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A mathematical model is developed to describe fatigue-damage accumulation in structural materials (metals and their alloys) on multiaxial paths of disproportionate combined heat and power loading. The effect of the shape of the strain path on the fatigue life of metals was studied to obtain qualitative and quantitative estimates of the obtained constitutive relations. It is shown that the proposed constitutive relations adequately describe the main elastoplastic deformation effects and damage accumulation in structural materials for arbitrary strain paths.Introduction. During long-term operation of equipment and systems of important engineering facilities under nonstationary heat and power loading, fatigue damage is accumulated in structural materials, leading to deterioration of the initial strength characteristics of the materials and development of defects. During a significant period of operation, these processes occur latently. In addition, the most dangerous zones determining the life of an element are as a rule inaccessible for nondestructive inspection. To ensure safe operation of engineering facilities, it is necessary to monitor damage development in the most dangerous zones of structural elements (exhausted life) and predict the development of these processes to the limiting states (residual life) [1].Simultaneous studies of deformation and fracture processes provides answer to the following questions: Where and when will macroscopic cracks arise for the first time in a body under specified load and temperature variations and how will these cracks further develop? Because damage accumulation depends significantly on the kinetics of the stress-strain state, the accuracy of estimation of the strength and life of structural elements depends on how precisely the equations of state describe kinetics under specified operation conditions. Viscoelastic deformation parameters such as the length and shape of the strain path, stress mode, its history, etc. have a significant effect on the rate of damage accumulation. The purpose of studies in this area is not so much to refine the various formulations required to determine macroscopic strains from specified loading history, but rather to study the main regularities of the determining and preceding processes.1. Constitutive Relations of Fracture Mechanics and Algorithm for Their Integration. The model for a damaged medium includes three components: a) relations determining the elastoplastic behavior of the material and dependent on the fracture process; b) equations describing the damage accumulation kinetics; c) strength criterion of the damaged material.1.1. Thermal Plasticity Relations. The constitutive relations of thermal plasticity are based on the following main principles: -The strain tensors e ij and strain rates tensorsė ij are the sums of the elastic strains e e ij and elastic strain rateṡ e e ij (independent of the loading history and determined by the final state of the process), and the plastic strains e p

В работе рассматриваются вопросы численного моделирования трансформации нелинейных поверхностных гравитационных волн в условиях мелководных заливов. Дискретная модель построена на основе нелинейных уравнений мелкой воды. Приведены граничные и начальные условия. Методом расщепления по физическим процессам получена система из трех уравнений. Определен порядок аппроксимации, исследованы условия устойчивости дискретной модели. Для решения системы уравнений использован метод прогонки. Представлены профили поверхностных гравитационных волн для различных этапов распространения. Ключевые слова: уравнения мелкой воды, численное моделирование, нелинейные поверхностные гравитационные волны, трансформация профилей

A mathematical model that describes the processes of fatigue damage accumulation in structural materials (metals and alloys) under multiaxial disproportionate combined thermomechanical loading is advanced from the standpoint of the damaged medium mechanics. Based on the results of basic experiments performed in a special way, an experimental-theoretical procedure for finding material parameters of the advanced constitutive relations of the damaged medium mechanics is put forward. The advanced version of the constitutive relations of the damaged medium mechanics is shown to adequately (qualitatively and quantitatively) reflect the main effects of elastoplastic deformation and damage accumulation in metals under low-cycle fatigue.

Пермский государственный национальный исследовательский университет, Пермь, Российская ФедерацияЧисленно, в двумерной постановке решена задача определения сил, действующих на постоянный магнит, помещенный в прямоугольную полость с концентрированной магнитной жидкостью. В общем случае результаты расчета зависят от интенсивности магнитофореза и диффузии частиц, размагничивающих полей и межчастичных взаимодействий. Рассчитаны размагничивающее поле и поле концентрации коллоидных частиц. Приведена зависимость результирующей силы, действующей на магнит, от его смещения из положения равновесия, параметра агрегирования и концентрации частиц. Показано, что учет магнитофореза и межчастичных взаимодействий может привести к многократному изменению этой силы. A boundary value problem of forces acting on a permanent magnet placed in a rectangular cavity with concentrated magnetic fluid is solved by the control-volume method. The solutions available in the current literature have been obtained for dilute solutions, in which the inter-particle interactions (steric, magnetodipole and hydrodynamic) and magnetic fields generated by the magnetic fluid are inessential. Moreover, these studies neglect the magnetophoresis of colloidal particles and diffusion processes, which strongly restrict the applicability range of the obtained results. The inter-particle interactions can significantly increase the intensity of the fluid magnetization, and disregard of the magnetophoresis and particle diffusion implies that the known solutions are valid only over a limited time interval, which is short compared to the time of the onset of equilibrium particle distribution in the cavity. The main objective of this study is to estimate quantitatively the contributions of all these factors. The selected problem geometry corresponds to a simple uniaxial magnetofluidic accelerometer. The solution is searched for a two-dimensional problem using the dynamic equation of mass transfer recently introduced in J. Chem. Phys., 2011, vol. 134, 184508. The calculations have been performed to evaluate the magnetic field generated by the fluid and the field of colloidal particle concentration. The plots of the resultant force acting on the magnet versus its displacement from the equilibrium, the energy of magnetodipole interactions and volume-averaged particle concentration are presented. The basic finding of this work is the establishment of a very strong dependence of the computation results on the selection of an adequate theoretical model. In particular, it has been shown that disregard of interparticle interactions in the fluid can lead to a computational error exceeding hundred percents.Key words: magnetic fluid, permanent magnet, hydrostatic pressure, magnetophoresis, interparticle interactions ВведениеЗадачи определения сил, действующих на тело, погруженное в магнитную жидкость, рассматриваются в литературе, начиная с классических работ Розенцвейга (см. [1]), в которых были выведены уравнение Бернулли для магнитной жидкости, магнитный скачок давления на г...