Browse ORBi

- What it is and what it isn't
- Green Road / Gold Road?
- Ready to Publish. Now What?
- How can I support the OA movement?
- Where can I learn more?

ORBi

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: 873 (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: 806 (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: 281 (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: 428 (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: 170 (18 UL)Reduced order methods Schenone, Elisa ; Hale, Jack ; Beex, Lars et al Presentation (2015, April 16) Detailed reference viewed: 252 (39 UL)Meshfree volume-averaged nodal projection method for nearly-incompressible elasticity using meshfree and bubble basis functions ; Hale, Jack ; in Computer Methods in Applied Mechanics and Engineering (2015), 285 We present a displacement-based Galerkin meshfree method for the analysis of nearly-incompressible linear elastic solids, where low-order simplicial tessellations (i.e., 3- node triangular or 4-node ... [more ▼] We present a displacement-based Galerkin meshfree method for the analysis of nearly-incompressible linear elastic solids, where low-order simplicial tessellations (i.e., 3- node triangular or 4-node tetrahedral meshes) are used as a background structure for numerical integration of the weak form integrals and to get the nodal information for the computation of the meshfree basis functions. 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 stability of the method is provided via bubble-like basis functions. Because the notion of an ‘ele- ment’ or ‘cell’ is not present in the computation of the meshfree basis functions such low-order tessellations can be used regardless of the order of the approximation spaces desired. First- and second-order meshfree basis functions are chosen as a particular case in the proposed method. Numerical examples are provided in two and three dimensions to demonstrate the robustness of the method, its ability to avoid volumetric locking in the nearly-incompressible regime, and its improved performance when compared to the MINI finite element scheme on the simplicial mesh. [less ▲] Detailed reference viewed: 282 (53 UL)Isogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates ; Hale, Jack ; et al in Composite Structures (2014), 118 An effective, simple, robust and locking-free plate formulation is proposed to analyze the static bending, buckling, and free vibration of homogeneous and functionally graded plates. The simple first ... [more ▼] An effective, simple, robust and locking-free plate formulation is proposed to analyze the static bending, buckling, and free vibration of homogeneous and functionally graded plates. The simple first-order shear deformation theory (S-FSDT), which was recently presented in Thai and Choi (2013) [11], is naturally free from shear-locking and captures the physics of the shear-deformation effect present in the original FSDT, whilst also being less computationally expensive due to having fewer unknowns. The S-FSDT requires C1-continuity that is simple to satisfy with the inherent high-order continuity of the non-uniform rational B-spline (NURBS) basis functions, which we use in the framework of isogeometric analysis (IGA). Numerical examples are solved and the results are compared with reference solutions to confirm the accuracy of the proposed method. Furthermore, the effects of boundary conditions, gradient index, and geometric shape on the mechanical response of functionally graded plates are investigated. [less ▲] Detailed reference viewed: 512 (27 UL)Multiscale computational mechanics: industrial applications Bordas, Stéphane ; ; Beex, Lars et al Presentation (2014, November 25) Detailed reference viewed: 199 (8 UL)Cardiff/Luxembourg Computational Mechanics Research Group Bordas, Stéphane ; ; Hale, Jack et al Poster (2014, November) Detailed reference viewed: 194 (7 UL)Discrete Multiscale Modelling and Future Research Plans concerning Metals Beex, Lars ; Bordas, Stéphane ; Rappel, Hussein et al Presentation (2014, October 14) Detailed reference viewed: 157 (11 UL)Discrete Multiscale Modelling and Future Research Plans concerning Metals (presentation) Beex, Lars ; Bordas, Stéphane ; Rappel, Hussein et al Presentation (2014, October 14) Detailed reference viewed: 159 (10 UL)Extension of 2D FEniCS implementation of Cosserat non-local elasticity to the 3D case ; Bordas, Stéphane ; Hale, Jack Report (2014) The objective of the study is the extension of the existing 2D FEniCS implementation of Cosserat elasticity to the 3D case. The first step is the implementation of a patch-test for a simple problem in ... [more ▼] The objective of the study is the extension of the existing 2D FEniCS implementation of Cosserat elasticity to the 3D case. The first step is the implementation of a patch-test for a simple problem in classical elasticity as a Timoshenko's beam - this study will show that DOLFIN could offer approximated solutions converging to the analytical solution. The second step is the computation of the stress in a plate with a circular hole. The stress concentration factors around the hole in classical and Cosserat elasticities will be compared, and a convergence study for the Cosserat case will be realised. The third step is the extension to the 3D case with the computation of the stress concentration factor around a spherical cavity in an infinite elastic medium. This computed value will be compare to the analytical solution described by couple-stress theory. [less ▲] Detailed reference viewed: 300 (7 UL)Meshfree methods for shear-deformable structures based on mixed weak forms Hale, Jack Scientific Conference (2014, July 24) Similarly to the finite element method, meshfree methods must be carefully designed to overcome the shear-locking problem when discretising the shear-deformable structural theories. Many successful ... [more ▼] Similarly to the finite element method, meshfree methods must be carefully designed to overcome the shear-locking problem when discretising the shear-deformable structural theories. Many successful treatments of shear-locking in the finite element literature are constructed through the application of a mixed variational form, where the shear stress is treated as an independent variational quantity in addition to the usual displacements. Because of its sound mathematical underpinnings this is the methodology I have chosen to solve the shear-locking problem when using meshfree basis functions. In this talk I will discuss the mathematical origins of the shear-locking problem and the applicability of the celebrated LBB stability condition for designing well-behaved mixed meshfree approximation schemes. I will show results from two new formulations that demonstrate the effectiveness of this approach. The first method is a meshfree formulation for the Timoshenko beam problem that converges to a classic inf-sup stable finite element method when using Maximum- Entropy basis functions. The second method is a generalised displacement meshfree method for the Reissner- Mindlin problem where the shear stress is eliminated prior to the solution of the linear system using a local patch-projection technique, resulting in a linear system expressed in terms of the original displacement unknowns only. Stability is ensured by using a stabilised weak form which is necessary due to the loss of kernel coercivity for the Reissner-Mindlin problem. [less ▲] Detailed reference viewed: 83 (7 UL)Parallel simulations of soft-tissue using an adaptive quadtree/octree implicit boundary finite element method Hale, Jack ; Bordas, Stéphane ; et al in 11th. World Congress on Computational Mechanics (2014, July 23) Octree (3D) and quadtree (2D) representations of computational geometry are particularly well suited to modelling domains that are defined implicitly, such as those generated by image segmentation ... [more ▼] Octree (3D) and quadtree (2D) representations of computational geometry are particularly well suited to modelling domains that are defined implicitly, such as those generated by image segmentation algorithms applied to medical scans [5]. In this work we consider the simulation of soft-tissue which can be modelled with a incompressible hyperelastic constitutive law. We include the effects of both non-linear geometry and material properties in our model. Similarly to Moumnassi et al. [2] we use the implicitly defined level set functions as the basis for a partition of unity enrichment to more accurately represent the domain boundary on the cartesian quadtree/octree mesh. In addition we introduce arbitrary cuts and discontinuities in the domain using ideas from the classical extended finite element method [3]. Because of its hydrated nature soft-tissue is nearly incompressible [1]. We explore the use of a classical two-field displacement-pressure (u-p) mixed approach to deal with the problem of volumetric-locking in the incompressible limit [4]. We exploit the existing parallel capabilities available in the open-souce finite element toolkit deal.ii [6], including the advanced mesh partitioning and balancing recently introduced in the p4est library [7]. The resulting method scales to run over hundreds of cores on the University of Luxembourg HPC platform. [less ▲] Detailed reference viewed: 500 (26 UL)Meshfree volume-averaged nodal projection methods for incompressible media problems ; Hale, Jack ; Scientific Conference (2014, July 21) Detailed reference viewed: 453 (5 UL)An overview of our research directions in advanced discretisation methods for PDEs Hale, Jack Presentation (2014, July 10) Detailed reference viewed: 56 (1 UL)Stress analysis, damage tolerance assessment and shape optimisation without meshing Hale, Jack ; Bordas, Stéphane ; et al Poster (2014, June 24) Detailed reference viewed: 130 (3 UL)Direct image-analysis methods for surgical simulation and mixed meshfree methods Hale, Jack ; Bordas, Stéphane ; et al Presentation (2014, May 28) Detailed reference viewed: 144 (11 UL)Reducing the Mesh-burden and Computational Expense in Multi-scale Free Boundary Engineering Problems Bordas, Stéphane ; ; Hale, Jack et al Presentation (2014, May 12) We present recent results aiming at affording faster and error-controlled simulations of multi scale phenomena including fracture of heterogeneous materials and cutting of biological tissue. In a second ... [more ▼] We present recent results aiming at affording faster and error-controlled simulations of multi scale phenomena including fracture of heterogeneous materials and cutting of biological tissue. In a second part, we describe methodologies to isolate the user from the burden of mesh generation and regeneration as moving boundaries evolve. Results include advances in implicit boundary finite elements, (enriched) isogeometric boundary elements and extended finite element methods for multi-crack propagation. ABOUT THE PRESENTER In 1999, Stéphane Bordas joined a joint graduate programme of the French Institute of Technology (Ecole Spéciale des Travaux Publics) and the American Northwestern University. In 2003, he graduated in Theoretical and Applied Mechanics with a PhD from Northwestern University. Between 2003 and 2006, he was at the Laboratory of Structural and Continuum Mechanics at the Swiss Federal Institute of Technology in Lausanne, Switzerland. In 2006, he became permanent lecturer at Glasgow University’s Civil Engineering Department. Stéphane joined the Computational Mechanics team at Cardiff University in September 2009, as a Professor in Computational Mechanics and directed the institute of Mechanics and Advanced Materials from October 2010 to November 2013. He is the Editor of the book series “Advances in Applied Mechanics” since July 2013. In November 2013, he joined the University of Luxembourg as a Professor in Computational Mechanics. The main axes of his research team include (1) free boundary problems and problems involving complex geometries, in particular moving boundaries and (2) ‘a posteriori’ discretisation and model error control, rationalisation of the computational expense. Stéphane’s keen interest is to actively participate in innovation, technological transfer as well as software tool generation. This has been done through a number of joint ventures with various industrial partners (Bosch GmbH, Cenaero, inuTech GmbH, Siemens-LMS, Soitec SA) and the release of open-source software. In 2012, Stéphane was awarded an ERC Starting Independent Research Grant (RealTcut), to address the need for surgical simulators with a computational mechanics angle with a focus on the multi-scale simulation of cutting of heterogeneous materials in real-time. [less ▲] Detailed reference viewed: 231 (6 UL) |
||