Hyperbolic hardening model for quasibrittle materials

In this study an elastoplastic hardening model for quasibrittle materials is presented. The yield surface exhibits hyperbolic meridians while its shape on the deviatoric plane is described by an elliptic function. The proposed hardening mechanism is controlled by the slope of the asymptotes of the hyperbolic meridians and thus by the mobilized friction of the material. The yield surface is capped during the first stages of hardening and opens up before reaching the peak strength. On the deviatoric plane the hardening is non-uniform producing changes in both the size and the shape of the yield surface. The proposed plastic potential is related with the yield function through a simple modification of its volumetric part. The model is equipped with a hardening rule that is a monotonically increasing elliptic function of the hardening parameter. The latter is given in its rate form and it is pressure dependent. A proposed ductility rule controls this pressure dependency and leads to brittle behavior in tension and ductile behavior at high confinement compression. All the parameters have physical interpretation and are directly related with measurable mechanical properties of the material in the lab. Most of them could be identified from a uniaxial compression test. The predictions of the model are compared against experimental datasets and it is shown that exhibit very good agreement.