A stress-strain relationship of soil based on the simple shear mechanism

A general stress-strain relationship of soil is shown in which friction and dilatancy properties are taken into account as well as the nonlinear and elasto-plastic properties. In the formation, the finite deformation theory of elasto-plasticity is used and the objective Green-Naghdi co-rotational stress rate and the stretching tensor are employed. On the assumption that the simple shear deformation always occurred along the single slip surface, which is defined in a specified direction in principal stress coordinate system, a stress-strain relationship is reduced and transformed to the spatially fixed coordinate system. A stress-strain relationship of soil is obtained by considering both the octahedral plane and the spatially mobilized plane as a simple shear plane.