ABSTRACT
Figure 1. Strain components on an arbitrary plane of normal n. numerically the real situation in sufficient detail. It appears obvious, therefore, that performance of numerical analysis of engineering problems involving this class of materials requires models capable of reproducing the different types of anisotropic behaviour by means of an equivalent continuum medium. This paper describes an approach for modelling anisotropy based on the use of microplane models. This technique uses micromechanical considerations, albeit simplified, to obtain a macroscopic stress/strain relationship based on the superposition of behaviour laws valid for planes of arbitrary orientation that cover all possible space orientations. Because of the nature of this technique, it is relatively simple to reproduce the anisotropy of the material without restricting it to a special configuration as is the case in some existing models. The original idea on which microplane models are based can be traced back to the 'slip theory' of metal plasticity and, more recently, to the 'multilaminate models' developed in Swansea by Pande and co-workers [1, 2, 3]. The microplane model has been developed in the last decade by Bazant and co-workers [4, 5, 6, 7, 8]. As pointed out above, in these models behaviour laws are defined on a plane arbitrarily orientated in order to add up afterwards the contributions of all planes to obtain the macroscopic stress/strain relationship. As there are only two stress and strain components (normal and tangential) on a plane, the formulation is simpler than the conventional tensorial formulation using six components. Moreover, in these models, tensorial invariance is automatically achieved through the appropriate superposition process.
