Relationships Between Stresses and Deformations in a Non-Linear Deformable Body. Part 3. Analytical Functions for Parameters of Concrete’s Plasticity

Part 3 of the article series is devoted to finding an analytical function for parameters of concrete's plasticity. The selection of approximating equations for φ and ψ parameters, taking into account the development of inelastic deformations in concrete, is based on the following hypotheses and assumptions: relative volume changes and shear on octahedral platforms are continuous nonlinear medium voltage functions, octahedral tangent stress and stress state; physical ratios at the starting point of deformation must correspond to the formulas of linear theory of elasticity; the transition from deformation curves and the condition of strength of concrete is ensured; theoretical volumetric and shear deformation curves pass through experimental points characteristic for the beginning of microfracturing. The latter condition is ensured by introducing into the functional dependencies for the plasticity parameters of the limit secant modules of bulk and shear deformation. The proposed non-linear dependencies for heavy concrete of high strength classes provide solutions not only for the volume condition of the material, but also for other cases of concrete resistance.