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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: 250 (20 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: 432 (14 UL)2015 Lab report - Legato report 001 Bordas, Stéphane Report (2016) Detailed reference viewed: 497 (12 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: 114 (2 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: 123 (3 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: 146 (15 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: 130 (5 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: 122 (3 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: 146 (15 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: 171 (18 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: 253 (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: 407 (19 UL)Multi-scale methods for fracture: model learning across scales, digital twinning and factors of safety
: primer on Bayesian Inference Bordas, Stéphane ; Hale, Jack ; Beex, Lars et al Speeches/Talks (2015) Fracture and material instabilities originate at spatial scales much smaller than that of the structure of interest: delamination, debonding, fibre break- age, cell-wall buckling, are examples of nano ... [more ▼] Fracture and material instabilities originate at spatial scales much smaller than that of the structure of interest: delamination, debonding, fibre break- age, cell-wall buckling, are examples of nano/micro or meso-scale mechanisms which can lead to global failure of the material and structure. Such mech- anisms 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 frac- ture. 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 era of factors of safety. [less ▲] Detailed reference viewed: 198 (5 UL)Using Bayes' theorem to infer the material parameters of human soft tissue Hale, Jack ; ; Bordas, Stéphane Presentation (2015, October 21) Detailed reference viewed: 132 (5 UL)Higher-order quasicontinuum methods for elastic and dissipative lattice models: uniaxial deformation and pure bending Beex, Lars ; ; et al in GAMM Mitteilungen (2015), 38(2), 344-368 The quasicontinuum (QC) method is a numerical strategy to reduce the computational cost of direct lattice computations - in this study we achieve a speed up of a factor of 40. It has successfully been ... [more ▼] The quasicontinuum (QC) method is a numerical strategy to reduce the computational cost of direct lattice computations - in this study we achieve a speed up of a factor of 40. It has successfully been applied to (conservative) atomistic lattices in the past, but using a virtual-power-statement it was recently shown that QC approaches can also be used for spring and beam lattice models that include dissipation. Recent results have shown that QC approaches for planar beam lattices experiencing in-plane and out-of-plane deformation require higher-order interpolation. Higher-order QC frameworks are scarce nevertheless. In this contribution, the possibilities of a second-order and third-order QC framework are investigated for an elastoplastic spring lattice. The higher-order QC frameworks are compared to the results of the direct lattice computations and to those of a linear QC scheme. Examples are chosen so that both a macroscale and a microscale quantity influences the results. The two multiscale examples focused on are (i) macroscopically prescribed uniaxial deformation and (ii) macroscopically prescribed pure bending. Furthermore, the examples include an individual inclusion in a large lattice and hence, are concurrent in nature. [less ▲] Detailed reference viewed: 338 (33 UL)Open-Cell Aluminium Foams with Graded Coatings as Passively Controllable Energy Absorbers ; Beex, Lars ; et al in Materials and Design (2015), 87 Compared to most bulk materials, open-cell aluminium (Al) foams (OCAFs) are light-weight and can absorb a significant amount of energy in compression, e.g. during impact.When coatedwith nickel (Ni), OCAFs ... [more ▼] Compared to most bulk materials, open-cell aluminium (Al) foams (OCAFs) are light-weight and can absorb a significant amount of energy in compression, e.g. during impact.When coatedwith nickel (Ni), OCAFs can absorb even more energy, making them more appropriate for impacts at higher velocities than uncoated OCAFs. When Ni-coated OCAFs experience low-velocity impact however, the stopping distance during the impact is small compared to that of uncoated OCAFs and hence, deceleration occurs fast. This exposes devices (and possibly human beings) protected by OCAFs to large internal forces leading to internal damage. An OCAF that combines the properties of uncoated and coated OCAFs can absorb energy during both low-velocity and high-velocity impact scenarios. This contribution introduces two of such OCAFs which are created by partially and gradually coating OCAFs. The general mechanics of the two OCAFs are revealed using experimental and numerical observation methods. [less ▲] Detailed reference viewed: 628 (27 UL)Isogeometric and multi-scale fracture Bordas, Stéphane Presentation (2015, July 31) Detailed reference viewed: 183 (13 UL)A Bayesian inversion approach to recovering material parameters in hyperelastic solids using dolfin-adjoint Hale, Jack ; ; Bordas, Stéphane Presentation (2015, July 01) In the first part of the talk I will describe in general terms the link between classical optimisation techniques and the Bayesian approach to statistical inversion as outlined in the seminal book of ... [more ▼] In the first part of the talk I will describe in general terms the link between classical optimisation techniques and the Bayesian approach to statistical inversion as outlined in the seminal book of [Kaipio and Somersalo, 2005]. Under the assumption of an additive Gaussian noise model, a Gaussian prior distribution and a linear parameter-to-observable map, it is possible to uniquely characterise the Bayesian posterior as Gaussian with the maximum aposteriori (MAP) point equal to the minimum of a classic regularised minimisation problem and covariance matrix equal to the inverse of the Hessian of the functional evaluated at the MAP point. I will also discuss techniques that can be used when these assumptions break down. In the second part of the talk I will describe a method implemented within dolfin-adjoint [Funke and Farrell, arXiv 2013] to quantify the uncertainty in the recovered material parameters of a hyperelastic solid from partial and noisy observations of the displacement field in the domain. The finite element discretisation of the adjoint and higher-order adjoint (Hessian) equations are derived automatically from the high-level UFL representation of the problem. The resulting equations are solved using PETSc. I will concentrate on finding the eigenvalue decomposition of the posterior covariance matrix (Hessian). The eigenvectors associated with the lowest eigenvalues of the Hessian correspond with the directions in parameter space least constrained by the observations [Flath et al. 2011]. This eigenvalue problem is tricky to solve efficiently because the Hessian is very large (on the order of the number of parameters) and dense (meaning that only its action on a vector can be calculated, each involving considerable expense). Finally, I will show some illustrative examples including the uncertainty associated with deriving the material properties of a 3D hyperelastic block with a stiff inclusion with knowledge only of the displacements on the boundary of the domain. J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems, vol. 160. New York: Springer-Verlag, 2005. S. W. Funke and P. E. Farrell, “A framework for automated PDE-constrained optimisation,” arXiv:1302.3894 [cs], Feb. 2013. H. P. Flath, L. C. Wilcox, V. Akçelik, J. Hill, B. van Bloemen Waanders, and O. Ghattas, “Fast Algorithms for Bayesian Uncertainty Quantification in Large-Scale Linear Inverse Problems Based on Low-Rank Partial Hessian Approximations,” SIAM J. Sci. Comput., vol. 33, no. 1, pp. 407–432, Feb. 2011. [less ▲] Detailed reference viewed: 785 (25 UL)Quasicontinuum methods for planar beam lattices (abstract) Beex, Lars ; ; et al Scientific Conference (2015, July) Detailed reference viewed: 312 (1 UL)Advances in error estimation for homogenisation ; ; et al in 13th U.S. National Congress on Computational Mechanics (2015, July) In this paper, the concept of modeling error is extended to the homogenisation of elliptic PDEs. The main difficulty is the lack of a full description of the diffusion coefficients. We overcome this ... [more ▼] In this paper, the concept of modeling error is extended to the homogenisation of elliptic PDEs. The main difficulty is the lack of a full description of the diffusion coefficients. We overcome this obstacle by representing them as a random a field. Under this framework, it is possible to quantify the accuracy of the surrogate model (the homogenised model) in terms of first moments of the energy norm and quantities of interest. This work builds on the seminal work of [1]. The methodology here presented rely on the Constitutive Relation Error (CRE) which states that a certain measures of the primal and dual surrogate model upper bound the exact error. The surrogate model, in agreement with homogenisation, is deterministic. This property exploited to obtain bounds whose computation is also deterministic. It is also shown that minimising the CRE in the set of homogenisation schemes leads us to an optimal surrogate that is closely related to the classical Voigt and Reuss models. Numerical examples demonstrate that the bounds are easy and affordable to compute, and useful as long as the mismatch between he diffusion coefficients of the microstructure remain small. In the case of high mismatch, extensions are proposed, through the introduction of stochastic surrogate models.. [1]Romkes, Albert, J. Tinsley Oden, and Kumar Vemaganti."Multi-scale goal-oriented adaptive modeling of random heterogeneous materials." Mechanics of materials 38.8(2006): 859-872. [less ▲] Detailed reference viewed: 120 (5 UL) |
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