A global model reduction approach for 3D fatigue crack growth with confined plasticity

Galland, Florent; Gravouil, Anthony; Malvesin, E.; Rochette, Michel

doi:10.1016/j.cma.2010.08.018

Cited by 39 publications

(40 citation statements)

References 48 publications

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“…Kerfriden et al [55,56], Galland et al [57], and Kerfriden et al [58]. It would be particularly interesting to investigate these model reduction techniques coupled with domain decomposition, so as to be able to reduce subdomains where non-linearities are weak and revert to full solutions of non-reducible subdomains, where non-linearities are too strong.…”

Section: Future Work Includesmentioning

confidence: 99%

Molecular Dynamics/Xfem Coupling by a Three-Dimensional Extended Bridging Domain With Applications to Dynamic Brittle Fracture

Talebi

Silani

Bordas

et al. 2013

Int J Mult Comp Eng

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We propose a method to couple a three-dimensional continuum domain to a molecular dynamics (MD) domain to simulate propagating cracks in dynamics. The continuum domain is treated by an extended finite element method, to handle the discontinuities. The coupling is based on the Bridging Domain Method (BDM) which blends the continuum and atomistic energies. The Lennard-Jones potential is used to model the interactions in the atomistic domain and the Cauchy-Born rule is used to compute the material behaviour in the continuum domain. To our knowledge, it is the first time that a three dimensional extended bridging domain method is reported. To show the suitability of the proposed method, a three-dimensional crack problem with an atomistic region around the crack front is solved.The results show that the method is capable of handling crack propagation and dislocation nucleation.

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Section: Future Work Includesmentioning

confidence: 99%

Molecular Dynamics/Xfem Coupling by a Three-Dimensional Extended Bridging Domain With Applications to Dynamic Brittle Fracture

Talebi

Silani

Bordas

et al. 2013

Int J Mult Comp Eng

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“…Consequently, each and every load angle leads to a different damage pattern which cannot be well represented by a linear combination of the cracks obtained for a limited number of snapshot solutions ( figure 4, bottom). In fact, the solution to parametric problems involving the evolution of topological changes cannot, in general, be obtained efficiently using a method based on the separation of variables (unless one manages to map the physical space to a reference space were correlation in the data can be retrieved [26]). One systematic way to circumvent the problem would be to enrich the snapshot "online" [25,56], but this leads to difficulties related to the cost of evaluating the projection error.…”

Section: Parametrised Problem Of Fracture-mentioning

confidence: 99%

“…Europe PMC Funders Author Manuscripts (25) or in the (Petrov-) Galerkin framework (26) The strategies proposed in the literature for this two subset of techniques differ in the way of building operator , which requires a critical trade-off between optimality, stability and tractability. In [34], is constructed such that the condition number of operator is minimised.…”

Section: Europe Pmc Funders Author Manuscriptsmentioning

confidence: 99%

“…The theory and applicability of various projection-based model order reduction methods such as component mode synthesis [13,7], the reduced basis method [14,15,16], the proper orthogonal decomposition [17,18,2] which will be used in this work, the a priori hyperreduction method [19,20] or the proper generalised decomposition [21,22,23] are now well-established in the linear to mildly nonlinear cases. Some attempts have been proposed to extend this concept to strong nonlinearities, in particular in structural mechanics [24,19,25,26]. This background makes it conceivable to use such methods in complex engineering problems such as fracture mechanics.…”

Section: Introductionmentioning

confidence: 99%

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A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics

Kerfriden

Goury

Rabczuk

et al. 2013

Computer Methods in Applied Mechanics and Engineering

117

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We propose in this paper a reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projectionbased model order reduction permits to focus the numerical effort where it is most needed: around the zones where damage propagates. No a priori knowledge of the damage pattern is required, the extraction of the corresponding spatial regions being based solely on algebra. The efficiency of the proposed approach is demonstrated numerically with an example relevant to engineering fracture.

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“…Thanks to progresses in computer technologies, resolution of problems involving millions of unknowns has become ordinary in engineering applications [17]. And such simulations should be performed as many times as possible in optimization contexts.…”

Section: Introductionmentioning

confidence: 99%

Space–time proper generalized decompositions for the resolution of transient elastodynamic models

Boucinha¹,

Gravouil²,

Ammar³

2013

Computer Methods in Applied Mechanics and Engineering

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. In this paper, we investigate ability of proper generalized decomposition (PGD) to solve transient elastodynamic models in space-time domain. Classical methods use time integration schemes and an incremental resolution process. We propose here to use standard time integration methods in a nonincremental strategy. As a result, PGD gives a separated representation of the space-time solution as a sum of tensorial products of space and time vectors, that we interpret as space-time modes. Recent time integration schemes are based on multi-field formulations. In this case, separated representation can be constructed using state vectors in space and same vectors in time. However, we have experienced bad convergence order using this decomposition. Furthermore, temporal approximation must be the same for all fields. Thus, we propose an extension of classical separated representation for multi-field problems. This multi-field PGD (MF-PGD) uses space and time vectors that are different for each field. Calculation of decomposition is done using a monolithic approach in space and time, potentially allowing the use of different approximations in space and time. Finally, several simulations are performed with the transient elastodynamic problem with one dimension in space. Different approximations in time are investigated: Newmark scheme, single field time discontinuous Galerkin method and two fields time continuous and discontinuous Galerkin methods.

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A global model reduction approach for 3D fatigue crack growth with confined plasticity

Cited by 39 publications

References 48 publications

Molecular Dynamics/Xfem Coupling by a Three-Dimensional Extended Bridging Domain With Applications to Dynamic Brittle Fracture

Molecular Dynamics/Xfem Coupling by a Three-Dimensional Extended Bridging Domain With Applications to Dynamic Brittle Fracture

A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics

Space–time proper generalized decompositions for the resolution of transient elastodynamic models

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