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Multiscale fracture: a natural connection between reduced order models and homogenisation Bordas, Stéphane ; Beex, Lars ; Chen, Li et al Scientific Conference (2019, May 13) Detailed reference viewed: 101 (9 UL)Multi-scale modelling of fracture Bordas, Stéphane ; ; et al Speeches/Talks (2016) We present recent models on complexity reduction for computational fracture mechanics Detailed reference viewed: 169 (7 UL)Simulating topological changes in real time for surgical assistance Bordas, Stéphane ; ; et al Speeches/Talks (2016) Detailed reference viewed: 421 (38 UL)Automatised selection of load paths to construct reduced-order models in computational damage micromechanics: from dissipation-driven random selection to Bayesian optimization ; ; Bordas, Stéphane et al in Computational Mechanics (2016) In this paper, we present new reliable model order reduction strategies for computational micromechanics. The difficulties rely mainly upon the high dimensionality of the parameter space represented by ... [more ▼] In this paper, we present new reliable model order reduction strategies for computational micromechanics. The difficulties rely mainly upon the high dimensionality of the parameter space represented by any load path applied onto the representative volume element. We take special care of the challenge of selecting an exhaustive snapshot set. This is treated by first using a random sampling of energy dissipating load paths and then in a more advanced way using Bayesian optimization associated with an interlocked division of the parameter space. Results show that we can insure the selection of an exhaustive snapshot set from which a reliable reduced-order model can be built. [less ▲] Detailed reference viewed: 306 (32 UL)Multi-scale methods for fracture: model learning across scales, digital twinning and factors of safety
: primer on Bayesian Inference Bordas, Stéphane ; Hale, Jack ; Beex, Lars et al Speeches/Talks (2015) Fracture and material instabilities originate at spatial scales much smaller than that of the structure of interest: delamination, debonding, fibre break- age, cell-wall buckling, are examples of nano ... [more ▼] Fracture and material instabilities originate at spatial scales much smaller than that of the structure of interest: delamination, debonding, fibre break- age, cell-wall buckling, are examples of nano/micro or meso-scale mechanisms which can lead to global failure of the material and structure. Such mech- anisms cannot, for computational and practical reasons, be accounted at structural scale, so that acceleration methods are necessary. We review in this presentation recently proposed approaches to reduce the computational expense associated with multi-scale modelling of frac- ture. In light of two particular examples, we show connections between algebraic reduction (model order reduction and quasi-continuum methods) and homogenisation-based reduction. We open the discussion towards suitable approaches for machine-learning and Bayesian statistical based multi-scale model selection. Such approaches could fuel a digital-twin concept enabling models to learn from real-time data acquired during the life of the structure, accounting for “real” environmental conditions during predictions, and, eventually, moving beyond the era of factors of safety. [less ▲] Detailed reference viewed: 137 (4 UL)Adaptive methods for multiscale fracture Bordas, Stéphane ; ; et al in International Journal of Engineering Science (2015, January 01) Adaptive methods for multiscale fracture In this work, we discuss two classes of methods to reduce the complexity of (multi scale) fracture simulations. In a first part, we discuss algebraic model ... [more ▼] Adaptive methods for multiscale fracture In this work, we discuss two classes of methods to reduce the complexity of (multi scale) fracture simulations. In a first part, we discuss algebraic model reduction. We show that algebraic model reduction such as the proper orthogonal decomposition cannot be used directly because of the lack of corelation introduced by the damage or cracks. We demonstrate the use of proper orthogonal decompositions by subdomains as a candidate to reduce computational expenses in non-linear fracture simulations whilst controlling the error level. We then consider algebraic model reduction, namely the proper orthogonal decomposition(POD) to drastically reduce the computational time associated with computing the response of representative volume elements (RVEs) used in homogenization, e.g. by the FE2 method. The snapshots are obtained by solving the RVE boundary value problem for various loading paths. To speed-up the computations, system approximation through the discrete empirical interpolation (DEIM) is used and allows the evaluation of the internal forces for only a small subset of the elements making the RVE structure. In a second part, we propose an adaptive hybrid multiscale method for modelling fracture in a heterogeneous material that is composed of orthotropic grains with cohesive interfaces between the grains. Instead of a direct solver, FE2 method [1] based on homogenisation is employed in order to compute the effective behaviour of the heterogeneous microscopic material on the coarser scale. At this scale the modelling error due to the homogenisation is still low [3]. The coarse scale is discretized with unstructured triangular finite elements, and adaptive mesh refinement is used to control the discretizsation error. While the mesh refinement keeps the discretisation error with in a certain range, the modelling error increases due to the fact that by refining the coarse elements, the scale separation assumption which is a key issue for homogenisation may no longer be fulfilled [4]. Whereas the modelling error is inversely proportional to the size of the coarse elements, a critical element size can be found that corresponds to the critical value of the modelling error. A critical zone emerges when the size of a coarse element reaches the critical size, or if the underlying representative volume element of the microstructure loses stability due to localisation (lack of scale separation). Thereafter, a zoom-in process is triggered that replaces the corresponding coarse elements of the critical zone with high resolution microscale mesh to which it glues the coarse scale mesh through a strong coupling technique using Lagrange multipliers [5]. The high resolution region can gradually be extended to include the newly emerging critical zones. A local arc-length technique is adopted to trace the highly non-linear curve of the global load-displacement by controlling the opening of microscopic cohesive cracks in the fully resolved regions. The proposed adaptive multiscale method allows us to introduce progressive discrete micro cracks at the macroscale. The unstructured mesh enables us to model problems with non-regular shapes, and the arc-length method, defined over multiple scales, allows the regularisation of softening problems that are treated in quasi-statics. We exercise this method on the simulation of polycrystalline fracture, where each grain is considered orthotropic and compare results to direct numerical simulation. [less ▲] Detailed reference viewed: 630 (22 UL)A model order reduction technique for speeding up computational homogenisation ; ; et al Scientific Conference (2014, July 24) Detailed reference viewed: 257 (5 UL)A model order reduction approach to construct efficient and reliable virtual charts in computational homogenisation ; ; et al in Proceedings of the 17th U.S. National Congress on Theoretical and Applied Mechanics (2014, June 15) Computational homogenisation is a widely spread technique to calculate the overall properties of a composite material from the knowledge of the constitutive laws of its microscopic constituents [1, 2 ... [more ▼] Computational homogenisation is a widely spread technique to calculate the overall properties of a composite material from the knowledge of the constitutive laws of its microscopic constituents [1, 2]. Indeed, it relies on fewer assumptions than analytical or semi-analytical homogenisation approaches and can be used to coarse-grain a large range of micro-mechanical models. However, this accuracy comes at large computational costs, which prevents computational homogenisation from being used routinely in optimisation, even in the context of linear elastic materials. Indeed, a unit cell problem has to be solved for each microscopic distribution of interest in order to obtain the corresponding homogenised material constants. In the context of nonlinear, time-dependant problem, the computational effort becomes even greater as computational homogenisation requires solving for the time-evolution of the microstructure at every point of the macroscopic domain. In this paper, we propose to address these two issues within the unified framework of projection-based model order reduction (see for instance [3, 4, 5, 6]). The smoothness of the solution of the unit cell problem with respect to parameter or time variations is used to create a reduced order model with very few degrees of freedom, hence reducing the computational burden by orders of magnitude. [1] Tarek J. Zohdi and Peter Wriggers. Introduction to Computational Micromechanics, volume 20 of lecture notes in applied and computational mechanics. Springer, 2005. [2] M.G.D. Geers, V.G. Kouznetsova, and W.A.M. Brekelmans. Multi-scale computational homogenization: Trends and challenges. J. Computational Applied Mathematics, 234(7):2175–2182, 2010. [3] D.B.P. Huynh G. Rozza and A.T. Patera. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations: Application to transport and continuum mechanics. Archives of Computational Methods in Engineering, 15(3):229–275, 2008. [4] D. Amsallem and C. Farhat. An Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity. AIAA Journal, 46(7):1803–1813, 2008. [5] P. Kerfriden, P. Gosselet, S. Adhikari, and S.P.-A. Bordas. Bridging proper orthogonal decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems. Computer Methods in Applied Mechanics and Engineering, 200(5- 8):850–866, 2011. [6] P. Kerfriden, J.-C. Passieux, and S.P.-A. Bordas. Local/global model order reduction strategy for the simulation of quasi-brittle fracture. International Journal for Numerical Methods in Engineering, 89(2):154–179, 2011. [7] M. Barrault, Y. Maday, N.C. Nguyen, and A.T. Patera. An ’empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations. Comptes Rendus de Math´ematiques, 339(9):667–672, 2004. [less ▲] Detailed reference viewed: 322 (6 UL)Reduced order modelling: towards tractable computational homogenisation schemes ; ; 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 ▲] Detailed reference viewed: 200 (7 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: 195 (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: 648 (17 UL)Model order reduction for speeding up computational homogenisation methods of type FE2 ; ; Bordas, Stéphane Presentation (2014) Detailed reference viewed: 103 (2 UL)A multiscale partitioned reduced order model applied to damage simulation ; ; Bordas, Stéphane Scientific Conference (2013, July) Simulating fracture in realistic engineering components is computationally expensive. In the context of early-stage design, or reverse engineering, such simulations might need to be performed for a large ... [more ▼] Simulating fracture in realistic engineering components is computationally expensive. In the context of early-stage design, or reverse engineering, such simulations might need to be performed for a large range of material and geometric parameters, which makes the solution to the parametric problem of fracture unaffordable. Model order reduction, such as the proper orthogonal decomposition (POD), is one way to reduce significantly the computational time by reducing the number of spatial unknowns. The solution is searched for in a reduced space spanned by a few well-chosen basis vectors only. In the context of solid mechanics involving structural softening, the strong topological changes in the zone where damage localises are extremely sensitive to variations of the parameters, which requires reduced spaces of prohibitively large dimensions in order to approximate the solution with a sufficiently high degree of accuracy. Introduced in [1], partitioned model order reduction is an alternative to global model order reduction that essentially divides up the problem into smaller regions. Each region can then be tackled using a reduced model of appropriate size, if at all, depending on the local material non-linearities in the region. In the context of multiscale homogenization, simulations of representative volume elements (RVE) have to be performed to obtain the material properties in the different elements of a coarse mesh. When considering a nonlinear material, those multiple RVE simulations can be com- putationally very expensive. They however only differ by the history of boundary conditions applied. This contribution proposes to apply partitioned model order reduction to those RVEs with reduced bases parametrized by the boundary conditions. REFERENCES [1] P. Kerfriden, O. Goury, T. Rabczuk, S. Bordas, A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics, Computer Methods in Applied Mechanics and Engineering, 256:169–188, 2013. [less ▲] Detailed reference viewed: 290 (5 UL)Dealing with interfaces in partitioned model order reduction for application to nonlinear problems ; ; Bordas, Stéphane Scientific Conference (2013) We propose a reduced order modelling technique based on a partitioning of the domain of study in the context of para- metric nonlinear problems. A formulation of the reduction of the displacement and of ... [more ▼] We propose a reduced order modelling technique based on a partitioning of the domain of study in the context of para- metric nonlinear problems. A formulation of the reduction of the displacement and of the interface tractions linking subdomains to each others will be performed in a FETI context. [less ▲] Detailed reference viewed: 282 (4 UL)Addressing lack of scale separation in fracture simulations ; ; et al Scientific Conference (2012, July) Detailed reference viewed: 293 (4 UL)ALGEBRAIC COARSE-GRAINING METHODS IN FRACTURE MECHANICS: TACKLING LOCAL LACK OF CORRELATION USING DOMAIN DECOMPOSITION ; ; et al Scientific Conference (2012, March) In this paper, we propose to couple model order reduction techniques with domain decomposition meth- ods for the solution to parametric problems of fracture. The nonlinear nature of the problems requires ... [more ▼] In this paper, we propose to couple model order reduction techniques with domain decomposition meth- ods for the solution to parametric problems of fracture. The nonlinear nature of the problems requires the use of a system approximation method to speed-up the assembly of the non-linear opreators. We show that the method efficiently computes a solution faster than a full order model for a given accuracy. The speed-up increases with the problem size. [less ▲] Detailed reference viewed: 218 (1 UL)Rationalised computational time in fracture simulation: adaptive model reduction and domain decomposition ; ; et al Scientific Conference (2011, June) Detailed reference viewed: 79 (1 UL) |
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