The textbook outlines the fundamentals of kinematics, theory of deformation, dynamics and thermodynamics of a continuous medium. The derivation of integral and differential conservation equations, as well as equations on discontinuity surfaces, is presented. The basics of tensor calculus and the theory of dimensions and similarity are given. Theoretical concepts are used to derive the basic equations of hydrodynamics, the theory of elasticity and plasticity, the theory of turbulence and multiphase media. The kinetic theory of rarefied gases is considered in detail.

Designed for undergraduate and graduate students of mechanics and mathematics, physics and physics and technology faculties of universities, as well as researchers working in the field of physics, mechanics, energy and technology development.

ContentsUse the arrow to expand or collapse this sectionDesignations of physical and mathematical quantitiesContinuum medium and its kinematicsBasic hypotheses. Model of a continuous medium (continuum). Material point and fields in continuum mechanics. Lagrangian description of the motion of a continuous medium. Eulerian description of the motion of a continuous medium. Scalar, vector and tensor fields. Differentiation by spatial coordinates and time. Steady, unsteady and potential movements. Stream line and trajectory. Strain tensor. Strain rate tensor. Equation of conservation of mass (continuity). Fundamentals of continuum dynamics. Forces and stressesForces and the corresponding fields in the MSS. Stress tensor. Equation of momentum of a continuous medium at a point. Equation of angular momentum. Principal stresses, principal axes of the stress tensor, normal and tangential stresses. Geometric representations of the stress state. Substantial time derivatives for the stress tensor. Differential equations of continuum mechanics in curvilinear coordinates. Integral, differential equations and equations on discontinuity surfaces following from conservation laws. Three theorems for integrals over volumes and their boundary surfaces from differentiable ones. functions. Integral and differential equations for the conservation of mass. Integral and differential equations for the conservation of momentum. Integral and differential equations for the conservation of angular momentum. Integral and differential equations for the conservation of total energy. Differential equations for internal energy - the first law of thermodynamics. Integral and differential equations for internal energy and entropy. General form of differential and integral conservation equations in continuum mechanics. Conservation equations on the surface of a discontinuity in a continuous medium. Shock discontinuity surface (shock shock). Shock adiabatic. Non-classical discontinuity surfaces. Classical theories of fluid and gas mechanics and solid deformable body System of equations of mass and momentum. Ideal liquid and gas. Potential (irrotational) flow of an ideal incompressible fluid. Linearly viscous and linearly elastic media. Linearly viscous isotropic fluids. Navier-Stokes law. Hydrostatics. Thermal conductivity in a stationary medium. Hooke's law for an isotropic linearly elastic medium. Theory of plasticity. Dislocation kinetics of plastic deformation. Propagation of small one-dimensional disturbances in an ideal fluid (linear theory). The theory of functions of a complex variable for the analysis of linear waves in a dissipative medium (using the example of a viscous compressible fluid or gas). Small disturbances in an isotropic linear-elastic medium. Differential equations of mass and momentum for one-dimensional motions with a plane , cylindrical and spherical symmetries. Spherical bubble in a liquid. Thermodynamics of a continuous medium. Basic principles of thermodynamics. The first law of thermodynamics. Entropy and the Carnot cycle for a perfect gas. The second law of thermodynamics. Entropy for a two-parameter liquid or gas. The second law of thermodynamics and entropy for multi-parameter media. Entropy and equations of state for two-parameter liquids and gases. Experimental method for determining equations states for two-parameter liquids or gases. Equations of state of ideal compressible media. Multicomponent multi-velocity continuum for describing mixtures. Thermodynamics of mixtures with physicochemical transformations. Mixture of gases. Energy conversion during physicochemical transformations. Thermodynamics of irreversible processes in single-component media. Thermodynamics of irreversible processes with chemical reactions and diffusion. The third law of thermodynamics. Multiphase media and turbulent flows. Main assumptions. Equations describing micromotion in heterogeneous media. Averaging in continuum mechanics. Averaged conservation equations for individual phases. Equations of turbulent flow of a viscous fluid. Equations of the mechanics of a collisionless monodisperse mixture. Liquid with gas bubbles. Porous medium saturated with liquid or gas. Equations of hydrodynamics of the ocean. Statistical dynamics of gases Rarefied gas. Distribution function and averaged parameters. Flow vectors. Boltzmann's equation. Boltzmann's H-theorem. Maxwell's distribution function and thermodynamic equilibrium. Initial and boundary conditions for the distribution function. Chapman's method — Enskog. Conservation equations and transfer equations. Analysis of the dimensions of physical quantities. Systems and classes of systems of units of measurement. Analysis of the dimensions of physical quantities. Defining parameters and the transition to dimensionless variables. Physical similarity. Application of the method of dimensional theory to the analysis of processes in the flow past unchanging bodies. Self-similar solutions in explosion theory. Application. Basics of tensor calculus Appendix. Generalized δ-function Dirac References. Subject index.