FETI-based algorithms for modelling of fibrous composite materials with debonding

Dostál, Zdeněk; Horák, David; Vlach, Oldřich

doi:10.1016/j.matcom.2007.01.026

Cited by 4 publications

(5 citation statements)

References 18 publications

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“…Actually, in this case, the interface solution is seeked at the local stage in a truncated space Γ Γ Γ, the solutions in the softening part of the local cohesive behaviour being unreachable. Figure (8) illustrates schematically this idea. The constitutive law of a cohesive interface and the search direction equation E + are projected on the normal direction to the interface, at a given integration point.…”

Section: Search Direction E +mentioning

confidence: 99%

“…Thus, the enrichment-based strategy might be difficult to use. Instead, we wish to use the second family of solvers for large numerical problems, which consists in computing the exact mesosolution everywhere in the process zones, using parallel iterative solvers [9,22,17,14,12,8]. Coupling the solution with a reduced model such as a plate model [31,4] will be the subject of further work, and is not dealt with in this paper.…”

Section: Introductionmentioning

confidence: 99%

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A three-scale domain decomposition method for the 3D analysis of debonding in laminates

2009

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The prediction of the quasi-static response of industrial laminate structures requires to use fine descriptions of the material, especially when debonding is involved. Even when modeled at the mesoscale, the computation of these structures results in very large numerical problems. In this paper, the exact mesoscale solution is sought using parallel iterative solvers. The LaTIn-based mixed domain decomposition method makes it very easy to handle the complex description of the structure; moreover the provided multiscale features enable us to deal with numerical difficulties at their natural scale; we present the various enhancements we developed to ensure the scalability of the method. An extension of the method designed to handle instabilities is also presented.

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Section: Search Direction E +mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A three-scale domain decomposition method for the 3D analysis of debonding in laminates

2009

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“…Next, in the correction step, the trial tractions are transformed into a physically admissible value using an interfacial constitutive law and the loop is repeated until convergence is achieved. It is fair to mention that, when compared to more sophisticated techniques based on quadratic programming [10,11,41], the current technique is definitely less robust due to the missing convergence theory. The definite advantage of the algorithm, on the other hand, is its simplicity; as illustrated in the sequel, the implementation systematically employs a standard FETI solver for linear elasticity, see e.g.…”

Section: Feti-based Solution To Unit Cell Problemmentioning

confidence: 99%

“…In this contribution, we present an alternative numerical approach to the numerical homogenization of debonding composites, which circumvents the previously mentioned obstacles. The method itself builds on the Finite Element Tearing and Interconnecting (FETI) solver due to Farhat and Roux [13] and adopts recent ideas in duality-based solvers [11,23,41] to the computational homogenization setting. The added value of the duality-and FETI-based framework can be summarized as follows:…”

Section: Introductionmentioning

confidence: 99%

Homogenization of composites with interfacial debonding using duality-based solver and micromechanics

Gruber,

Zeman,

Kruis

et al. 2009

Preprint

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One of the key aspects governing the mechanical performance of composite materials is debonding: the local separation of reinforcing constituents from matrix when the interfacial strength is exceeded. In this contribution, two strategies to estimate the overall response of particulate composites with rigid-brittle interfaces are investigated. The first approach is based on a detailed numerical representation of a composite microstructure. The resulting problem is discretized using the Finite Element Tearing and Interconnecting method, which, apart from computational efficiency, allows for an accurate representation of interfacial tractions as well as mutual inter-phase contact conditions. The candidate solver employs the assumption of uniform fields within the composite estimated using the Mori-Tanaka method. A set of representative numerical examples is presented to assess the added value of the detailed numerical model over the simplified micromechanics approach.

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“…These methods have been developed initially for large linear problems for which they can now be considered mature. The most well-known methods are FETI [18] and BDD [41] which where designed for perfect interface and extended, in the case of FETI, to contact (with or without friction) [16] or prescribed displacement gaps [32]. FETI and BDD rely on a static condensation for each sub-domain.…”

Section: Introductionmentioning

confidence: 99%

Virtual Delamination Testing through Non-Linear Multi-Scale Computational Methods: Some Recent Progress

Allix,

Gosselet,

Kerfriden

et al. 2013

Preprint

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This paper deals with the parallel simulation of delamination problems at the mesoscale by means of multi-scale methods, the aim being the Virtual Delamination Testing of Composite parts. In the non-linear context, Domain Decomposition Methods are mainly used as a solver for the tangent problem to be solved at each iteration of a Newton-Raphson algorithm. In case of strongly non linear and heterogeneous problems, this procedure may lead to severe difficulties. The paper focuses on methods to circumvent these problems, which can now be expressed using a relatively general framework, even though the different ingredients of the strategy have emerged separately. We rely here on the micro-macro framework proposed in [36]. The method proposed in this paper introduces three additional features: (i) the adaptation of the macro-basis to situations where classical homogenization does not provide a good preconditioner, (ii) the use of non-linear relocalization to decrease the number of global problems to be solved in the case of unevenly distributed non-linearities, (iii) the adaptation of the approximation of the local Schur complement which governs the convergence of the proposed iterative technique. Computations of delamination and delamination-buckling interaction with contact on potentially large delaminated areas are used to illustrate those aspects.

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FETI-based algorithms for modelling of fibrous composite materials with debonding

Cited by 4 publications

References 18 publications

A three-scale domain decomposition method for the 3D analysis of debonding in laminates

A three-scale domain decomposition method for the 3D analysis of debonding in laminates

Homogenization of composites with interfacial debonding using duality-based solver and micromechanics

Virtual Delamination Testing through Non-Linear Multi-Scale Computational Methods: Some Recent Progress

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