2016, March 31) We present a statistical method for recovering the material parameters of a heterogeneous hyperelastic body. Under the Bayesian methodology for statistical inverse problems, the posterior distribution ... [more ▼] We present a statistical method for recovering the material parameters of a heterogeneous hyperelastic body. Under the Bayesian methodology for statistical inverse problems, the posterior distribution encodes the probability of the material parameters given the available displacement observations and can be calculated by combining prior knowledge with a finite element model of the likelihood. In this study we concentrate on a case study where the observations of the body are limited to the displacements on the surface of the domain. In this type of problem the Bayesian framework (in comparison with a classical PDE-constrained optimisation framework) can give not only a point estimate of the parameters but also quantify uncertainty on the parameter space induced by the limited observations and noisy measuring devices. There are significant computational and mathematical challenges when solving a Bayesian inference problem in the case that the parameter is a field (i.e. exists infinite-dimensional Banach space) and evaluating the likelihood involves the solution of a large-scale system of non-linear PDEs. To overcome these problems we use dolfin-adjoint to automatically derive adjoint and higher-order adjoint systems for efficient evaluation of gradients and Hessians, develop scalable maximum aposteriori estimates, and use efficient low-rank update methods to approximate posterior covariance matrices. [less ▲] Detailed reference viewed: 182 (18 UL)Energy minimizing multi-crack growth in linear elastic fracture using the extended finite element method Sutula, Danas ; Bordas, Stéphane in ACME-UK 2016 24th Conference on Computational Mechanics (2016, March 31) We investigate multiple fracture evolution under quasi-static conditions in an isotropic linear elastic solid based on the principle of minimum potential elastic energy in the framework of the extended ... [more ▼] We investigate multiple fracture evolution under quasi-static conditions in an isotropic linear elastic solid based on the principle of minimum potential elastic energy in the framework of the extended finite element method. The technique enables a minimization of the potential energy with respect to all crack increment directions. Results show that the maximum hoop stress criterion and the energy minimization approach converge to the same fracture path. It is found that the converged solution lies in between the fracture paths obtained by each criterion for coarser meshes. This presents an opportunity to estimate an upper and lower bound of the true fracture path as well as an error on the crack path. [less ▲] Detailed reference viewed: 110 (1 UL)Blood flow simulation using smoothed particle hydrodynamics: application to thrombus generation ; ; Bordas, Stéphane Scientific Conference (2016, March 31) Blood flow rheology is considered to be a complex phenomenon. In order to understand the characteristics of blood flow, it is important to identify key parameters those influence the flow behaviour of ... [more ▼] Blood flow rheology is considered to be a complex phenomenon. In order to understand the characteristics of blood flow, it is important to identify key parameters those influence the flow behaviour of blood. Further, the characterisation of blood flow will also enable us to understand flow parameters associated with physiological conditions such as atherosclerosis. Thrombosis plays a crucial role in atherosclerosis, or to stop bleeding when a blood vessel is injured. This article focuses on using meshless particle-based Lagrangian numerical technique named smoothed particles hydrodynamic (SPH) method to study the flow behaviour of blood and to explore flow condition that induces formation of thrombus in a blood vessel. Due its simplicity and effectiveness, the SPH method is employed here to simulate the process of thrombogenesis under the influence of various blood flow parameters. In the present SPH simulation, blood is modelled by particles that have characteristics of plasma and of platelets. To simulate coagulation of platelets which forms thrombus, the adhesion and aggregation process of platelets are modelled by an effective inter-particle force model. With these models, platelet motion in the flowing blood and platelet adhesion and aggregation are effectively coupled with viscous blood flow. In this study, the adhesion and aggregation of blood particles are performed on a bifurcated artery under a various low Reynolds number scenarios. The results are compared with experimental results and a good agreement is found between the simulated and experimental results. [less ▲] Detailed reference viewed: 387 (12 UL)Isogeometric boundary element methods for linear elastic fracture mechanics ; ; et al Report (2016) Detailed reference viewed: 353 (20 UL)An introduction to Bayesian inference for material parameter identification Rappel, Hussein ; Beex, Lars ; Hale, Jack et al Presentation (2016, February 04) Detailed reference viewed: 123 (16 UL)2015 Lab report - Legato report 001 Bordas, Stéphane Report (2016) Detailed reference viewed: 450 (12 UL)Using Bayesian inference to recover the material parameters of a heterogeneous hyperelastic body Hale, Jack ; ; Bordas, Stéphane Scientific Conference (2016) We present a method for calculating a Bayesian uncertainty estimate on the recovered material parameters of a heterogeneous geometrically non-linear hyperelastic body. We formulate the problem in the ... [more ▼] We present a method for calculating a Bayesian uncertainty estimate on the recovered material parameters of a heterogeneous geometrically non-linear hyperelastic body. We formulate the problem in the Bayesian inference framework [1]; given noisy and sparse observations of a body, some prior knowledge on the parameters and a parameter-to-observable map the goal is to recover the posterior distribution of the parameters given the observations. In this work we primarily focus on the challenges of developing dimension-independent algorithms in the context of very large inverse problems (tens to hundreds of thousands of parameters). Critical to the success of the method is viewing the problem in the correct infinite- dimensional function space setting [2]. With this goal in mind, we show the use of automatic symbolic differentiation techniques to construct high-order adjoint models [3], scalable maximum a posteriori (MAP) estimators, and efficient low-rank update methods to calculate credible regions on the posterior distribution [4]. [less ▲] Detailed reference viewed: 113 (14 UL)Discretization Correction Particle Strength Exchange (DC PSE) method for Linear Elasticity Bourantas, Georgios ; Bordas, Stéphane Report (2016) Detailed reference viewed: 145 (3 UL)Hybrid mesh/particle meshless method for modeling geological flows with discontinuous transport properties Bourantas, Georgios ; ; van Dam, Tonie et al E-print/Working paper (2016) In the present paper, we introduce the Finite Difference Method-Meshless Method (FDM-MM) in the context of geodynamical simulations. The proposed numerical scheme relies on the well-established FD method ... [more ▼] In the present paper, we introduce the Finite Difference Method-Meshless Method (FDM-MM) in the context of geodynamical simulations. The proposed numerical scheme relies on the well-established FD method along with the newly developed “meshless” method and, is considered as a hybrid Eulerian/Lagrangian scheme. Mass, momentum, and energy equations are solved using an FDM method, while material properties are distributed over a set of markers (particles), which represent the spatial domain, with the solution interpolated back to the Eulerian grid. The proposed scheme is capable of solving flow equations (Stokes flow) in uniform geometries with particles, “sprinkled” in the spatial domain and is 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. The present hybrid approach allows for the accurate calculation of fine thermal structures, offering local type adaptivity through the flexibility of the particle method. [less ▲] Detailed reference viewed: 207 (15 UL) |
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