Mechanics Of Continuous Media Research Articles

EXPERIMENTAL-COMPUTATIONAL ANALYSIS OF HIGH-SPEED INTERACTION OF A SOLID WITH WATER BARRIERS

The stress−strain state of projectiles is investigated when a high-speed projectile enters water and interacts with barriers protected by a water layer. Experimental investigations are carried out using a high-speed ballistic setup. Calculations are performed within the framework of the mechanics of continuous media for an elastoplastic model of a solid with allowance for fracture and a hydrodynamic water model. Depending on the projectile speed, different stress−strain state regimes are observed: from little deformed one at a speed of about 1 km/s to a fractured one at a speed of about 2 km/s. The calculation technique allows the distances in water to be determined at which a metal barrier can be punched in the inertial model.

An analytical model of coal wellbore stability based on block limit equilibrium considering irregular distribution of cleats

An analytical model of coal wellbore stability is established based on the block limit equilibrium method, taking the irregular distribution of cleats into account. Because coal seam is cut into discontinuous blocks with different shapes and sizes, block slip can be treated as the symbol of coal wellbore instability. According to the geometric characteristic of blocks, blocks surrounding the wellbore can be divided into 3 categorizes: type I, type II and type III. To evaluate the block slip, the stress distribution near the wellbore is determined based on the continuous medium mechanics and the fracture mechanics. Using Mohr–Coulomb criterion and limit equilibrium method, the critical conditions of block slip are derived by defining the failure coefficient, including type I, type II and type III. The proposed model is verified by comparison of the obtained results from the proposed analytical method with the discrete element method as well as the actual drilling. It can be proved that the proposed model can predict accurately block slip. Additionally, the effect of drilling fluid pressures on the wellbore stability is specially investigated. The results show that with the increasing of drilling fluid pressure, the degree of wellbore collapse may be more severe. Meanwhile, the analysis method of reasonable drilling fluid pressure for coal drilling is proposed based on the interval theory, combining the slip area of blocks. Finally, the parametric study is focused on investigating the effects of the internal friction angle of face cleats, the cohesion of face cleats and the tensile strength of butt cleats on the failure coefficients of blocks.

Theoretical Investigations of the Influence of Defects Under Pulsed Mechanical Excitation of Concrete

Based on the developed physical and mathematical model of the electric response, parameters of electric signal from samples of concrete are theoretically calculated using apparatus of mechanics of continuous media. It is established that the presence of defects in the concrete causes changes in the amplitude-frequency characteristic of the calculated electric signal.

Study on the steady and transient pressure characteristics of shale gas reservoirs

The flow law was obtained by combining the mechanics of continuous media and molecular kinematics method for shale gas reservoirs with nano/micropores. The new non-linear seepage model considering the diffusion, slippage and desorption effects was established and simplified. The steady and transient governing equations were constructed on the basis of the non-linear model. The pressure characteristic analytical solution was then obtained. The permeability adjustment factor changes largely when the pore throat radius is less than 100 nm. Therefore, the flow law in nano/micropore departs significantly from Darcy's law. Numerical simulation results show that the flux of gas changes significantly with the permeability of the pore throat radius, and the flow in nano/micropore reservoir shows the microscale effect. Compared with the pressure distribution calculated by Darcy's law, the pressure distribution calculated by the new model decreases slowly because of the diffusion and desorption effect. The results provide a theoretical foundation for developing shale gas reservoirs.

Fluid Mechanics in Sommerfeld's School

Sommerfeld's affiliation with fluid mechanics started when he began his career as an assistant of the mathematician Felix Klein at Göttingen. He always regarded fluid mechanics as a particular challenge. In 1904, he published a theory of hydrodynamic lubrication. Four years later, he conceived an approach for the analysis of flow instability (the Orr-Sommerfeld approach) as an attempt to account for the transition from laminar to turbulent flow. The onset of turbulence also became a major challenge for some of his pupils, in particular Ludwig Hopf and Fritz Noether. Both contributed considerably to elaborate the Orr-Sommerfeld theory. Heisenberg's doctoral work was another attempt in this quest. When Sommerfeld published his lectures on theoretical physics during World War II, he dedicated one of the six volumes to the mechanics of continuous media. With chapters on boundary layer theory and turbulence, it exceeded the scope of contemporary theoretical physics—revealing Sommerfeld's persistent appreciation of fluid mechanics. He resorted to Prandtl's Göttingen school of fluid mechanics in order to stay abreast of the rapid development of these specialties.

Method of molecular dynamics in mechanics of deformable solids

The basic principles of the method of molecular dynamics are analyzed. Symplectic difference schemes for the numerical solution of molecular dynamics equations are considered. Stability is studied, and the errors in the energy conservation law, which are induced by using these schemes, are estimated. Equations of mechanics of continuous media are derived by means of averaging over the volume of an atomic system. Expressions for the stress tensor are obtained by using the virial principle and the method of averaging over the volume. The principles of construction of EAM and MEAM potentials of atomic interaction in crystals are analyzed. Two problems of fracture of copper-molybdenum composites are solved by the method of molecular dynamics.

Strain localization peculiarities and distribution of acoustic emission sources in rock samples tested by uniaxial compression and exposed to electric pulses

Strain localization peculiarities and distribution of acoustic emission sources in rock samples tested by uniaxial compression and exposed to electric pulses

Theoretical and Experimental Study of Strain Localization and Energy Dissipation at Fatigue Crack Tip

This work includes both experimental and theoretical studies of crack propagation under cyclic loading. The theoretical part is devoted to the description of energy balance under plastic deformation based on the results of statistical model of mesodefect ensemble proposed in the Institute of continuous media mechanics UB RAS and application of this model to the calculation of strain energy distribution at crack tip. The experimental part of the work is devoted to the study of the temperature evolution at crack tip with high spatial and time resolution. The thermodynamic measurement was combined with study of strain field at crack tip based on the digital image correlation technique. The analysis of experimental data allows us to determine the evolution of plastic deformation zone and dissipation energy at the crack tip.

Some Thoughts on Logic and Intuition in Science and Chemical Engineering

The role of the logic and intuition in the chemical engineering is presented. Basic rules of logic in chemical engineering are used: “Construction of mathematical models of chemical engineering structures use the general rules (approximations) of the continuous media mechanics” and “A full correspondence between physical effects and mathematical operators (in the form of functions and their derivatives) in the mathematical models”. The basic mathematical operators as gradient, divergence and Laplace operator are associated with the physical effects in the models. The intuition-judgments in the chemical engineering are the axioms as “Stokes postulate for the linear relationship between stress and strain rate”, “linear relationship between the diffusion flux and the concentration gradient (Fick’s first law)”, “linear relationship between heat flux and temperature gradient (Fourier’s first law)”. The intuition-judgments (axioms) of the linear and non- linear mass transfer theories are presented too.

Mathematical modeling of residual stresses and distortions induced by gas nitriding of 32CrMoV13 steel

The aim of this paper is to provide a model simulating the nitriding of 32CrMoV13 low alloy steels. The model is based on thermodynamics of irreversible processes and chemical kinetics. The mechanical approach is based on the mechanics of continuous media and considers an elasto-viscoplastic constitutive law. A self-consistent scale transition scheme establishes the link between chemical and mechanical calculations. The simulation describes the diffusion of nitrogen and carbon, the main precipitations with the associated volume changes, the residual stresses developed during treatment, and the distortions of complex structural parts. It enables evaluating the macroscopic volumetric eigenstrains, the thermal strain and the variation of Young’s modulus induced by the treatment. The problem is solved by Finite Element calculations. The unknown inputs of the model are identified through an inverse method using different kinds of experimental data such as nitrogen and carbon mass fractions, distortions and residual stresses. Flat and cylindrical samples are employed for that purpose. These specimens are gas nitrided during 120h at 550°C. The simulation program is finally validated on a sample of complex geometry treated in the same conditions. The distortions predicted by the model are therefore compared to results of measurements carried out by 3D full-field optical scanning.

Mathematical modeling of metallochemical reactions in a two-species reacting disperse mixture

A heterogeneous model of gasless combustion of binary disperse systems is proposed. The model combines the description of microscale processes of interphase interaction in the cell of the mixture with the macroscale description, which allows physicochemical transformations to be described on the basis of the continuum approach of mechanics of continuous media and the phase composition of the final products to be calculated. Schemes of metallochemical reactions of formation and decomposition of intermetallic phases are proposed, based on an analysis of the state diagram of the Ni-Al system. A problem of SHS wave propagation and evolution of the spatial distribution of concentrations of intermetallic phases during combustion of a mixture of Ni and Al powders is solved numerically. A two-wave structure of the combustion wave is obtained, and comparisons with experimental data are performed.

Special features of high-speed projectile interaction with barriers protected by a water layer

The stress–strain state (SSS) of projectiles is investigated when a high-speed projectile enters water and interacts with barriers protected by a water layer. Experimental investigations are carried out using a high-speed ballistic setup. Calculations are performed within the framework of mechanics of continuous media for an elastic plastic model of a solid with allowance for fracture and hydrodynamic water model. Depending on the projectile speed, different SSS regimes are observed: from small deformed at a speed of ≈1 km/s to fractured at a speed of ≈2 km/s. Calculation technique allows distances in water to be determined at which the metal barrier can be punched for the inertial model.

A constitutive model of shape memory alloy with temperature memory effect

Temperature memory effect occurring in some shape memory alloys has potential values in various fields such as smart materials and structures, and so on. It is of theoretical and practical interests to develop a new constitutive model of shape memory alloy to overcome the limitation that the previous constitutive models of shape memory alloy failed to express the temperature memory effect of shape memory alloy. This paper focuses on the foregoing issue based on the previous work of the authors. A new shape memory equation is developed to describe the relationship of shape memory factor, stress and temperature in shape memory alloy using the differential relationship of phase transformation free energy and martensitic volume fraction and the concept of shape memory factor defined by the author of this paper. A new mechanical constitutive equation is developed to predict the relationship of strain, stress and temperature in shape memory alloy based on the thermodynamics and continuum medium mechanics. The supposed constitutive model of shape memory alloy, which includes the new shape memory equation and new mechanical constitutive equation, is able to overcome the limitation that previous constitutive models of shape memory alloy failed to express the temperature memory effect of shape memory alloy. This work can provide a theoretical basis for the practical applications of temperature memory effect of shape memory alloy in various fields.

Current Models of Dynamic Deformation and Fracture of Condensed Matter

The main types (groups) of models of deformation and the fracture, used for the solution of problems of dynamic and shock wave deformation of materials, are considered. All models are divided into three main groups: macroscopic (models of mechanics of continuous medium), microstructural (based on the description of evolutions of ensemble of defects ) and atomistic (are used in calculations by methods of molecular dynamics and quantum mechanics). The short characteristic of models of the listed groups is given. Some approaches to development of the most perspective multilevel models are described. The simple test for applicability of models for the description of shock and wave processes are offered. Approaches to the description of destruction of materials and used at this criterion are considered. The perspective directions of development of models of dynamic deformation and fracture are suggested.

Relation between the electric response and the characteristics of elastic waves under shock excitation of heterogeneous dielectric materials with piezoelectric inclusions

A physicomathematical model is proposed for the electric response to elastic shock excitation of piezo-containing heterogeneous materials. The parameters of the electric signal under a pulsed action on a dielectric sample containing a piezoelectric inclusion are calculated theoretically using the apparatus of the mechanics of continuous media, and the conformity to experimental results is observed.

Lifting regimes of thermal plumes in vertical layer

Theoretical investigation of the dynamics of free thermal plumes in a thin vertical layer has been performed for the case of a cavity heated from below by means of a dotted thermoelement. Three-dimensional numerical modeling has been carried out with the help of package OpenFOAM. This integrable platform is meant for calculations in the area of continuous media mechanics. Four basic plume growth types (viscous-diffusive, inviscid-diffusive, viscous-nondiffusive and inviscid-nondiffusive regimes) are found. Animated images for various lifting regimes are obtained to observe the time-dependent behavior of thermal plumes. The stages of plume formation in a relatively thin layer, its steady lifting and deceleration by the top boundary have been analyzed for different profiles of the plume front. The interaction of two synchronous plumes is studied numerically, and the formation of a common thermal front is demonstrated.

The co-divergence of vector valued currents

In the context of stress theory of the mechanics of continuous media,a generalization of the boundary operator for de Rham currents---theco-divergence operator---is introduced. While the boundary operatorof de Rham's theory applies to real valued currents, the co-divergenceoperator acts on vector valued currents, i.e., functionals dual todifferential forms valued in a vector bundle. From the point of viewof continuum mechanics, the framework presented here allows for theformulation of the principal notions of continuum mechanics on a manifoldthat does not have a Riemannian metric or a connection while at thesame time allowing irregular bodies and velocity fields.

Rheological aspects of multilayer materials

The issues related to renewal of worn-out parts of a rolling stock with the layered coatings are considered in the article. In developing a mathematical model of wearing a multilayer material as an object of rheology certain assumptions, which enable using the methods of mechanics and mechanics of continuous medium, are done.

Geometry of a quasilinear system of two partial differential equations of the 1st and 2nd order in two functions of two independent variables

Introduction. In 1904–1905, the paper [5] of French mathematician E. Cartan was published. In Moscow State University (MGU), the ideas of Cartan were applied by Prof. S. P. Finikov [7], and also by his students G. F. Laptev, A. M. Vasil’ev, and many others. In the 40s–80s of the 20th century, in Moscow State University and in other colleges inside Russia and outside Russia, representatives of geometers of these scientific schools worked. In Moscow State University, there was the scientific workshop on theory of differential-geometric structures chaired by A. M. Vasil’ev. The work [17] is one of the first works devoted to the geometry of three partial differential equations (in two independent variables) that reduce to a system of three exterior differential equations of the second degree in a five-dimensional manifold. This work considers a wide range of problems related to differential-geometric structures should be noted. The description of intermediate integrals, the invariant linearizability criteria of the system considered, the methods for finding conservation laws and their use for reducing systems to simpler ones, and also the illustration of all this via examining the classical systems of continuous medium mechanics. A considerable part of these results was generalized by Kh. O. Kil’p [8–10] to quasilinear systems of n equations with n unknowns and two independent variables. The corresponding structures are no longer g-structures, as in the cases n = 2, 3. However, it was revealed that the method for their studying was not more complicated than that for g-structures. Kh. O. Kil’p also studied systems of three first-order partial differential equations without additional conditions [8] and a number of special problems referring to particular classes of quasilinear systems [9], and others. In the works of E. M. Kan, the case of a quasilinear system of four equations with pairwise coinciding characteristics was considered in detail, and in the works [13, 14] of L. N. Orlova, the case of a system of two equations, one of which contains first-order partial derivatives and the other firstand secondorder partial derivatives, was considered.

Damage Analysis on a Frame Structure under Repeatedly Blasting Vibration

Blasting is a conventional technique for mining, but structures adjacent to open pit mines are often damaged by blasting vibration, therefore, durability and safety of these structures are affected. Damage characteristics of a three-floor frame structure on the top of an open pit mine under repeatedly blasting vibration is studied in this paper. The damage model of structural members is made based on the theory of damage mechanics of continuous medium, and an overall damage model of the structure is also established by the method of frequency. The results showed that the Young’s modulus, frequency of the structure decreased as increasing of the blasting times, the damage factors of structural members are bigger than that of the structure; the strength of the structure decreased greatly under repeatedly blasting vibration, the strength of the structure is low. The durability of structures is affected, but the structure will not collapse. The research is helpful for blasting control in open pit mines and design on structures adjacent to open pit mines.