Plasticity constitutive theory considering material length parameters

Abstract The traditional continuous medium theory introduces the homogenization assumption that the material remains constant from the macroscopic to the microscopic view, which has been successfully applied to the analysis of the macroscopic mechanical properties. When the dimensions are reduced to the microscopic view, the internal defects of the material start to appear, leading to the inhomogeneity of the material properties, which is, in practice, manifested as a ruler effect. Therefore, it is necessary to introduce the material length parameter into the structural theory to model the mechanical response of new materials. Based on the theory of size effect, many scholars have carried out a large number of studies. The most widely used theories are strain gradient theory and differential nonlocal model, mainly the first strain gradient theory, the second strain gradient theory, and the simplified strain gradient theory. Some scholars define it from the kinetic point of view, but most of these consider the intrinsic relationship of elastic materials. To further investigate the plasticity intrinsic theory, some scholars have proposed the gradient plasticity theory, the nonlocal plasticity theory, and so on. In this paper, based on the previous research results, we briefly summarize the development and outlook of the plasticity eigenstructure theory under the consideration of the length parameter of the material. Then, we derive the plasticity eigenstructure relation equation, the full-volume theoretical model, and the yield criterion corresponding to the Mises material under the consideration of the endowment size of the material from the perspective of the gradient theory of plasticity, and finally, put forward a new plasticity eigenstructure theory-higher-order nonlocal gradient theory. A new plasticity constitutive theory, the higher-order nonlocal gradient theory, is finally proposed, and the defining equations and their constitutive relations are derived in detail. The proposed theory is intended to provide a theoretical basis for analyzing the microdefects in materials.