No abstract

The paper considers the dynamic pressing-in indenter in a plane elastic-plastic statement. A general statement of the problem of a rigid body under a flexible stamp pressing-in is given; it allows considering the elastic and plastic properties of the material and the process of the stress-strain state formation. The problem of a flexible stamp action on the outer boundary is realized using the finite-difference method. By solving the problem for a quadrangular profile, the distribution of the stress-strain state of the body under consideration and the formation of stresses over time are shown. The effect of plastic properties of the material on the stress state of the body is assessed by comparative analysis.

A model of plasticity for a transversely isotropic material with allowance for complex loading is developed, based on results of experiments with homogeneous cylindrical specimens of isotropic materials. An empirical model of plasticity for isotropic metals is constructed with allowance for vector properties of the material. The model is extended to a particular case of anisotropy. Model of Plasticity for Isotropic Metals.According to the isotropy postulate [1], the process of loading and deformation at an arbitrary point of the body is determined by defining five components of the stress and strain vectors, and the process intensity and direction depend only on the internal geometry of the strain path. The material is assumed to be plastically incompressible. The stress vector is presented in the orthonormalized local Frenet reference frame in the following form: σ = P n q n (q n are the unit Frenet vectors).In the general case, the components of the Frenet reference frame are determined by the formulaHere q 1 = d /ds; χ 0 = χ 5 = 0; χ 1 , χ 2 , χ 3 , and χ 4 are the parameters of curvature and twisting of the strain path.In terms of velocities, the above-given presentation acquires the form [2]where A i are plasticity functionals andσ = σ/|σ|. Constructing the functionals is a complicated task; therefore, hypotheses within the framework of Il'yushin's theory of the processes are used. One of them is the hypothesis about the complanarity of the vectorsσ,σ, and q 1 . In this case, we have A 3 = A 4 = A 5 = 0. Some theories of plasticity based on the associated law of the flow can also be constructed within the framework of the complanarity hypothesis. Let the vectorsσ, q 1 , and q 2 be complanar. For two-dimensional problems (three-dimensional trajectories in Il'yushin's vector space), this means that the stress vector σ lies in the osculating plane of the strain path. In this case, the approximating relation can be written in the form σ = P 1 q 1 + P 2 q 2 ,(1.1)where P 1 = |σ| cos ϕ and P 2 = −|σ| sin ϕ (ϕ is the variable angle between the vectors σ and d /ds). Generally speaking, this assumption is justified only for two-dimensional trajectories. Thus, by defining the law of variation of the convergence angle ϕ and also the dependence σ ∼ s, we can set the constitutive relation for the plastic material. The function |σ| = F (s), where F (s) is the strain path, can be Mechanics and Seismology Institute, Academy of Sciences, Republic of Uzbekistan, Tashkent, Uzbekistan 100125; rustam abirov@mail.ru.

The new approach for numerical calculating of stress and strain state of underground structures is presented in this issue. The advantage of this method is using in design scheme a real diagram of concrete and reinforcement materials. Also, these calculations are allowed to trace the process of deformation of reinforced concrete in each of the sections of the structure. In the technique, static calculations of reinforced structural elements when changing their initial conditions or stress state after strengthening are carried out taking into account new data. A three-dimensional finite element calculation is also carried out while taking into account regulatory loads. Assessment of levels of tangential and tensile stresses in walls makes it possible to target reinforcement and parameters of monolithic stiffness belts. Numerical results for discussion are presented in this paper.

No abstract