1. Introduction

The general objective of developing « micro-macro » functionalities in Code_Aster is to be able to integrate models at several scales in a modular way (with the possibility of choosing laws of behavior, location rules, types of microstructures). This can lead to different types of calculations (polycrystalline calculations, use of a Berveiller-Zaoui type law or a model law « rule in \(\beta\) « , calculations of multi-crystalline aggregates with a microstructure mesh,…).

The approach presented here consists in allowing the decoupling, by modularity, of the various elements that constitute a law of behavior. This flexibility is accessible directly to the user. In addition, for the developer, it is possible to easily add a law of crystalline behavior by simply defining the partial derivatives of the problem, in terms of internal variables. This is sufficient if you are satisfied with an explicit integration; for an implicit integration, you must also define the tangent operator.

More precisely, for the behavior aspect MONOCRISTAL, at each point of integration of a given finite element, the behavior is that of a monocrystal having a given orientation, and a certain number of sliding systems. Each family of sliding systems has its own local law of behavior.

In the case of a polycrystalline model, it is assumed that at a material point (point of integration of a finite element), several metallurgical phases are present simultaneously, each phase being able to consist of grains with given orientations, each grain having a certain number of sliding systems (not necessarily the same for each phase). The representation of the material is based on a simplified self-consistent approach 5 or possibly extended for non-radial or cyclic loadings 4. Each family of sliding systems has its own local law of behavior. The crystallographic structure, the law of crystalline viscoplasticity and the scale transition rules are thus found separately. This mode of separation is also extended to the law of viscoplasticity itself, with a separation between the elasticity, the criterion and the law of flow.