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See detailA two-dimensional isogeometric boundary element method for linear elastic fracture
Peng, Xuan; Atroshchenko, Elena; Kulasegaram, Sivakumar et al

Report (2014)

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See detailDamage tolerance assessment directly from CAD: (extended) isogeometric boundary element methods
Peng, Xuan; Atroshchenko, Elena; Bordas, Stéphane UL

Scientific Conference (2014, June)

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See detailDirect image-analysis methods for surgical simulation and mixed meshfree methods
Hale, Jack UL; Bordas, Stéphane UL; Kerfriden, Pierre et al

Presentation (2014, May 28)

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See detailA hybrid T-Trefftz polygonal finite element for linear elasticity
Bhattacharjee, Kalyan; Natarajan, Sundararajan; Bordas, Stéphane UL

E-print/Working paper (2014)

In this paper, we construct hybrid T-Trefftz polygonal finite elements. The displacement field within the polygon is repre- sented by the homogeneous solution to the governing differential equation, also ... [more ▼]

In this paper, we construct hybrid T-Trefftz polygonal finite elements. The displacement field within the polygon is repre- sented by the homogeneous solution to the governing differential equation, also called as the T-complete set. On the boundary of the polygon, a conforming displacement field is independently defined to enforce continuity of the displacements across the element boundary. An optimal number of T-complete functions are chosen based on the number of nodes of the polygon and degrees of freedom per node. The stiffness matrix is computed by the hybrid formulation with auxiliary displacement frame. Results from the numerical studies presented for a few benchmark problems in the context of linear elasticity shows that the proposed method yield highly accurate results. [less ▲]

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See detailReduced order modelling: towards tractable computational homogenisation schemes
Kerfriden, Pierre; Goury, Olivier; Akbari, Ahmad et al

Presentation (2014, May 15)

Towards rationalised computational expense for simulating fracture over multiple scales The project focuses on the numerical simulation of the failure of complex, heterogeneous structures. The simulation ... [more ▼]

Towards rationalised computational expense for simulating fracture over multiple scales The project focuses on the numerical simulation of the failure of complex, heterogeneous structures. The simulation of such physical phenomena is of particular interest to practitioners as it enables to limit the number of destructive tests required to design and assess structures, and, ultimately, to decrease the safety factors used in design. In such heterogeneous media, the description of crack or damage initiation and propagation must be done at the scale of the inhomogeneities (e.g. aggregates in a concrete structure) in order for the results to be predictive. If one uses such a fine-scale material model to simulate structures at an engineering scale (e.g. an aircraft composite panel or a concrete beam), very large numerical problems need to be solved. In addition, there is a strong need for engineers to run their models numerous times, for different sets of the design parameters (e.g. loading conditions, geometry or material properties). Tackling such parametric multiscale problems is prohibitively expensive when using brute force parallel computing. However, one can use the fact that solutions to parametric problems usually evolve in a relatively coarse space: solutions to nearby parameter sets are usually close in a certain sense. This idea is classically used in Model Order Reduction, which proposes to reduce the size of the initial problem by several order of magnitude by simply reusing the information generated when solving the initial problem for several different sets of parameters. However, in the case of fracture, the information provided by the initial problem is most of the time insufficient to describe the behaviour of the system for arbitrary parameters. Crack paths, defects, and subsequent ultimate strengths are strongly influenced by an even slight variation in the parameter set. Fortunately, we showed in our previous research that this characteristic only affects a local region surrounding the structural defects, whilst the behaviour far from these regions is remains relatively unchanged for a wide range of parameter values. The proposed project will make use of this observation in a generic way, by coupling Reduced Order Modeling and Domain Decomposition. The structure will be divided in smaller subcomponents, on which Reduced Order Modeling will be applied separately. The consequence will be that the computational efforts will be greatly decreased in the regions that are far away from the damaged zone. Within the process zone itself, the substructuring framework will allow us to automatically switch to classical direct solvers. In this sense, the research aims at rationalising the computational costs associated to the simulation of parametrised multiscale fracture simulations, by concentrating the numerical effort where it is most required and with minimal intervention of the user. [less ▲]

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See detailReducing the Mesh-burden and Computational Expense in Multi-scale Free Boundary Engineering Problems
Bordas, Stéphane UL; Kerfriden, Pierre; Hale, Jack UL 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 ▲]

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See detailModel and mesh-burden reduction for multiscale fracture: applications to polycrystals, delamination and surgical simulation
Bordas, Stéphane UL; Kerfriden, Pierre; Hale, Jack UL 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 ▲]

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See detailAdaptive methods for multiscale fracture and surgical simulation

Bordas, Stéphane UL

Presentation (2014, April 11)

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See detailFrom image to analysis: an extended finite element method to simulate the mechanical response of soft-tissue
Hale, Jack UL; Bordas, Stéphane UL; Kerfriden, Pierre

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 ▲]

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See detailMultiscale simulations of fracture, mesh burden reduction with applications to surgical simulation
Bordas, Stéphane UL

Presentation (2014, April 10)

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 ▲]

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See detailAn enriched quadtree/octree implicit boundary finite element method for the simulation of incompressible hyperelastic materials
Hale, Jack UL; Bordas, Stéphane UL; Kerfriden, Pierre 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 ▲]

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See detailGlobal energy minimization for multi-crack growth in linear elastic fracture using the extended finite element method
Bordas, Stéphane UL

Scientific Conference (2014, April 02)

We investigate multiple fracture evolution under quasi-static conditions in an isotropic linear elastic solid based on the principle of minimum potential elastic energy in the framework of the extended ... [more ▼]

We investigate multiple fracture evolution under quasi-static conditions in an isotropic linear elastic solid based on the principle of minimum potential elastic energy in the framework of the extended finite element method. The technique enables a minimization of the potential energy with respect to all crack increment directions. Results show that the maximum hoop stress criterion and the energy minimization approach converge to the same fracture path. It is found that the converged solution lies in between the fracture paths obtained by each criterion for coarser meshes. This presents an opportunity to estimate an upper and lower bound of the true fracture path as well as an error on the crack path [less ▲]

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See detailSummation rules for higher order Quasi-continuum methods
Heaney, Claire; Beex, Lars; Bordas, Stéphane UL et al

Presentation (2014, April)

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See detailmatlab code of 2D nurbs-based IGABEM shape optimisation
Lian, Haojie; Bordas, Stéphane UL

Learning material (2014)

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See detailDiscretisation, Multiscale Fracture Mechanics Problems, Cutting & Surgical Simulation: extended finite element method, meshfree methods and isogeometric analysis
Bordas, Stéphane UL

Speeches/Talks (2014)

MATERIALS & SURFACE SCIENCE INSTITUTE PRESENTATION BY Professor Stéphane P. A. Bordas University of Luxembourg and Cardiff University PRESENTATION TITLE Cutting in Real-time in Co-rotational Elasticity ... [more ▼]

MATERIALS & SURFACE SCIENCE INSTITUTE PRESENTATION BY Professor Stéphane P. A. Bordas University of Luxembourg and Cardiff University PRESENTATION TITLE Cutting in Real-time in Co-rotational Elasticity and Perspectives on Simulating Cuts ABSTRACT We focus on the simulation of surgical acts of types similar to cutting and needle insertion in soft tissue, in real time (500Hz), where the scale of the surgical instrument is several orders of magnitude smaller than that of the organ. We provide review of the state of the art and make propositions to address some of the main difficulties in this area: complex geometries - implicit boundaries, XFEM, meshless, advanced meshing; multiple scales (large gradients) - domain decomposition and model reduction; error control and adaptivity; parallel implementation Graphical Processing Units (GPUs). We then describe a series of contributions in the field of real-time simulation of soft tissue biomechanics. These contributions address various requirements for interactive simulation of complex surgical procedures. In particular, we present results in the areas of soft tissue deformation, contact modelling, simulation of cutting, and haptic rendering, which are all relevant to a variety of medical interventions. The contributions we describe share a common underlying model of deformation and rely on GPU implementations to significantly reduce computational expense. Since the commencement of the ERC RealTcut Starting Research Grant, we have made a number of advances, in particular in the area of real-time simulation of cutting. We have started implementing a novel cutting algorithm and investigating co-rotational elasticity to non-linear materials. We have shown that it is possible to cut non-linear solids formulated within a co-rotational formalism in real-time with a tetrahedron subdivision method and a Sherman-Morrison update. The next steps include assessing the error associated with the single Newton iteration, extending to non-linear materials, and investigating the improvements enabled by enriched approximations. These results will form the basis of the real-time work. 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. He has been collaborating with over 110 academic partners over the last 10 years. 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. DATE: Monday, 10 February 2014 TIME: 15h30 VENUE: MSB-012 MSSI Building REFRESHMENTS WILL BE PROVIDED AT 15h15 For further information, please contact: Professor Michael McCarthy, Tel. No: (061) 202222 or Email: michael.mccarthy@ul.ie [less ▲]

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See detailCertification of projection-based reduced order modelling in computational homogenisation by the Constitutive Relation Error
Kerfriden, Pierre; Ródenas, Juan-José; Bordas, Stéphane UL

in International Journal for Numerical Methods in Engineering (2014), 97(6), 395-422

In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction ... [more ▼]

In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction of a reduced model for the stress field. Upon ensuring that the reduced stress satisfies the equilibrium in the nite element sense, the desired bounding property is obtained. The lower bound is obtained by defining a hierarchical enriched reduced model for the displacement. We show that the sharpness of both error estimates can be seamlessly controlled by adapting the parameters of the corresponding reduced order model. [less ▲]

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See detailMeshless Elasticity Model and Contact Mechanics-based Verification Technique
Aras, Rifat; Shen, Yuzhong; Audette, Michel et al

in MICCAI Computational Biomechanics for Medicine (2014, January 01)

Mesh-based techniques are well studied and established methods for solving continuum biomechanics problems. When the problem at hand involves extreme deformations or artificial discontinuities, meshless ... [more ▼]

Mesh-based techniques are well studied and established methods for solving continuum biomechanics problems. When the problem at hand involves extreme deformations or artificial discontinuities, meshless methods provide sev-eral advantages over the mesh-based methods. This work discusses the Moving Least Square approximation-based meshless collocation method for simulating de-formable objects and presents a verification technique that is based on the Hertzian theory of non-adhesive elastic contact. The effectiveness of the Hertzian contact theory as a means for verification was first tested and proven through a well-established FEM code, FEBio. The meshless method was implemented as a reusable component for the SOFA framework, an open source software library for real-time simulations. Through experimentation, the Hertzian theory has been tested against SOFA hexahedral FEM and the meshless models within the SOFA framework. Convergence studies and L2 error curves are provided for both mod-els. Experimental results demonstrated the effectiveness of the implementation of the meshless method. [less ▲]

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