Multi-scale modelling of fracture

Speeches/Talks (2016)

We present recent models on complexity reduction for computational fracture mechanics

Automatised selection of load paths to construct reduced-order models in computational damage micromechanics: from dissipation-driven random selection to Bayesian optimization

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 ▲]

Adaptive methods for multiscale fracture

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 ▲]

A model order reduction approach to construct efficient and reliable virtual charts in computational homogenisation

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 ▲]

Reducing the Mesh-burden and Computational Expense in Multi-scale Free Boundary Engineering Problems

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 ▲]

Model order reduction for speeding up computational homogenisation methods of type FE2

Presentation (2014)

Dealing with interfaces in partitioned model order reduction for application to nonlinear problems

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 ▲]

ALGEBRAIC COARSE-GRAINING METHODS IN FRACTURE MECHANICS: TACKLING LOCAL LACK OF CORRELATION USING DOMAIN DECOMPOSITION

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 ▲]