Space/time global/local noninvasive coupling strategy: Application to viscoplastic structures

The purpose of this paper is to extend the non-invasive global/local iterative coupling technique [15] to the case of large structures undergoing nonlinear time-dependent evolutions at all scales. It appears that, due to the use of legacy codes, the use of different time grids at the global and local levels is mandatory in order to reach a satisfying level of precision. In this paper two strategies are proposed and compared for elastoviscoplastic models. The questions of the precision and performance of those schemes with respect to a monolithic approach is addressed. The methods are first exposed on a 2D example and then applied on a 3D part of industrial complexity

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

This paper deals with the parallel simulation of delamination problems at the meso-scale 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 nonlinear 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 (Ladev\`eze, Loiseau, and Dureisseix, 2001). 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

Nonintrusive coupling of 3D and 2D laminated composite models based on finite element 3D recovery

In order to simulate the mechanical behavior of large structures assembled from thin composite panels, we propose a coupling technique which substitutes local 3D models for the global plate model in the critical zones where plate modeling is inadequate. The transition from 3D to 2D is based on stress and displacement distributions associated with Saint-Venant problems which are precalculated automatically for a simple 3D cell. The hybrid plate/3D model is obtained after convergence of a series of iterations between a global plate model of the structure and localized 3D models of the critical zones. This technique is nonintrusive because the global calculations can be carried out using commercial software. Evaluation tests show that convergence is fast and that the resulting hybrid model is very close to a full 3D model

Toward a non intrusive method for solving coupled direct retrograde problem in transient dynamics

The objective of this work is to solve within a standard Finite Element software, the direct retrograde coupled hyperbolic problems that arise when dealing with identification of material parameters in dynamic for corrupted measurements by means of the adjoint state approach. This question as given rise among others to Riccati and shooting methods. Those methods have several drawbacks, their numerical complexity, and the fact that their implementation in a commercial software would require to re-design such software which is nearly impossible. Therefore we are seeking for an iterative method which could be easily implemented. The method solves alternatively a direct problem and a retrograde one. In order to ensure its convergence a relaxation scheme as to be applied and optimized. Examples of comparison of those methods in terms of complexity , numerical cost and robustness will be presented for an elastic bar

Vers une approche locale-globale de la rupture en interaction fluide structure

Le contexte de ce travail est celui de la prédiction de la tenue de structures complexes au moyen de modèles matériaux fins comme ceux utilisés par exemple pour les structures composites. Jusqu'ici le LMT-Cachan a travaillé sur des chargements imposés donnés et développé des méthodes ad hoc et notamment sur l'adaptation d'une stratégie multiéchelle avec homogénéisation. Dans le cadre de problèmes d'interaction fluide structure jusqu'à rupture la question posée est celle de l'adaptation de ce type de méthode. Ce travail exploratoire est une première tentative dans ce sens

A mesomodel for localisation and damage computation in laminates

International audienceThe basic aspects of a material mesomodel dedicated to composite laminates and capable of simulating complete fracture phenomena are discussed. Attention is focused herein on damage computation and, in particular, on the description of localisation phenomena. Both quasi-static and dynamic loadings are considered

Multilevel Global-Local techniques for adaptive ductile phase-field fracture

This paper outlines a rigorous variational-based multilevel Global-Local formulation for ductile fracture. Here, a phase-field formulation is used to resolve failure mechanisms by regularizing the sharp crack topology on the local state. The coupling of plasticity to the crack phase-field is realized by a constitutive work density function, which is characterized through a degraded stored elastic energy and the accumulated dissipated energy due to plasticity and damage. Two different Global-Local approaches based on the idea of multiplicative Schwarz' alternating method are proposed: (i) A global constitutive model with an elastic-plastic behavior is first proposed, while it is enhanced with a single local domain, which, in turn, describes an elastic-plastic fracturing response. (ii) The main objective of the second model is to introduce an adoption of the Global-Local approach toward the multilevel local setting. To this end, an elastic-plastic global constitutive model is augmented with two distinct local domains; in which, the first local domain behaves as an elastic-plastic material and the next local domain is modeled due to the fracture state. To further reduce the computational cost, predictor-corrector adaptivity within Global-Local concept is introduced. An adaptive scheme is devised through the evolution of the effective global plastic flow (for only elastic-plastic adaptivity), and through the evolution of the local crack phase-field state (for only fracture adaptivity). Thus, two local domains are dynamically updated during the computation, resulting with two-way adaptivity procedure. The overall response of the Global-Local approach in terms of accuracy/robustness and efficiency is verified using single-scale problems. The resulting framework is algorithmically described in detail and substantiated with numerical examples.Comment: 50 pages, 24 Figures, 4 Table

Adaptation d'une stratégie de calcul multiéchelle pour les calculs de délaminage dans les composites stratifiés

Cet article présente la simulation numérique du délaminage de composites stratifiés par utilisation d'une stratégie de calcul multiéchelle de décomposition de domaine, avec homogénéisation en espace. Le calcul non-linéaire d'évolution correspondant au chargement progressif du composite est poussé jusqu'à la ruine complète de la structure. L'accent est porté sur l'optimisation de la stratégie utilisée

Identification robuste en dynamique transitoire des paramètres matériau gouvernant la rupture d'un composite

International audienceThe objective of this study is to develop an identification strategy of parameters of a damage model with localization in the case of dynamic tests with corrupted measurements. An identification method based on the Constitutive Relation Error (Ladevèze, 1998) and the LATIN method (Ladevèze, 1999) is developed in the cases of elastic and viscoplastic behavior (Allix et al., 2005) (Nguyen et al., 2006). Its application in the case of rupture of a composite material is presented here. The proposed identification method is thus shown very robust with respect to the corrupted measurements in the 1D exemple treated.L'objectif de ce travail est l'identification des paramètres associés à la localisation de l'endommagement d'une loi d'évolution à taux limité à partir de mesures d'essai dynamique fortement perturbées sur des composites stratifiés. Une méthode d'identification basée sur la méthode d'Erreur en Relation de Comportement modifiée (Ladevèze, 1998) et la méthode LATIN (Ladevèze, 1999) a été développée dans les cas élastique (Allix et al., 2005) et viscoplastique (Nguyen et al., 2006). Son adaptation au cas de la rupture d'un composite est présentée ici. La méthode d'identification proposée s'avère très robuste face aux perturbations de mesure dans l'exemple 1D traitée

Numerical studies of different mixed phase-field fracture models for simulating crack propagation in punctured EPDM strips

We consider a monolithic phase-field description for fractures in nearly incompressible materials, i.e., carbon black filled ethylene propylene diene monomer rubber (EPDM). A quasi-static phase-field fracture problem is formulated in mixed form based on three different energy functionals (AT2, AT1 and Wu’s model) combined with two different stress splitting approaches (according to Miehe and Amor). It leads to six different phase-field fracture formulations in mixed form. The coupled variational inequality systems are solved in a quasi-monolithic manner with the help of a primal-dual active set method handling the inequality constraint. Further, adaptive mesh refinement is used to get a sharper crack zone. Numerical results based on the six different problem setups are validated on crack propagation experiments of punctured EPDM strips with five different test configurations. As a quantity of interest, the crack paths of experiments and numerical computations are discussed