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Well Conditioned and Optimally Convergent Extended Finite Elements and Vector Level Sets for Three-Dimensional Crack Propagation Agathos, Konstantinos ; ; et al Scientific Conference (2016, June) A three-dimensional (3D) version of the vector level set method [1] is combined to a well conditioned and optimally convergent XFEM variant in order to deal with non-planar three dimensional crack ... [more ▼] A three-dimensional (3D) version of the vector level set method [1] is combined to a well conditioned and optimally convergent XFEM variant in order to deal with non-planar three dimensional crack propagation problems. The proposed computational fracture method achieves optimal convergence rates by using tip enriched elements in a fixed volume around the crack front (geometrical enrichment) while keeping conditioning of the resulting system matrices in acceptable levels. Conditioning is controlled by using a three dimensional extension of the degree of freedom gathering technique [2]. Moreover, blending errors are minimized and conditioning is further improved by employing weight function blending and enrichment function shifting [3,4]. As far as crack representation is concerned, crack surfaces are represented by linear quadrilateral elements and the corresponding crack fronts by ordered series of linear segments. Level set values are obtained by projecting points at the crack surface and front respectively. Different criteria are employed in order to assess the quality of the crack representation. References [1] Ventura G., Budyn E. and Belytschko T. Vector level sets for description of propagating cracks in finite elements. Int. J. Numer. Meth. Engng. 58:1571-1592 (2003). [2] Laborde P., Pommier J., Renard Y. and Salaün M. High-order extended finite element method for cracked domains. Int. J. Numer. Meth. Engng. 64:354-381 (2005). [3] Fries T.P. A corrected XFEM approximation without problems in blending elements. Int. J. Numer. Meth. Engng. 75:503-532 (2008). [4] Ventura G., Gracie R. and Belytschko T. Fast integration and weight function blending in the extended finite element method. Int. J. Numer. Meth. Engng. 77:1-29 (2009). [less ▲] Detailed reference viewed: 189 (15 UL)Virtual-power-based quasicontinuum methods for discrete dissipative materials Beex, Lars ; Bordas, Stéphane Scientific Conference (2016, June) Detailed reference viewed: 94 (2 UL)Linear smoothing over arbitrary polytopes for compressible and nearly incompressible linear elasticity ; Tomar, Satyendra ; Bordas, Stéphane et al Scientific Conference (2016, June) We present a displacement based approach over arbitrary polytopes for compressible and nearly incompressible linear elastic solids. In this approach, a volume-averaged nodal projection operator is ... [more ▼] We present a displacement based approach over arbitrary polytopes for compressible and nearly incompressible linear elastic solids. In this approach, a volume-averaged nodal projection operator is constructed to project the dilatational strain into an approximation space of equal or lower-order than the approximation space for the displacement field, resulting in a locking-free method. The formulation uses the usual Wachspress interpolants over arbitrary polytopes and the stability of the method is ensured by the addition of bubble like functions. The smoothed strains are evaluated based on the linear smoothing procedure. This further softens the bilinear form allowing the procedure to search for a solution satisfying the divergence- free condition. The divergence-free condition of the proposed approach is verified through systematic numerical study. The formulation delivers optimal convergence rates in the energy and L2-norms. Inf-sup tests are presented to demonstrated the stability of the formulation. [less ▲] Detailed reference viewed: 244 (3 UL)Numerical study of magnetic particles concentration in biofluid (blood) under the influence of high gradient magnetic field in microchannel ; Bourantas, Georgios ; et al Scientific Conference (2016, June) A meshless numerical scheme [1] is developed in order to simulate the magnetically mediated separation of biological mixture used in lab-on-chip devices as solid carriers for capturing, transporting and ... [more ▼] A meshless numerical scheme [1] is developed in order to simulate the magnetically mediated separation of biological mixture used in lab-on-chip devices as solid carriers for capturing, transporting and detecting biological magnetic labeled entities [2], as well as for drug delivering, magnetic hyperthermia treatment, magnetic resonance imaging, magnetofection, etc. A modified one-way particle-fluid coupling analysis is considered to model the interaction of the base fluid of the mixture with the distributed particles motion. In details, bulk flow influences particle motion (through a simplified Stokes drag relation), while it is strongly dependent on particle motion through (particle) concentration. Due to the imposed magnetic field stagnation regions are developed, leading to the accumulation of the magnetic labeled species and finally to their collection from the heterogeneous mixture. The role of (i) the intensity of magnetic field and its gradient, (ii) the position of magnetic field, (iii) the magnetic susceptibility of magnetic particles, (iv) the volume concentration of magnetic particles (nanoparticles) and their size, (v) the flow velocity in the magnetic- fluidic interactions and interplay between the magnetophoretic mass transfer and molecular diffusion are thoroughly investigated. Both Newtonian and non-Newtonian blood flow models are considered, along with different expressions for the concentration and numerical results are presented for a wide range of physical parameters (Hartmann number (Ha), Reynolds number (Re)). A comprehensive study investigates their impact on the biomagnetic separation. For verification purposes, the numerical results obtained by the proposed meshless scheme were compared with established numerical results from the literature, being in excellent agreement. [less ▲] Detailed reference viewed: 393 (11 UL)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: 158 (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: 425 (16 UL)3D Crack Detection Using an XFEM Variant and Global Optimization Algorithms Agathos, Konstantinos ; ; Bordas, Stéphane Scientific Conference (2016, May) Detailed reference viewed: 250 (20 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: 141 (4 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: 443 (14 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: 271 (20 UL)2015 Lab report - Legato report 001 Bordas, Stéphane Report (2016) Detailed reference viewed: 503 (12 UL)Discrete mechanical models and upscaling techniques for discrete materials Beex, Lars ; Bordas, Stéphane Poster (2016) Numerous natural and man-made materials are essentially discrete structures at the mesoscale or microscale (see Fig. 1). Discrete mechanical models can be formulated to capture typical mechanical ... [more ▼] Numerous natural and man-made materials are essentially discrete structures at the mesoscale or microscale (see Fig. 1). Discrete mechanical models can be formulated to capture typical mechanical phenomena arising from this discreteness. Failure in these materials, which often starts with the fracture of an individual bond, can be predicted based on the small-scale mechanics with these models. For failure, but also for non-local mechanics, no phenomenological descriptions are required in these models. This makes them more predictive than constitutive material models for this type of materials. [less ▲] Detailed reference viewed: 140 (5 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: 156 (15 UL)Stable 3D extended finite elements with higher order enrichment for accurate non planar fracture Agathos, Konstantinos ; ; Bordas, Stéphane in Computer Methods in Applied Mechanics and Engineering (2016), 306 An extended finite element method (XFEM) for three dimensional (3D) non-planar linear elastic fracture is introduced, which provides optimal convergence through the use of enrichment in a fixed area ... [more ▼] An extended finite element method (XFEM) for three dimensional (3D) non-planar linear elastic fracture is introduced, which provides optimal convergence through the use of enrichment in a fixed area around the crack front, while also improving the conditioning of the resulting system matrices. This is achieved by fusing a novel form of enrichment with existing blending techniques. Further, the adoption of higher order terms of theWilliams expansion is also considered and the effects in the accuracy and conditioning of the method are studied. Moreover, some problems regarding the evaluation of stress intensity factors (SIFs) and element partitioning are dealt with. The accuracy and convergence properties of the method as well as the conditioning of the resulting stiffness matrices are investigated through the use of appropriate benchmark problems. It is shown that the proposed approach provides increased accuracy while requiring, for all cases considered, a reduced number of iterations for the solution of the resulting systems of equations. The positive impact of geometrical enrichment is further demonstrated in the accuracy of the computed SIFs where, for the examined cases, an improvement of up to 40% is achieved. [less ▲] Detailed reference viewed: 130 (3 UL)A fast, certified and "tuning free" two-field reduced basis method for the metamodelling of affinely-parametrised elasticity problems ; ; Bordas, Stéphane in Computer Methods in Applied Mechanics and Engineering (2016), 298 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 in an 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 shown to be significantly more efficient in terms of computational expense than competing methodologies. [less ▲] Detailed reference viewed: 176 (18 UL)Modelling interfacial cracking with non-matching cohesive interface elements Nguyen, Viet Ha ; ; Bordas, Stéphane et al in Computational Mechanics (2016), 58(5), 731-746 Interfacial cracking occurs in many engineering problems such as delamination in composite laminates, matrix/interface debonding in fibre reinforced composites etc. Computational modelling of these ... [more ▼] Interfacial cracking occurs in many engineering problems such as delamination in composite laminates, matrix/interface debonding in fibre reinforced composites etc. Computational modelling of these interfacial cracks usually employs compatible or matching cohesive interface elements. In this paper, incompatible or non-matching cohesive interface elements are proposed for interfacial fracture mechanics problems. They allow non-matching finite element discretisations of the opposite crack faces thus lifting the constraint on the compatible discretisation of the domains sharing the interface. The formulation is based on a discontinuous Galerkin method and works with both initially elastic and rigid cohesive laws. The proposed formulation has the following advantages compared to classical interface elements: (i) non-matching discretisations of the domains and (ii) no high dummy stiffness. Two and three dimensional quasi-static fracture simulations are conducted to demonstrate the method. Our method not only simplifies the meshing process but also it requires less computational demands, compared with standard interface elements, for problems that involve materials/solids having a large mismatch in stiffnesses. [less ▲] Detailed reference viewed: 135 (4 UL)Reducing non-linear PDEs using a reduced integration proper orthogonal decomposition method ; Hale, Jack ; Beex, Lars et al Scientific Conference (2016) Detailed reference viewed: 155 (15 UL)On the convergence of stresses in fretting fatigue ; Bordas, Stéphane ; Tomar, Satyendra et al in Materials (2016), 9(8), Fretting is a phenomenon that occurs at the contacts of surfaces that are subjected to oscillatory relative movement of small amplitudes. Depending on service conditions, fretting may significantly reduce ... [more ▼] Fretting is a phenomenon that occurs at the contacts of surfaces that are subjected to oscillatory relative movement of small amplitudes. Depending on service conditions, fretting may significantly reduce the service life of a component due to fretting fatigue. In this regard, the analysis of stresses at contact is of great importance for predicting the lifetime of components. However, due to the complexity of the fretting phenomenon, analytical solutions are available for very selective situations and finite element (FE) analysis has become an attractive tool to evaluate stresses and to study fretting problems. Recent laboratory studies in fretting fatigue suggested the presence of stress singularities in the stick-slip zone. In this paper, we constructed finite element models, with different element sizes, in order to verify the existence of stress singularity under fretting conditions. Based on our results, we did not find any singularity for the considered loading conditions and coefficients of friction. Since no singularity was found, the present paper also provides some comments regarding the convergence rate. Our analyses showed that the convergence rate in stress components depends on coefficient of friction, implying that this rate also depends on the loading condition. It was also observed that errors can be relatively high for cases with a high coefficient of friction, suggesting the importance of mesh refinement in these situations. Although the accuracy of the FE analysis is very important for satisfactory predictions, most of the studies in the literature rarely provide information regarding the level of error in simulations. Thus, some recommendations of mesh sizes for those who wish to perform FE analysis of fretting problems are provided for different levels of accuracy. [less ▲] Detailed reference viewed: 121 (2 UL)Implementation of regularized isogeometric boundary element methods for gradient-based shape optimization in two-dimensional linear elasticity ; ; Bordas, Stéphane in International Journal for Numerical Methods in Engineering (2015) Detailed reference viewed: 265 (16 UL)Multi-scale methods for fracture: model learning across scales, digital twinning and factors of safety Bordas, Stéphane ; Beex, Lars ; et al Scientific Conference (2015, November 18) Authors: S. P. A. Bordas, L. A. A. Beex, P. Kerfriden, D. A. Paladim, O. Goury, A. Akbari, H. Rappel Multi-scale methods for fracture: model learning across scales, digital twinning and factors of safety ... [more ▼] Authors: S. P. A. Bordas, L. A. A. Beex, P. Kerfriden, D. A. Paladim, O. Goury, A. Akbari, H. Rappel Multi-scale methods for fracture: model learning across scales, digital twinning and factors of safety Fracture and material instabilities originate at spatial scales much smaller than that of the structure of interest: delamination, debonding, fibre breakage, cell-wall buckling, are examples of nano/micro or meso-scale mechanisms which can lead to global failure of the material and structure. Such mechanisms cannot, for computational and practical reasons, be accounted at structural scale, so that acceleration methods are necessary. We review in this presentation recently proposed approaches to reduce the computational expense associated with multi-scale modelling of fracture. In light of two particular examples, we show connections between algebraic reduction (model order reduction and quasi-continuum methods) and homogenisation-based reduction. We open the discussion towards suitable approaches for machine-learning and Bayesian statistical based multi-scale model selection. Such approaches could fuel a digital-twin concept enabling models to learn from real-time data acquired during the life of the structure, accounting for “real” environmental conditions during predictions, and, eventually, moving beyond the “factors of safety” era. [less ▲] Detailed reference viewed: 424 (19 UL) |
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