Version of the deformation theory of plastic ductility of concrete in a plane stress state

Abstract

Reinforced concrete as one of the main materials for a wide class of building structures for civil, industrial and transport purposes has a number of specific properties: physical nonlinearity, anisotropy, and crack formation. The behavior of reinforced concrete in the elastoplastic stage before its destruction is more characterized by deformation of concrete. It is shown that the physical nonlinearity of concrete is due to plastic deformations, which are characteristic of various types of stress state. For a triaxial stress state, the system of equations in the mechanics of a deformable solid, it includes two groups of formulas that combine nine equations that include 15 unknowns (three displacements, six strain components, and six stress components). In order for the system to be closed, it is necessary to supplement it with six equations. Such equations are the basic physical relationships that relate the six stress components to the six strain components. The use of linear relationships between stresses and strains introduces the greatest error in the assessment of the stress-strain state (NDS) of structures made of materials with the properties of nonlinearly deformable bodies. In this regard, the more correctly the physical law defining the correlation reflects the material, according to which the material resists various types of deformations, the less error will be allowed in the assessment of the NDS of structures. The article proposes a new approach to the construction of basic physical relationships based on an invariant solution to the problems of mechanics of a deformable solid for concrete in a plane stress state. The correspondence of the proposed dependences to the real stress and deformable state of the material is shown.