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Phase field approach to fracture: Towards the simulation of cutting soft tissues Ziaei Rad, Vahid ; Hale, Jack ; et al Scientific Conference (2016, June 08) Detailed reference viewed: 335 (11 UL)Efficient propagation of uncertainty through an inverse non-linear deformation model of soft tissue Hauseux, Paul ; Hale, Jack ; Bordas, Stéphane Scientific Conference (2016, June) Detailed reference viewed: 183 (24 UL)A Bayesian approach for parameter identification in elastoplasticity Rappel, Hussein ; Beex, Lars ; Hale, Jack et al Scientific Conference (2016, June) Detailed reference viewed: 187 (28 UL)POD-based Reduction Methods, the Quasicontinuum Method and their Resemblance ; Hale, Jack ; Beex, Lars Scientific Conference (2016, June) POD-based reduction methods and the quasicontinuum method share two similar reduction steps to increase the computational speed of large mechanical models. Here, they are compared with each other. Detailed reference viewed: 91 (8 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: 161 (12 UL)Bayesian inference for material parameter identification Rappel, Hussein ; Beex, Lars ; Hale, Jack et al Report (2016) Detailed reference viewed: 156 (14 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: 239 (20 UL)Orchestrating clinical simulations with FEniCS ; ; Hale, Jack Scientific Conference (2016, May) Detailed reference viewed: 82 (5 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: 244 (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: 161 (17 UL)Reduced order method combined with domain decomposition Baroli, Davide ; Bordas, Stéphane ; Beex, Lars et al Scientific Conference (2016) The complexities and nonlinearity of the PDEs in biomechanics and the requirement for rapid solution pose significant challenges for the biomedical applications. For these reasons, different methods for ... [more ▼] The complexities and nonlinearity of the PDEs in biomechanics and the requirement for rapid solution pose significant challenges for the biomedical applications. For these reasons, different methods for reducing the complexity and solving efficiently have been investigated in the last 15 years. At the state-ofart, due to spatial different behaviours and highly accurate simulation required, a decomposition of physical domain is deeply investigated in reduced basis element method approaches. In this talk, the main focus is devoted to present suitable reduction strategy which combines a domain decomposition approach and a proper interface management with a proper orthogonal decomposition. We provide numerical tests implemented in DOLFIN[4] using SLEPc [3] and PETSc [1, 2] that show a speed up in forward runtime model. [less ▲] Detailed reference viewed: 125 (8 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: 143 (15 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: 145 (15 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: 196 (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: 131 (5 UL)fenics-shells: a UFL-based library for simulating thin structures ; Hale, Jack ; Bordas, Stéphane et al Scientific Conference (2015, July 01) Shell, plate and beam (thin) structures are widely used in civil, mechanical and aeronautical engineering because they are capable of carrying high loads with a minimal amount of structural mass. Because ... [more ▼] Shell, plate and beam (thin) structures are widely used in civil, mechanical and aeronautical engineering because they are capable of carrying high loads with a minimal amount of structural mass. Because the out-of-plane dimension is usually much smaller than the two in-plane dimensions, it is possible to asymptotically reduce the full 3D equations of elasticity to a whole variety of equivalent 2D models posed on a manifold embedded in 3D space. This reduction results in massively reduced computational expense and remains a necessity for practical large-scale computation of structures of real engineering interest such as the fuselage of an aircraft. The numerical solution of such mathematical models is a challenging task, especially for very thin shells when shear and membrane locking effects require special attention. As originally noted by [Hale and Baiz, 2013], the high-level form language UFL provides an excellent framework for writing extensible, reusable and pedagogical numerical models of thin structures. To our knowledge fenics-shells represents the first unified open-source implementation of a wide range of thin structural models, including Reissner-Mindlin, Kirchhoff-Love, Von Karman and hierarchical (higher-order) plates, and Madare-Naghdi and Madare-Koiter shell models. Because of the broad scope of fenics-shells, in this talk we will focus on how to cure numerical locking by applying the Mixed Interpolation of Tensorial Components (MITC) approach of [Dvorkin and Bathe, 1986] and [Lee and Bathe, 2010] to a shell with an initially flat reference configuration. The MITC approach consists of an element-by-element interpolation of the degrees of freedom of the rotations onto the degrees of freedom of a reduced rotation space, the latter typically constructed using H(curl) conforming finite elements such as the rotated Raviart-Thomas-Nédélec elements. Then, the bilinear form is constructed on the underlying H(curl) space. Because of the interpolation operator, the original problem is expressed in terms of the degrees of freedom for the rotations only. Within DOLFIN we have implemented this projection operation using two UFL forms within a custom assembler compiled just-in-time using Instant. We show numerical convergence studies that match the apriori bounds available in the literature. E. N. Dvorkin and K.-J. Bathe, “A continuum mechanics based four-node shell element for general non-linear analysis,” Engineering Computations, vol. 1, no. 1, pp. 77–88, 1984. P. S. Lee and K. J. Bathe, “The quadratic MITC plate and MITC shell elements in plate bending,” Advances in Engineering Software, vol. 41, no. 5, pp. 712–728, 2010. J. S. Hale and P. M. Baiz, “Towards effective shell modelling with the FEniCS project” presented at the FEniCS Conference 2013, Jesus College, Cambridge, 19-Mar-2013. [less ▲] Detailed reference viewed: 840 (25 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: 773 (25 UL)Large scale phase field model of fracture and cutting in soft tissues ; Hale, Jack ; et al Scientific Conference (2015, July) The phase field method has proven to be an important tool in computational mechanics in that it is able to deal naturally with crack nucleation and branching [1]. In this contribution, we demonstrate a ... [more ▼] The phase field method has proven to be an important tool in computational mechanics in that it is able to deal naturally with crack nucleation and branching [1]. In this contribution, we demonstrate a large scale phase field model of fracture and cutting of soft tissues undergoing non-linear deformations with a material law defined by a hyperelastic energy density functional. We will also provide some initial thoughts on the how the effect of a porous medium can be incorporated into the phase field model. We implement this work using the FEniCS project and PETSc software packages [2, 3]. [less ▲] Detailed reference viewed: 257 (9 UL)Hyperelastic Elastography in a Large-Scale Bayesian Inversion Setting Hale, Jack ; ; Bordas, Stéphane Scientific Conference (2015, July) We consider the problem of recovering the material parameters of a hyperelastic material [1] in the Bayesian inversion setting. In the Bayesian setting we can extract the statistics associated with ... [more ▼] We consider the problem of recovering the material parameters of a hyperelastic material [1] in the Bayesian inversion setting. In the Bayesian setting we can extract the statistics associated with various sources of uncertainty, including noise, experimental deficiencies and incomplete observations of the domain. This will allow medical practitioners to make superior diagnosis decisions when presented with a quantitative measure of uncertainty in the recovered parameters. On the assumption of a Gaussian additive noise model, a Gaussian prior and a linear forward model, the posterior distribution of the material parameters given the observations will also be Gaussian. To ensure that the assumption of a linear forward model is valid, and that the posterior is approximated sufficiently well by a Gaussian distribution, we place a limit on the strain regime in which our current methodology applies. We are developing MCMC methods for exploring the non-Gaussian statistics of the posterior distribution. In the linear case, the covariance matrix of the posterior distribution is then characterised by the inverse of the Hessian of the objective functional evaluated at its minimiser. To extract statistical information from the large and dense Hessian we perform a low-rank approximation of the Hessian [2]. The eigenvectors associated with the lowest eigenvalues are the directions in parameter space that are least constrained by the observations. We implement this work within the dolfin-adjoint [3] software package. We derive the MPI-parallel finite element discretisation of the forward, adjoint (1st and 2nd order), and tangent linear models using the high-level differentiation tools available within the FEniCS project. We show results demonstrating the effects of partial observations and poor experimental design on the reliability of the recovered parameters. [1] N. H. Gokhale, P. E. Barbone, and A. A. Oberai, “Solution of the nonlinear elasticity imaging inverse problem: the compressible case,” Inverse Problems, 10.1088/0266-5611/24/4/045010 [2] 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., 10.1137/090780717 [3] P. Farrell, D. Ham, S. Funke, and M. Rognes, “Automated Derivation of the Adjoint of High-Level Transient Finite Element Programs,” SIAM J. Sci. Comput., 10.1137/120873558 [less ▲] Detailed reference viewed: 399 (17 UL)FEniCS in Linux Containers Hale, Jack ; ; Poster (2015, June 29) We present a collection of Docker images for running FEniCS in Linux containers. With one command, a user can launch a lightweight container that provides a consistent environment for using or developing ... [more ▼] We present a collection of Docker images for running FEniCS in Linux containers. With one command, a user can launch a lightweight container that provides a consistent environment for using or developing FEniCS. Once the initial image has been fetched, 'FEniCS terminals' can be launched near-instantly. We show through a range of tests that performance within a container is to equal to that on the host system. Moreover, MPI programs can be run from inside the container, and host CPU vectorisation features can be exploited. In practice, container versions of FEniCS will be faster than user installations as the container images can be carefully tuned for performance. Live demonstrations of user and developer container use will be presented. The containers are built and hosted on Docker Hub [less ▲] Detailed reference viewed: 164 (18 UL) |
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