The hypoelastic-based plastic constitutive model has been developed to describe the wide class of elastoplastic deformation behavior of solids. The physical and mathematical backgrounds of the hypoelastic-based plasticity, i.e. (i) the transformation of the material-time derivative of general scalar-valued tensor function to the corotational-time derivative required for the derivation of the consistency condition fulfilling the objectivity, (ii) the requirement for the derivation of the additive decomposition of the strain rate and the continuum spin into the elastic and the plastic parts from the multiplicative decomposition of the deformation gradient, (iii) the mechanical requirements for elastoplastic constitutive equations, i. e. the continuity and the smoothness conditions and (iv) the derivation of the general loading criterion are deliberated first. Then, the subloading surface model is formulated in the framework of the hypoelastic-based plasticity. It materializes the pertinent descriptions of wide classes of deformations, i. e. the monotonic, the non-proportional and the cyclic loadings, the rate-dependent deformation behavior in a general rate up to the impact load for wide classes of materials, e. g. metals and soils and the friction phenomena between solids and further the deformation behavior of metallic materials within the framework of the crystal plasticity. In addition, it possesses the distinctive advantage in numerical analysis such that the judgment of yielding is not required in the loading criterion and the stress is automatically attracted to the yield surface in the plastic loading process, engendering a high efficiency in numerical calculations.
