Description of Equivalent States of Solids Under Complex Stress-Strain Conditions Based on Nominal Strain Analysis.

The paper presents a methodology for determining the complete strain diagrams of materials in a complex stress state using the criteria of equivalence, which take into account the different behavior of the material under tension and compression. The proposed methodology is based on determining the relationship between the stress and strain surfaces. Since it is difficult to describe the deformation surface due to the volumetric influence of deformations, it is proposed to introduce the concept of "nominal strain." In this case, the general relationship between the stress and the nominal strain, for the case of a complex stress state, is defined as the relationship between the Euclidean norms of the stress and nominal strain tensors. The obtained dependences show the relations between the real values of stress and nominal strain, preserve the dynamics of change in the secant modulus, and, accordingly, allow comparison with other dependences obtained for a different stress state. The definition of the loading surface, as some geometric figure, is based on the fulfillment of differential conditions that are imposed on this surface and the possibility of determining a sufficient number of points for its construction. In this work, it is proposed to consider the loading surface in the form of a circular paraboloid. Under active loading, this surface expands to its limits – the fracture surface. To determine the characteristics of the above-mentioned surfaces and the law of their expansion, it is sufficient to conduct two basic experiments – for compression and for tension. The work provides a general methodology for determining the internal constants of the equation that describe the selected loading and nominal strain surfaces. [ABSTRACT FROM AUTHOR]