MATHEMATICAL MODELS OF FIBER CONCRETE

Abstract

The work is devoted to the development of a mathematical model of fiber concrete with additional dispersed steel fiber reinforcement and a review of other most popular mathematical models. When studying the physical and mechanical properties of fiber concrete, two approaches are used, which are usually used when working with composites - phenomenological and structural. In the first case, the material is considered as some kind of isotropic system to which the methods of the mechanics of a deformable solid body are applicable. At the same time, the characteristics of the material are determined on the basis of laboratory studies and tests using methods of the theory of experiment planning and mathematical statistics. In the second case, a structural analysis is used, which assumes the expression of the mechanical characteristics of the material through similar indicators of its components, the coefficient of fiber reinforcement, the type and geometric dimensions of the fiber, etc. The authors propose the construction of a mathematical model of fiber concrete based on the determination of its effective stiffness characteristics. Fiber concrete made on the basis of steel fiber with bent ends is considered as the researched material. When building a mathematical model of fiber concrete, it is important to determine its effective properties, which, in turn, implies the procedure for selecting and modeling a representative volume of the material. Equations of the linear theory of elasticity are used to build the model. But, since the considered medium is heterogeneous, the well-known Eshelby principle is taken into account, which allows you to calculate the deformation energy of the system containing inclusions. The dependencies obtained in the work can be used not only for steel fiber fibers, but also for any other (polymeric, glass, etc.), and the specification of the expressions for the effective elastic characteristics will depend exclusively on the geometric shape of the fiber fiber and the type of its deformation. Structural modeling of fiber concrete, finite element models of I.M. Galieva and V´ıtor M.C.F. Cunha, as well as fiber concrete modeling capabilities in the two most powerful programs - ANSYS and NASTRAN.