| An advanced time-independent constitutive model for frictional materials with non-associated flow plasticity has been developed. The model has new capabilities, capturing all essential elasto-plastic behaviors of frictional materials subjected to arbitrary stress or strain paths, including large stress or strain reversals where plasticity is re-established in any new direction, and stress field rotations, also when principal stresses remain constant. The new model employs rational physical principles to control the evolution of shear plasticity. Through multiple so-called friction elements with fixed shear yield surfaces, the new model captures Bauschinger effect and elasto-plastic effects of stress field rotations, entirely without the complexity of hardening principles such as expanding and rotating yield surfaces and plastic potential surfaces.;At the outset, a new type of parallel plasticity is investigated to look into the possibility of creating positively stable, time independent, constitutive models for frictional materials with non-associated flow. For all stress paths within failure limits, it is shown that parallel plasticity models actually can be designed to guarantee positive definiteness of the incremental, non-symmetric elasto-plastic stiffness matrix resulting from the models. The purely parallel models, however, also show problems in capturing some aspects of real behaviors of frictional materials, as observed in physical tests on sand.;The new constitutive model has been developed out of solving the problems of the purely parallel models. The model takes advantage of the parallel plasticity idea of employing multiple plasticity elements to describe the evolution of shear plasticity in the material. A clear distinction is made between pressure plasticity (crushing processes) and shear plasticity (sliding processes). A new "stick-slip" type of shear plasticity is introduced in multiple friction elements, making a parallel split of the stress tensor into friction stress and deviatoric excess stress, following the same kinematic rules as apply to an elastically supported friction block on a rough plane.;The model has been developed in flexibility form as well as stiffness form, allowing both the determination of elasto-plastic strains from applied stresses, and vice versa, the determination of stresses from applied elasto-plastic strains. This shows great potential for the applicability and practical value of the model. |
