# Studies of properties of advanced structural materials and elaboration of mathematical models for the description of their behavior

The results of recent studies of deformation softening and post-critical deformation of steels are presented and the corresponding criteria are formulated for complex loading conditions. The elastic and strength properties of different grades of graphite materials as well as their fracture toughness properties are studied. The method for the determination of crack length and the values of fracture toughness characteristics of materials during stable equilibrium crack growth under bending conditions is considered. The unstable or non-equilibrium crack growth from short initial crack is observed in experiments, and corresponding theoretical explanation is given. The process of unstable crack growth is analyzed for different loading conditions. It has been shown that in the cases of short cracks, some part of stored energy transforms into kinetic energy, which can be described by the equation of energy balance during unstable crack growth.

Many structural materials, which are preferred for the developing of advanced constructions, are inhomogeneous ones. These materials have complex internal structure and properties, which make them to be more effectual in the solution of special problems required for development engineering. On the other hand, in consequence of this internal heterogeneity, they exhibit complex mechanical properties. In this work, the analysis of some features of the behavior of composite materials under different loading conditions is carried out. The dependence of nonlinear elastic response of composite materials on loading conditions is studied. Several approaches to model elastic nonlinearity such as different stiffness for particular type of loadings and nonlinear shear stress–strain relations are considered. Instead of a set of constant anisotropy coefficients, the anisotropy functions are introduced. Eventually, the combined constitutive relations are proposed to describe simultaneously two types of physical nonlinearities, one of which characterizes the nonlinearity of shear stress–strain dependency and another one determines the stress state susceptibility of material properties. The method for experimental determination of material’s functions is proposed. Quite satisfactory correlation between the theoretical dependencies and the results of experimental studies is demonstrated.