YIELD SURFACES AND PRINCIPLE OF SUPERPOSITION - REVISIT THROUGH INCREMENTALLY NONLINEAR CONSTITUTIVE RELATIONS

Incrementally piece-wise linear constitutive relations are well adapte d to the description of the behaviour of monocrystals (HILL [1967]). F or geomaterials (soils, rocks,concretes) it could be more appropriate to use incrementally non linear models. In such a case it is no more n eeded to decompose the incremental strain into an elastic part and a p lastic one. :Therefore any yield surface is not introduced into the mo del. II thus becomes interesting to compute approximated yield surface s by simulating numerically with the constitutive model the same loadi ng history as the one which is applied experimentally in order to obta in measured yield surfaces. This question constitutes the first part o f this paper. The second part is devoted to a numerical testing proced ure of the validity of the principle of superposition for incremental loading. In a general manner this ''principle'' is valid only inside t he linearity domains of the constitutive relation. It implies that for incrementally non-linear constitutive models this ''principle'' is ne ver verified. However, if we consider experimental results issued from electronically controlled testing machines it is known from experimen ts that this ''principle'' is approximately valid. In the same spirit as for the numerical study of yield surfaces we have simulated numeric ally stress-strain histories with multiple sharp bends which can be co nsidered as close ''enough'' to rectilinear proportional stress or str ain loading paths, and compared both types of responses. These aspects are presented in the second part of this paper.