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

Reduced order methods Schenone, Elisa ; Hale, Jack ; Beex, Lars et al Presentation (2015, April 16) Detailed reference viewed: 242 (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: 267 (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: 488 (27 UL)Multiscale computational mechanics: industrial applications Bordas, Stéphane ; ; Beex, Lars et al Presentation (2014, November 25) Detailed reference viewed: 189 (7 UL)Cardiff/Luxembourg Computational Mechanics Research Group Bordas, Stéphane ; ; Hale, Jack et al Poster (2014, November) Detailed reference viewed: 185 (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: 147 (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: 148 (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: 276 (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: 80 (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: 479 (26 UL)Meshfree volume-averaged nodal projection methods for incompressible media problems ; Hale, Jack ; Scientific Conference (2014, July 21) Detailed reference viewed: 442 (5 UL)An overview of our research directions in advanced discretisation methods for PDEs Hale, Jack Presentation (2014, July 10) Detailed reference viewed: 54 (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: 122 (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: 134 (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: 223 (6 UL)Model and mesh-burden reduction for multiscale fracture: applications to polycrystals, delamination and surgical simulation Bordas, Stéphane ; ; Hale, Jack et al Presentation (2014, April 23) ABSTRACT 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 ... [more ▼] ABSTRACT 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 extended boundary elements/finite element methods for multi-crack propagation and an asynchronous GPU/CPU method for contact and cutting of heterogeneous materials in real-time with applications to surgical simulation. 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: 683 (17 UL)From image to analysis: an extended finite element method to simulate the mechanical response of soft-tissue Hale, Jack ; Bordas, Stéphane ; Presentation (2014, April 10) In this seminar we consider the problem of constructing a numerical method particularly well suited to modelling domains described by segmented image data of the human body. Instead of constructing a ... [more ▼] In this seminar we consider the problem of constructing a numerical method particularly well suited to modelling domains described by segmented image data of the human body. Instead of constructing a conforming mesh of the problem domain, we use implicitly defined domains described using the level-set method. We then include information about the implicitly defined domains by enriching the usual finite element basis functions defined on a cartesian quadtree or octree mesh with hanging nodes. This approach introduces significant complexities compared with classical finite element methods. We will discuss difficulties with the treatment of hanging nodes, numerical integration and imposing Dirichlet boundary conditions. We will discuss the possible future of extensions of this work, including cutting of soft tissue, multiscale problems with complex microstructure, and model order reduction problems. [less ▲] Detailed reference viewed: 170 (8 UL)Meshfree volume-averaged nodal pressure methods for incompressible elasticity Hale, Jack ; ; Scientific Conference (2014, April 03) We present a generalisation of the meshfree method for incompressible elasticity developed in Ortiz et al. (10.1016/j.cma.2010.02.013). We begin with the classical u-p mixed formulation of incompressible ... [more ▼] We present a generalisation of the meshfree method for incompressible elasticity developed in Ortiz et al. (10.1016/j.cma.2010.02.013). We begin with the classical u-p mixed formulation of incompressible elasticity before eliminating the pressure using a volume-averaged nodal projection technique. This results in a family of projection methods of the type Q_p/Q_p-1 where Q_p is an approximation space of polynomial order p. These methods are particularly robust on low-quality tetrahedral meshes. Our framework is generic with respects to the type meshfree basis function used and includes various types of existing finite element methods such as B-bar and nodal-pressure techniques. As a particular example, we use maximum-entropy basis functions to build a scheme Q_1+/Q_1 with the displacement field being enriched with bubble-like functions for stability. The flexibility of the nodal placement in meshfree methods allows us to demonstrate the importance of this bubble-like enrichment for stability; with no bubbles the pressure field is liable to oscillations, whilst with bubbles the oscillation is eliminated. Interestingly however with half the bubbles removed, a scheme we call Q_1*/_Q_1, certain undesirable tendencies of the full bubble scheme are also eliminated. This has important applications in non-linear hyperelasticity. We also discuss some difficulties associated with moving to second-order maximum entropy shape functions associated with numerical integration errors. [less ▲] Detailed reference viewed: 94 (8 UL)An enriched quadtree/octree implicit boundary finite element method for the simulation of incompressible hyperelastic materials Hale, Jack ; Bordas, Stéphane ; et al Scientific Conference (2014, April 03) Octree (and quadtree) representations of computational geometry are particularly well suited to modelling domains that are defined implicitly, such as those generated by image segmentation algorithms ... [more ▼] Octree (and quadtree) 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. In this work we consider the simulation of soft-tissue which can be modelled with a hyperelastic constitutive law. We include the effects of both non-linear geometry and material properties. Similarly to Legrain et al. (10.1002/nme.3070) and Moumnassi et al. (10.1016/j.cma.2010.10.002) we use the implicitly designed level set functions as the basis for a partition of unity enrichment to more accurately represent the domain boundary. Furthermore we use traditional extended finite element (XFEM) ideas to introduce arbitrary cuts and discontinuities in the domain. We explore the use of a two-field u-p mixed approach as well as a smoothed finite element method (SFEM) to deal with the problem of volumetric-locking in the incompressible limit. We will discuss the extension of our method towards both traditional parallel and GPU implementation. We aim to solve extremely large problems as well as produce snapshots to feed into model order reduction methods for real-time surgical simulations. [less ▲] Detailed reference viewed: 415 (26 UL)Meshless Methods for the Reissner-Mindlin Plate Problem based on Mixed Variational Forms Hale, Jack Presentation (2013, October 31) Meshless numerical methods such as the element free Galerkin (EFG) method and $hp$-clouds method rely on a field of particles to construct a basis for the solution of partial differential equations (PDEs ... [more ▼] Meshless numerical methods such as the element free Galerkin (EFG) method and $hp$-clouds method rely on a field of particles to construct a basis for the solution of partial differential equations (PDEs). This is in contrast with methods such as the finite element method (FEM) and finite difference method (FDM) which rely upon a mesh or grid. Because of this increased flexibility, meshfree methods have shown themselves to be effective tools for simulating difficult problems such as those with discontinuities, complex geometries and large deformations. The Reissner-Mindlin problem is widely used by engineers to describe the deformation of a plate including the effects of transverse shear. A well-known problem which must be overcome when designing an effective numerical method for the Reissner-Mindlin problem is shear-locking. Shear-locking is the inability of the constructed approximation space (meshless or otherwise) to richly represent the limiting Kirchhoff mode. This inability manifests itself as an entirely incorrect solution as the thickness of the plate approaches zero. We will demonstrate and explain the shear-locking problem and potential solutions to it using a simple one-dimensional example. The most effective, robust and general approaches to the shear-locking problem developed in the FEM literature are based on mixed variational forms, where a combination of displacements, stresses and strains are approximated directly. In our approach we start with a mixed variational form before eliminating the extra stress unknowns using the local patch projection technique of A Ortiz et. al. We will discuss the issues presented by the well-known LBB stability conditions and present a solution based upon the stabilising properties of both the augmented Lagrangian and additional `bubble' type functions. We will then show the good performance of the method and its shear-locking free properties. [less ▲] Detailed reference viewed: 79 (7 UL) |
||