CONSTITUTIVE EQUATIONS FOR ISOTROPIC MULTIMODULUS MEDIA. II. NONLINEAR EQUATIONS

The resistance of many structural materials to deformation depends on the form of the stress state [1-8]. The stress-strain relations for such materials were constructed in a number of works by utilizing either quasilinear [9-12]^2 or nonlinear [4, 7, 8, 14, 18-22] equations. Serious drawbacks of these models were analyzed in [23,24]. The familiar experimental studies [1-8] indicate that the dependence of the deformation characteristics of multimodulus materials on the nature of the stress state manifests itself especially in the nonlinear part of the stress-strain curve, in which the plastic processes develop. The classical theories of plasticity adopt the hypothesis of the "unified curve" assuming that the plastic deformation does not lead to the residual change of the volume. However, as shown in [1-8], these assumptions are not satisfied by a large number of materials. The stress-strain curves for concrete, gray cast iron, structural graphites, and fluoroplastic depend substantially on the form of the stress state. The deformation process in these materials is dilatational. Unlike the conventional approaches, the relations suggested in [25] define the stress state of isotropic deformable media in terms of the parameters of the normalized space of principal stresses. In [23], this stress state was defined in terms of the parameters of the normalized space related to octahedral areas. The quantitative and qualitative parameters of these two normalized spaces make it possible to obtain rather universal constitutive equations for multimodulus materials, the stress-strain curves of which allow linear approximations. With some constraints for the normalized stresses, these equations generalize most of the familiar models of elasticity for materials with different moduli. These equations permit one to describe the states of some materials with sufficiently high accuracy. The one-to-one relations between the parameters of the normalized spaces [23,25] and the corresponding potential equations were established in [24]. Moreover, it was confirmed that these equations are highly accurate for a wider class of materials with different moduli in tension and compression. In [24], the possibility of constructing the nonlinear equations taking into account the elastoplastic deformation was also discussed. The present work is a development of [23-25].