Yield surfaces and principle of superposition: Revisit through incrementally non-linear constitutive relations

Incrementally piece-wise linear constitutive relations are well adapted to the description of the behaviour of monocrystals (HILL [1967]). For geomaterials (soils, rocks,concretes) it could be more appropriate to use incrementally non linear models. In such a case it is no more needed to decompose the incremental strain into an elastic part and a plastic one. :Therefore any yield surface is not introduced into the model. II thus becomes interesting to compute approximated yield surfaces by simulating numerically with the constitutive model the same loading history as the one which is applied experimentally in order to obtain measured yield surfaces. This question constitutes the first part of this paper. The second part is devoted to a numerical testing procedure of the validity of the principle of superposition for incremental loading. In a general manner this ''principle'' is valid only inside the linearity domains of the constitutive relation. It implies that for incrementally non-linear constitutive models this ''principle'' is never verified. However, if we consider experimental results issued from electronically controlled testing machines it is known from experiments that this ''principle'' is approximately valid. In the same spirit as for the numerical study of yield surfaces we have simulated numerically stress-strain histories with multiple sharp bends which can be considered as close ''enough'' to rectilinear proportional stress or strain loading paths, and compared both types of responses. These aspects are presented in the second part of this paper.