The traditional unified viscoplasticity constitutive model can be only applied to metal materials. The study of the unified constitutive theory for metal materials has discovered the correlation between the classical plasticity theory and the unified viscoplasticity constitutive model, thus leading to the concepts of the classic plastic potential and yield surface in the unified constitutive model. Moreover, this research has given the continuous expression of the classical plastic multiplier and presented the corresponding constructive method, which extends its physical significance and lays down a good foundation for the application of the unified constitutive theory to the material analysis in more fields. This paper also introduces the unified constitutive model for metal materials and geo-materials. The numerical simulation indicates that the construction should be both reasonable and practical.viscoplasticity, classical plasticity, unified constitutive model, plastic potential, yield surface Particles or specimens of continuum are described by two kinds of variables: One is the external state variables, which are obtained directly from external observations; the other is the internal state variables, which cannot be measured directly but can be calculated under certain hypothesis. Nowadays, there are two kinds of methods to calculate the plastic strain: One is the yield surface theory, i.e., the classical plasticity theory; the other is no-yield-surface theory, which concludes the intrinsic time theory and the unified viscoplasticity constitutive theory.Classical plasticity models were derived from the idealized tensile curves. With the development of 140 years, they form a refined system in theory and obtain widespread applications. In classical plasticity models, the yield conditions are given to determine the boundary of the elastic region. A consistency condition is also supplemented to judge whether the points on the yield surface are elastic or elastic-plastic. In fact, it is very difficult to determine the yield point strictly from the tensile curves for many metal materials, such as type 304 stainless steel, copper, aluminum, etc. Generally, a deformation value has to be specified to tell the material whether in elastic stage or in plastic stage. If the deformation is smaller than the specified deformation value, the material is in the elastic stage. Or else, the material is in the plastic stage. Thus, this method makes trouble for the classical plasticity theory to determine the deformation behavior of materials. Unified viscoplasticity constitutive model is an internal state variable constitutive model, which is not based on the existence of the initial yield surface. A set of coupled internal state variable evolution equations are used to describe the changes in the microstructure of the materials and the inelastic strain, and thus the effect of stress histories is included; namely, 'loading history dependence' is included in the model. By means of the evolutions taking place in the isotropic har...
