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A Tutorial on Bayesian Inference to Identify Material Parameters in Solid Mechanics Rappel, Hussein ; Beex, Lars ; Hale, Jack et al in Archives of Computational Methods in Engineering (2019) The aim of this contribution is to explain in a straightforward manner how Bayesian inference can be used to identify material parameters of material models for solids. Bayesian approaches have already ... [more ▼] The aim of this contribution is to explain in a straightforward manner how Bayesian inference can be used to identify material parameters of material models for solids. Bayesian approaches have already been used for this purpose, but most of the literature is not necessarily easy to understand for those new to the field. The reason for this is that most literature focuses either on complex statistical and machine learning concepts and/or on relatively complex mechanical models. In order to introduce the approach as gently as possible, we only focus on stress–strain measurements coming from uniaxial tensile tests and we only treat elastic and elastoplastic material models. Furthermore, the stress–strain measurements are created artificially in order to allow a one-to-one comparison between the true parameter values and the identified parameter distributions. [less ▲] Detailed reference viewed: 342 (63 UL)A hyper-reduction method using adaptivity to cut the assembly costs of reduced order models Hale, Jack ; ; Baroli, Davide et al E-print/Working paper (2019) At every iteration or timestep of the online phase of some reduced-order modelling schemes, large linear systems must be assembled and then projected onto a reduced order basis of small dimension. The ... [more ▼] At every iteration or timestep of the online phase of some reduced-order modelling schemes, large linear systems must be assembled and then projected onto a reduced order basis of small dimension. The projected small linear systems are cheap to solve, but assembly and projection are now the dominant computational cost. In this paper we introduce a new hyper-reduction strategy called reduced assembly (RA) that drastically cuts these costs. RA consists of a triangulation adaptation algorithm that uses a local error indicator to con- struct a reduced assembly triangulation specially suited to the reduced order basis. Crucially, this reduced assembly triangulation has fewer cells than the original one, resulting in lower assembly and projection costs. We demonstrate the efficacy of RA on a Galerkin-POD type reduced order model (RAPOD). We show performance increases of up to five times over the baseline Galerkin-POD method on a non-linear reaction-diffusion problem solved with a semi-implicit time-stepping scheme and up to seven times for a 3D hyperelasticity problem solved with a continuation Newton-Raphson algorithm. The examples are implemented in the DOLFIN finite element solver using PETSc and SLEPc for linear algebra. Full code and data files to produce the results in this paper are provided as supplementary material. [less ▲] Detailed reference viewed: 126 (20 UL)A volume-averaged nodal projection method for the Reissner-Mindlin plate model ; ; Hale, Jack et al in Computer Methods in Applied Mechanics & Engineering (2018), 341 We introduce a novel meshfree Galerkin method for the solution of Reissner-Mindlin plate problems that is written in terms of the primitive variables only (i.e., rotations and transverse displacement) and ... [more ▼] We introduce a novel meshfree Galerkin method for the solution of Reissner-Mindlin plate problems that is written in terms of the primitive variables only (i.e., rotations and transverse displacement) and is devoid of shear-locking. The proposed approach uses linear maximum-entropy approximations and is built variationally on a two-field potential energy functional wherein the shear strain, written in terms of the primitive variables, is computed via a volume-averaged nodal projection operator that is constructed from the Kirchhoff constraint of the three-field mixed weak form. The stability of the method is rendered by adding bubble-like enrichment to the rotation degrees of freedom. Some benchmark problems are presented to demonstrate the accuracy and performance of the proposed method for a wide range of plate thicknesses. [less ▲] Detailed reference viewed: 104 (13 UL)Simple and extensible plate and shell finite element models through automatic code generation tools Hale, Jack ; ; Bordas, Stéphane et al in Computers & Structures (2018), 209 A large number of advanced finite element shell formulations have been developed, but their adoption is hindered by complexities of transforming mathematical formulations into computer code. Furthermore ... [more ▼] A large number of advanced finite element shell formulations have been developed, but their adoption is hindered by complexities of transforming mathematical formulations into computer code. Furthermore, it is often not straightforward to adapt existing implementations to emerging frontier problems in thin structural mechanics including nonlinear material behaviour, complex microstructures, multi-physical couplings, or active materials. We show that by using a high-level mathematical modelling strategy and automatic code generation tools, a wide range of advanced plate and shell finite element models can be generated easily and efficiently, including: the linear and non-linear geometrically exact Naghdi shell models, the Marguerre-von K ́arm ́an shallow shell model, and the Reissner-Mindlin plate model. To solve shear and membrane-locking issues, we use: a novel re-interpretation of the Mixed Interpolation of Tensorial Component (MITC) procedure as a mixed-hybridisable finite element method, and a high polynomial order Partial Selective Reduced Integration (PSRI) method. The effectiveness of these approaches and the ease of writing solvers is illustrated through a large set of verification tests and demo codes, collected in an open-source library, FEniCS-Shells, that extends the FEniCS Project finite element problem solving environment. [less ▲] Detailed reference viewed: 385 (32 UL)Uncertainty Quantification in Finite Element Models:Application to SoftTissue Biomechanics Hauseux, Paul ; Hale, Jack ; Bulle, Raphaël et al Scientific Conference (2018, July 23) We present probabilistic approaches aiming at the selection of the best constitutive model and to identify their parameters from experimental data. These parameters are always associated with some degree ... [more ▼] We present probabilistic approaches aiming at the selection of the best constitutive model and to identify their parameters from experimental data. These parameters are always associated with some degree of uncertainty. It is therefore important to study how this statistical uncertainty in parameters propagates to a safety-critical quantity of interest in the output of a model. Efficient Monte Carlo methods based on variance reduction techniques (Sensitivity Derivatives Monte Carlo methods [Hauseux et al. 2017] and MultiLevel Monte Carlo [Giles 2015] methods) are employed to propagate this uncertainty for both random variables and random fields. Inverse and forward problems are strongly connected. In a bayesian setting [Matthies et al. 2017], developing methods that reduce the number of evaluations of the forward model to an absolute minimum to achieve convergence is crucial for tractable computations. Numerical results in the context of soft tissue biomechanics are presented and discussed. [less ▲] Detailed reference viewed: 111 (1 UL)XDMF and ParaView: checkpointing format Habera, Michal ; Zilian, Andreas ; Hale, Jack et al Scientific Conference (2018, March 21) Checkpointing, i.e. saving and reading results of finite element computation is crucial, especially for long-time running simulations where execution is interrupted and user would like to restart the ... [more ▼] Checkpointing, i.e. saving and reading results of finite element computation is crucial, especially for long-time running simulations where execution is interrupted and user would like to restart the process from last saved time step. On the other hand, visualization of results in thid-party software such as ParaView is inevitable. In the previous DOLFIN versions (2017.1.0 and older) these two functionalities were strictly separated. Results could have been saved via HDF5File interface for later computations and/or stored in a format understood by ParaView - VTK’s .pvd (File interface) or XDMF (XDMFFile interface). This led to data redundancy and error-prone workflow. The problem essentially originated from incompatibilities between both libraries, DOLFIN and ParaView (VTK). DOLFIN’s internal representation of finite element function is based on vector of values of degrees of freedom (dofs) and their ordering within cells (dofmap). VTK’s representation of a function is given by it’s values at some points in cell, while ordering and geometric position of these points is fixed and standardised within VTK specification. For nodal (iso- and super-parametric) Lagrange finite elements (Pk , dPk ) both representations coincide up to an ordering. This allows to extend XDMF specification and introduce intermediate way of storing finite element function - intrinsic to both, ParaView and DOLFIN. The necessary work was done as a part of Google Summer of Code 2017 project Develop XDMF for- mat for visualisation and checkpointing, see https://github.com/michalhabera/gsoc-summary. New checkpointing functionality is exposed via write checkpoint() and read checkpoint() methods. [less ▲] Detailed reference viewed: 159 (24 UL)Using higher-order adjoints to accelerate the solution of UQ problems with random fields Hale, Jack ; Hauseux, Paul ; Bordas, Stéphane Poster (2018, January 08) A powerful Monte Carlo variance reduction technique introduced in Cao and Zhang 2004 uses local derivatives to accelerate Monte Carlo estimation. This work aims to: develop a new derivative-driven ... [more ▼] A powerful Monte Carlo variance reduction technique introduced in Cao and Zhang 2004 uses local derivatives to accelerate Monte Carlo estimation. This work aims to: develop a new derivative-driven estimator that works for SPDEs with uncertain data modelled as Gaussian random fields with Matérn covariance functions (infinite/high-dimensional problems) (Lindgren, Rue, and Lindström, 2011), use second-order derivative (Hessian) information for improved variance reduction over our approach in (Hauseux, Hale, and Bordas, 2017), demonstrate a software framework using FEniCS (Logg and Wells, 2010), dolfin-adjoint (Farrell et al., 2013) and PETSc (Balay et al., 2016) for automatic acceleration of MC estimation for a wide variety of PDEs on HPC architectures. [less ▲] Detailed reference viewed: 148 (22 UL)ECCOMAS Newsletter - Computational and Data Sciences in Luxembourg Beex, Lars ; Bordas, Stéphane ; Hale, Jack et al Report (2018) Detailed reference viewed: 636 (71 UL)Quantifying the uncertainty in a hyperelastic soft tissue model with stochastic parameters Hauseux, Paul ; Hale, Jack ; et al in Applied Mathematical Modelling (2018), 62 We present a simple open-source semi-intrusive computational method to propagate uncertainties through hyperelastic models of soft tissues. The proposed method is up to two orders of magnitude faster than ... [more ▼] We present a simple open-source semi-intrusive computational method to propagate uncertainties through hyperelastic models of soft tissues. The proposed method is up to two orders of magnitude faster than the standard Monte Carlo method. The material model of interest can be altered by adjusting few lines of (FEniCS) code. The method is able to (1) provide the user with statistical confidence intervals on quantities of practical interest, such as the displacement of a tumour or target site in an organ; (2) quantify the sensitivity of the response of the organ to the associated parameters of the material model. We exercise the approach on the determination of a confidence interval on the motion of a target in the brain. We also show that for the boundary conditions under consideration five parameters of the Ogden-Holzapfel-like model have negligible influence on the displacement of the target zone compared to the three most influential parameters. The benchmark problems and all associated data are made available as supplementary material. [less ▲] Detailed reference viewed: 705 (116 UL)Calculating the Malliavin derivative of some stochastic mechanics problems Hauseux, Paul ; Hale, Jack ; Bordas, Stéphane in PLoS ONE (2017), 12(12), 0189994 The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to ... [more ▼] The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper. [less ▲] Detailed reference viewed: 181 (26 UL)Micro-structured materials: inhomogeneities and imperfect interfaces in plane micropolar elasticity, a boundary element approach ; Hale, Jack ; et al in Engineering Analysis with Boundary Elements (2017), 83 In this paper we tackle the simulation of microstructured materials modelled as heterogeneous Cosserat media with both perfect and imperfect interfaces. We formulate a boundary value problem for an ... [more ▼] In this paper we tackle the simulation of microstructured materials modelled as heterogeneous Cosserat media with both perfect and imperfect interfaces. We formulate a boundary value problem for an inclusion of one plane strain micropolar phase into another micropolar phase and reduce the problem to a system of boundary integral equations, which is subsequently solved by the boundary element method. The inclusion interface condition is assumed to be imperfect, which permits jumps in both displacements/microrotations and tractions/couple tractions, as well as a linear dependence of jumps in displacements/microrotations on continuous across the interface tractions/couple traction (model known in elasticity as homogeneously imperfect interface). These features can be directly incorporated into the boundary element formulation. The BEM-results for a circular inclusion in an in finite plate are shown to be in excellent agreement with the analytical solutions. The BEM-results for inclusions in finite plates are compared with the FEM-results obtained with FEniCS. [less ▲] Detailed reference viewed: 161 (12 UL)Uncertainty Quantification (Monte Carlo methods) - Sensitivity Analysis - Biomechanics Hauseux, Paul ; Hale, Jack ; Bordas, Stéphane Presentation (2017, September) Detailed reference viewed: 64 (2 UL)Containers for portable, productive and performant scientific computing Hale, Jack ; ; et al in Computing in Science & Engineering (2017) Containers are an emerging technology that hold promise for improving productivity and code portability in scientific computing. We examine Linux container technology for the distribution of a non-trivial ... [more ▼] Containers are an emerging technology that hold promise for improving productivity and code portability in scientific computing. We examine Linux container technology for the distribution of a non-trivial scientific computing software stack and its execution on a spectrum of platforms from laptop computers through to high performance computing (HPC) systems. We show on a workstation and a leadership-class HPC system that when deployed appropriately there are no performance penalties running scientific programs inside containers. For Python code run on large parallel computers, the run time is reduced inside a container due to faster library imports. The software distribution approach and data that we present will help developers and users decide on whether container technology is appropriate for them. We also provide guidance for the vendors of HPC systems that rely on proprietary libraries for performance on what they can do to make containers work seamlessly and without performance penalty. [less ▲] Detailed reference viewed: 124 (18 UL)Accelerating Monte Carlo estimation with derivatives of high-level finite element models Hauseux, Paul ; Hale, Jack ; Bordas, Stéphane in Computer Methods in Applied Mechanics & Engineering (2017), 318 In this paper we demonstrate the ability of a derivative-driven Monte Carlo estimator to accelerate the propagation of uncertainty through two high-level non-linear finite element models. The use of ... [more ▼] In this paper we demonstrate the ability of a derivative-driven Monte Carlo estimator to accelerate the propagation of uncertainty through two high-level non-linear finite element models. The use of derivative information amounts to a correction to the standard Monte Carlo estimation procedure that reduces the variance under certain conditions. We express the finite element models in variational form using the high-level Unified Form Language (UFL). We derive the tangent linear model automatically from this high-level description and use it to efficiently calculate the required derivative information. To study the effectiveness of the derivative-driven method we consider two stochastic PDEs; a one- dimensional Burgers equation with stochastic viscosity and a three-dimensional geometrically non-linear Mooney-Rivlin hyperelastic equation with stochastic density and volumetric material parameter. Our results show that for these problems the first-order derivative-driven Monte Carlo method is around one order of magnitude faster than the standard Monte Carlo method and at the cost of only one extra tangent linear solution per estimation problem. We find similar trends when comparing with a modern non-intrusive multi-level polynomial chaos expansion method. We parallelise the task of the repeated forward model evaluations across a cluster using the ipyparallel and mpi4py software tools. A complete working example showing the solution of the stochastic viscous Burgers equation is included as supplementary material. [less ▲] Detailed reference viewed: 1326 (219 UL)Strain smoothed for compressible and nearly-incompressible finite elasticity ; ; Hale, Jack et al in Computers & Structures (2017), 182 We present a robust and efficient form of the smoothed finite element method (S-FEM) to simulate hyperelastic bodies with compressible and nearly-incompressible neo-Hookean behaviour. The resulting method ... [more ▼] We present a robust and efficient form of the smoothed finite element method (S-FEM) to simulate hyperelastic bodies with compressible and nearly-incompressible neo-Hookean behaviour. The resulting method is stable, free from volumetric locking and robust on highly distorted meshes. To ensure inf-sup stability of our method we add a cubic bubble function to each element. The weak form for the smoothed hyperelastic problem is derived analogously to that of smoothed linear elastic problem. Smoothed strains and smoothed deformation gradients are evaluated on sub-domains selected by either edge information (edge-based S-FEM, ES-FEM) or nodal information (node-based S-FEM, NS-FEM). Numerical examples are shown that demonstrate the efficiency and reliability of the proposed approach in the nearly-incompressible limit and on highly distorted meshes. We conclude that, strain smoothing is at least as accurate and stable, as the MINI element, for an equivalent problem size. [less ▲] Detailed reference viewed: 225 (27 UL)Reduced basis Nitsche-based domain decomposition: a biomedical application Baroli, Davide ; Beex, Lars ; Hale, Jack et al Scientific Conference (2017, March 10) Nowadays, the personalized biomedical simulations demand real-time efficient and reliable method to alleviate the computational complexity of high-fidelity simulation. In such applications, the necessity ... [more ▼] Nowadays, the personalized biomedical simulations demand real-time efficient and reliable method to alleviate the computational complexity of high-fidelity simulation. In such applications, the necessity of solving different substructure, e.g. tissues or organs, with different numbers of the degrees of freedom and of coupling the reduced order spaces for each substructure poses a challenge in the on-fly simulation. In this talk, this challenge is taken into account employing the Nitsche-based domain decomposition technique inside the reduced order model [1]. This technique with respect to other domain decomposition approach allows obtaining a solution with the same accuracy of underlying finite element formulation and to flexibly treat interface with non-matching mesh. The robustness of the coupling is determined by the penalty coefficients that is chosen using ghost penalty technique [2]. Furthermore, to reduce the computational complexity of the on-fly assembling it is employed the empirical interpolation approach proposed in [3]. The numerical tests, performed using FEniCS[4], petsc4py and slepc4py [5], shows the good performance of the method and the reduction of computation cost. [1] Baroli, D., Beex L. and Bordas, S. Reduced basis Nitsche-based domain decomposition. In preparation. [2] Burman, E., Claus, S., Hansbo, P., Larson, M. G., & Massing, A. (2015). CutFEM: Discretizing geometry and partial differential equations. International Journal for Numerical Methods in Engineering, 104(7), 472-501. [3] E. Schenone, E., Beex,L., Hale, J.S., Bordas S. Proper Orthogonal Decomposition with reduced integration method. Application to nonlinear problems. In preparation. [4] A. Logg, K.-A. Mardal, G. N. Wells et al. Automated Solution of Differential Equations by the Finite Element Method, Springer 2012. [5] L. Dalcin, P. Kler, R. Paz, and A. Cosimo, Parallel Distributed Computing using Python, Advances in Water Resources, 34(9):1124-1139, 2011. http://dx.doi.org/10.1016/j.advwatres.2011.04.013 [less ▲] Detailed reference viewed: 220 (10 UL)Uncertainty Quantification - Sensitivity Analysis / Biomechanics Hauseux, Paul ; Hale, Jack ; Bordas, Stéphane Presentation (2017, February) Detailed reference viewed: 83 (9 UL)Image to analysis pipeline: single and double balloons kyphoplasty Baroli, Davide ; Hauseux, Paul ; Hale, Jack et al Poster (2016, December 12) In this work, we present a semi-automatic pipeline from image to simulation of a patient fractured vertebra after the kyphoplastic augmentation with two balloons. In this procedure, the CT-scan medical ... [more ▼] In this work, we present a semi-automatic pipeline from image to simulation of a patient fractured vertebra after the kyphoplastic augmentation with two balloons. In this procedure, the CT-scan medical image are pre-processed using open-source software Slice3D for segmentation and 3D reconstruction operation. Then, using geometric processing the 3D surface geometry is enhanced to avoid degenerate element and trigging phenomena on vertebra and cement area. We perform a finite element analysis to evaluate the risk of subsequent vertebral fracture. Finally using Monte-Carlo technique, we assess the propagation of uncertainty of material parameter on the evaluation of this risk. Based on the developed semi-automatic pipelines, it is possible to perform a patient-specific simulation that assesses the successful of kyphoplasty operation. [less ▲] Detailed reference viewed: 171 (35 UL)Elastography under uncertainty Hale, Jack ; ; Bordas, Stéphane Poster (2016, December 12) Detailed reference viewed: 156 (11 UL)Bayesian inference for parameter identification in computational mechanics Rappel, Hussein ; Beex, Lars ; Hale, Jack et al Poster (2016, December 12) Detailed reference viewed: 141 (9 UL) |
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