Frédéric Feyel

Multiscale FE2 elastoviscoplastic analysis of composite structures

This paper discusses modelling of the behaviour of structures reinforced by long fibre SiC/Ti composite material with a periodic microstructure. A new multiscale behaviour model based on a multilevel finite element (FE2) approach is used to take into account heterogeneities in the behaviour between the fibre and matrix. It is shown that combining this model with parallel computation techniques now makes it possible to consider realistic composite structural computations yielding a detailed geometric description and constitutive equations giving access to microstructural data, instead of only to phenomenological macroscopic data difficult to correlate with the local mechanical state.

Some elements of microstructural mechanics

Abstract Microstructural mechanics combines the computational methods of structural mechanics and materials sciences. It is dedicated to the mechanics of heterogeneous materials. On the one hand, it can be used to compute industrial components for which the size of the heterogenities is of the order of magnitude of the size of the structure itself or of holes or notches. On the other hand, the computation of representative volume elements of heterogeneous materials enables one to predict the influence of phase morphology and distribution on the linear or non-linear effective properties, having in view microstructure optimization. Such computations provide the local stress–strain fields that can be used to predict damage or crack initiation. This work focuses on the modern tools available for reconstructing realistic three-dimensional microstructures and for computing them, including parallel computing. The choice of the local non-linear constitutive equations and the difficulty of identification of the corresponding parameters remain the weakest link in the methodology. The main example detailed in this work deals with polycrystalline plasticity and illustrates the tremendous heterogeneity of local stress and strain, and the effect of grain boundary or free surfaces. The computations are finally used to calibrate a simplified homogenization polycrystal model.

F.E. computation of a triaxial specimen using a polycrystalline model

Abstract The crystallographic approach provides an improved framework with respect to the classical macroscopic models to predict the stress-strain behavior of polycrystalline material. The model consists in a set of equations to represent the phase behavior, and a concentration rule. The present paper shows a numerical implementation of such a model, written in the framework of viscoplasticity with a threshold, in a parallel version of the F.E. code ZeBuLoN. Heavy computations can then be made. The system is used to simulate the mechanical response of a biaxial specimen developed at Laboratoire de Mecanique et Technologie de Cachan. This type of specimen is specially designed to support three-dimensional non-proportional loading paths, which are badly represented by classical models. The response obtained with the polycrystalline model is shown, and compared with the experimental data at the global scale. Local information concerning the stress and strain heterogeneity and the slip system activity are also available from the computation.

A Local Contact Detection Technique for Very Large Contact and Self-Contact Problems: Sequential and Parallel Implementations

The local contact detection step can be very time consuming for large contact problems reaching the order of time required for their resolution. At the same time, even the most time consuming technique all-to-all does not guarantee the correct establishment of contact elements needed for further contact problem resolution. Nowadays the limits on mesh size in the Finite Element Analysis are largely extended by powerful parallelization methods and affordable parallel computers. In the light of such changes an improvement of existing contact detection techniques is necessary. The aim of our contribution is to elaborate a very general, simple and fast method for sequential and parallel detection for contact problems with known a priori and unknown master-slave discretizations. In the proposed method the strong connections between the FE mesh, the maximal detection distance and the optimal dimension of detection cells are established. Two approaches to parallel treatment of contact problems are developed and compared: SDMR/MDMR – Single/Multiple Detection, Multiple Resolution. Both approaches have been successfully applied to very large contact problems with more than 2 million nodes in contact.

Application of parallel computation to material models with a large number of internal variables

Abstract.The finite element code ZeBuLoN has been parallelized using the FETI subdomain decomposition method for the use of non-linear mechanical behavior models which require a high number of inte...

Predicting size effects in nickel-base single crystal superalloys with the Discrete-Continuous Model

The Discrete-Continuous Model, a coupling between dislocation dynamics and finite elements simulations, is used for modelling size effects in the mechanical properties of single-crystal superalloys. Both formation and evolution of the dislocation microstructures are analysed, and the crucial role of the storage of signed dislocations at the interfaces is discussed. The onset of plasticity is found to scale as the inverse of the channel width, and polarised dislocation networks at the interfaces significantly increase the flow stress with respect to a bulk crystal.

A parallel algorithm for direct solution of large sparse linear systems, well suitable to domain decomposition methods

The goal of this paper is to develop a parallel algorithm for the direct solution of large sparse linear systems and integrate it into domain decomposition methods. The computational effort for these linear systems, often encountered in numerical simulation of structural mechanics problems by finite element codes, is very significant in terms of run-time and memory requirements.In this paper, a two-level parallelism is exploited. The exploitation of the lower level of parallelism is based on the development of a parallel direct solver with a nested dissection algorithm and to introduce it into the FETI methods. This direct solver has the advantage of handling zero-energy modes in floating structures automatically and properly. The upper level of parallelism is a coarse-grain parallelism between substructures of FETI. Some numerical tests are carried out to evaluate the performance of the direct solver.