Classical and Multi-Level Constitutive Models for Describing the Behavior of Metals and Alloys: Problems and Prospects (as a Matter for Discussion)

— The need to improve existing and develop new effective technologies for processing metal materials by pressure (including those with severe plastic deformations that make it possible to obtain products with an ultrafine-grained structure), constantly increasing requirements for the accuracy of strength calculations, emerging new materials with complex properties (including gradient materials), the need to design and create functional materials require mechanicians and material physicists to constantly work on constitutive models (constitutive relations) to describe the behavior of various materials. In this case, the models used to describe the processes of thermomechanical processing attract the greatest interest, since it is such models that the main performance characteristics of finished products are formed. The physical and mechanical characteristics (including strength) of the materials of the products are determined mainly by the microstructure formed as a result of processing. In this regard, the most popular are the models that allow explicitly describing the evolving microstructure of various structural and scale levels. At the same time, currently, the most common among specialists in the field of solid mechanics, technologists, and engineers are macrophenomenological constitutive relations based on processing the results of macro experiments and not using an explicit description of the material structure. Along with the constitutive relations of this class, in the last 15–20 years, multilevel models based on the introduction of internal variables and physical theories of elastoplasticity (elastoviscoplasticity) are gaining wider acceptance for analyzing the behavior of materials under thermomechanical (and more complex, for example, radiation) effects. In this article, we have made an attempt to compare the advantages and disadvantages of the models of these classes, assess the areas of their applicability, as well as formulate some problematic questions, answers to which the author have not found in the existing literature on mechanics of solids and materials science.