Solids with bounded tensile stress and hardening/softening behaviour

Many authors have studied no-tension solids. Del Piero [1] studied this material as solids subjected to internal constraints (the Chauchy stress tensor T is constrained to be negative-semidefinite). Under the hypotheses of infinitesimal elasticity, no-tensile strength and the postulate of normality, it is possible to determine the constitutive equation for an elastic no-tension material. In the hypothesis of isotropic elastic material it is possible to explain that the stress tensor T, the total infinitesimal strain tensor E and the anelastic infinitesimal strain tensor Ea are coaxial, that is they have the same characteristic space and the same eigenvectors. Lucchesi et al. propose a numerical method to solve equilibrium problems of no-tension solids for plane cases [2] and furnish some explicit solutions for rectangular panels [3]. The constitutive equation is generalized for 3D-case and for thermal loads [4]; the numerical procedure is applied to the analysis of “Buti’s bell tower” (Pisa) [5]; Degl’Innocenti et al. [6] extend the numerical method to dynamic analysis. Padovani [7] deals with a family of non-linear elastic materials depending on a parameter , so that for =0 the material corresponds to the no-tension solids described in Del Piero [1]. It is possible to generalize the model in order to consider the solid as a material with bounded tensile strength [8]. The application of this constitutive equation to masonry solids can just provide approximate information on the stress state, because it supposes constant tensile strength. Two regions of the body separated by a crack transmit each other a constant tensile stress for any width of the crack.