The aim of the study is to identify the asymptotic stress, creep strain rate and continuity fields behavior in the proximity of the crack tip under creep conditions, taking into account the damage accumulation process, based on the finite element analysis of the stress-strain state at the crack tip in the finite element software SIMULIA Abaqus using the UMAT procedure, which allows us to describe constitutive equations that are absent in the standard set of defining equations of the FEM complex, and incorporate the damage accumulation processes into the design scheme of the FEM software. The damage accumulation phenomenon is described using the classical Kachanov–Rabotnov model, which postulates a power law linking creep strain rates and stresses, and a power law of damage accumulation, in a coupled formulation. Finite element modeling of loading of a plate with a central horizontal and inclined crack under conditions of steady state creep is performed under the assumption of the realization of a plane stress state. It is shown that in the case of steady-state creep without taking into account the process of damage accumulation, the finite element solution clearly has the asymptotic behavior of the classical Hutchinson-Rice-Rosengren solution. With the help of the developed user procedure UMAT, the coupling of two processes is realized in the computational scheme of the finite element method: the evolution of mechanical fields and the increase of damage in the vicinity of the crack tip in accordance with the canonical Kachanov-Rabotnov damage evolution model. On the basis of the analysis of the stress field obtained by finite element computations, in the vicinity of the crack tip, taking into account the damage, a new asymptotic of stress fields near the crack tip in a plate under uniaxial tension conditions was revealed, different from the asymptotic corresponding to the Hutchinson-Rice-Rosengren solution.

The features of macroscopic localization of plastic flow during uniaxial tension of a flat bimetallic plate are discussed. The extension axis of the sample was oriented normally to the direction of rolling. The studied bimetal "low-carbon steel - stainless steel" is used in chemical engineering for the manufacture of reaction columns, autoclaves, reactors, and heat exchangers. The plastic flow curve of the bimetal after the yield point in the area of large plastic deformations is located between the curves for its components - austenitic stainless steel (AISI 304) and low-carbon steel (ASTM A414 grade A). The visualization of localized plastic deformation bands and registration of the kinetics of their movement were carried out on the working part of the sample by the method of digital speckle photography. It has been established that at the yield plateau, plastic deformation in the form of Lüders fronts originates at the interface between the cladding layer and the base bimetal layer and propagates in the base layer of low-carbon steel, while the less plastic cladding layer of stainless steel deforms elastically. Then, together with the base one, the cladding layers also begin to plastically deform in the form of the propagation of Portevin-Le Chatelier fronts. The process of failure of a bimetal also begins with the localization of plastic deformation near structural inhomogeneities and stress concentrators in the area of contact between layers of two dissimilar metals. The stress concentrators formed at the early stages of plastic flow in this region initiate the formation of a high-amplitude peak of strain localization, which is a precursor to the formation of a neck in the sample and further ductile failure of the bimetal.

The deformation of an adhesive layer of finite thickness connecting two bodies with an overlap in a linear elastic formulation is considered. The stressed state of the layer is considered on the basis of the average thickness and the associated equilibrium conditions of boundary stresses. The deformed state of the layer is determined by its boundary displacements. Based on the system of variational equilibrium equations for the composite coupled by the displacement field of the adhesive layer, a numerical solution to the problem was obtained using the finite element method. To approximate the displacement field of load-bearing bodies, allowing to take into account tensile and compressive deformations in two orthogonal directions, an analytical solution to the corresponding problem is obtained. The qualitative similarity of solutions for average stresses in the layer is shown in comparison with the solution within the framework of classical plate theory. A comparison is made of the known analytical concepts for this problem, the obtained numerical and simplified analytical solutions. Taking into account the change along the length of the layer of average stress, orthogonal to the separation of the layer at a finite thickness, in the proposed formulation of the problem can affect the value of the boundary tangential stresses, and a change in the average shear stress of the layer leads to a difference in the separation stresses along the boundaries of the adhesive layer. This effect cannot be taken into account in models that use the hypothesis of homogeneity of the stress state throughout the layer thickness without taking into account boundary stresses. Using the boundary stresses of the layer introduced into the model as criterion characteristics, it is possible to simulate the detachment of the adhesive from the load-bearing bodies along the mating surfaces. It is shown that for the problem under consideration, achieving the criterion characteristics for detachment and shear leads to destruction of the adhesive layer along identical surfaces.

The theory of filtration of liquids and gases through porous media has historically been used to solve a large number of applied problems, ranging from the movement of groundwater to the regularities of consolidation of biological tissues. This work examines two basic problems of the physics of oil and gas reservoirs - plane-parallel and plane-radial flows of liquid and ideal gas. Darcy's linear law is used as the equation of fluid motion. The constitutive equations for the skeleton include a term that takes into account the effect of fluid pressure on its deformation. The constitutive equations for the fluid take account of the influence of the skeleton on the compressibility of the fluid. In this way, a coupled problem is formulated for the elastic regime of fluid filtration. The model is verified based on analytical solutions, as well as numerical solutions obtained by other authors. It is shown that the obtained numerical solutions, namely, the distributions of pore pressure, filtration rates and mass flow rates, with a high accuracy coincide with analytical solutions. Additionally, fluid filtration through a quasi-isotropic medium is considered. It is shown that the presence of a layer with reduced permeability does not lead to nonlinearity in the velocity distribution for liquids and in the product of density and velocity for gas, but their values decrease. On the contrary, the pressure distribution profile changes abruptly when moving from layer to layer. Formulas are proposed for determining the effective permeability of a medium based on numerical simulation data of a plane-parallel flow. The results obtained can be used in calculating the operating parameters of oil and gas fields.