Conditions for Development of Cavitation in Scleronomous Media

An energy inequality that determines the conditions for development of cavitation in scleronomous media in the range from liquid (bitumens, paints, and gels) to solid (lead, aluminum, copper, etc.) plastic media is constructed upon pulse tension in terms of the viscoelastic–plastic model. A relation that allows one to determine the time of negative–pressure relaxation during the growth of cavitating pores in a medium is derived. With allowance for the previously obtained conditions for development of bubble cavitation in a relaxing field of negative pressure in shock wave–loaded liquids, this result allows one to separate a class of condensed media capable to cavitate under pulse loading.     

On equilibrium stability of an elastic-viscoplastic medium

We consider the stability of an elastic-plastic medium when one part of the body is in an elastic state and the other part in a plastic state.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 86–92, September–October, 1970.     

Rheological model of volume stretching of newtonian liquids

An equation of state for a volumetrically stretched cavitating liquid medium that holds in the entire span of volume concentrations of bubbles ranging from cavitation nuclei to the stage of formation of a cellular foam structure is obtained based on a proposed macrorheological model. The dependence of the modulus of volume elasticity of a liquid on the volume concentration of bubbles is plotted, and a method for estimating the relaxation time for tensile stresses in cavitating liquid media is proposed. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 35–46, January–February, 1998.     

Modeling and computation of cavitation in vortical flow

The paper presents an investigation of Euler–Lagrangian methods for cavitating two-phase flows. The Euler–Euler methods, widely used for simulations of cavitating flows in ship technology, perform well in regions of moderate flow changes but fail in zones of strong, vortical flow. Reasons are the strong approximations of cavitation models in the Euler concept. Alternatively, Euler–Lagrangian concepts enable more detailed formulations for transport, dynamics and acoustic of discrete vapor bubbles. Test calculations are performed to study the influence of different parameters in the equations of motion and in the Rayleigh–Plesset equation for bubble dynamics. Results confirm that only Lagrangian models are able to describe correctly the bubble behavior in vortices, while Eulerian results deviate strongly. Lagrangian formulations enable additionally the determination of acoustic pressure of cavitation noise. Two-way coupling between the phases is required for large regions of the vapor phase. A new coupling concept between continuous fluid flow and discrete bubble phase is developed and demonstrated for flow through a nozzle. However, the iterative coupling between the phases via volume fractions is computationally expensive and should therefore be applied only in regions where Eulerian treatment fails. A corresponding local concept for combination with an Euler–Euler method is outlined and is in progress.     

Local instability of horizontal tunnels of polygonal shape in viscoelastoplastic masses

The local instability of a horizontal mine tunnel with a regular polygonal cross section in a viscoelastoplastic rock mass is studied within the framework of the exact three-dimensional stability equations. The effect of rock-mass parameters on the critical pressure is estimated.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 141–150, March–April, 2005.     

Localized viscoelastoplastic strain in mesovolume of heterogeneous medium under different loading types

The localized viscoelastoplastic strain in the mesovolume of heterogeneous media under quasi-static and dynamic loading is investigated. The generalized Bingham–Shwedov model is used; it consists of a combination of Dragon–Mroz's for elastoplasticity and Maxwell's model of viscoelasticity. Any variational finite-difference scheme for solving the quasi-static problem of elastoplastic yielding of a heterogeneous solid can be taken into account. A modified Lagrange's variance equation for analyzing the stress–strain state can be described by the non-symmetric stress tensor. Approximation of spatial derivatives is made by using the twofold partition of spatial domain in tetrahedronal or three-angular (in two-dimensional space) unit cell of mesh-work. Finite difference for deformation is made use of in two or three space dimensions and time. Results for heterogeneous medium with complex form and large number of interior surfaces are obtained for quasi-static and dynamics problems.     

Variational method for solving problems of the plasticity of compressible media

Variational methods used in the theory of plastic flow are formulated on the assumption of the incompressibility of the deformable medium. In solving problems of the mechanics of soils and friable media and technological problems of the plastic shaping of uncompacted materials it is very important to take account of irreversible volumetric change. Extremum and variational theorems are proved in [1, 2] for rigid-plastic and viscoplastic expanding bodies. A variational equation equivalent to a complete system of differential equations is derived for a compressible plastic body.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 153–155, September–October, 1977.     

J-integral and crack driving force in elastic–plastic materials

This paper discusses the crack driving force in elastic–plastic materials, with particular emphasis on incremental plasticity. Using the configurational forces approach we identify a “plasticity influence term” that describes crack tip shielding or anti-shielding due to plastic deformation in the body. Standard constitutive models for finite strain as well as small strain incremental plasticity are used to obtain explicit expressions for the plasticity influence term in a two-dimensional setting. The total dissipation in the body is related to the near-tip and far-field J-integrals and the plasticity influence term. In the special case of deformation plasticity the plasticity influence term vanishes identically whereas for rigid plasticity and elastic-ideal plasticity the crack driving force vanishes. For steady state crack growth in incremental elastic–plastic materials, the plasticity influence term is equal to the negative of the plastic work per unit crack extension and the total dissipation in the body due to crack propagation and plastic deformation is determined by the far-field J-integral. For non-steady state crack growth, the plasticity influence term can be evaluated by post-processing after a conventional finite element stress analysis. Theory and computations are applied to a stationary crack in a C(T)-specimen to examine the effects of contained, uncontained and general yielding. A novel method is proposed for evaluating J-integrals under incremental plasticity conditions through the configurational body force. The incremental plasticity near-tip and far-field J-integrals are compared to conventional deformational plasticity and experimental J-integrals.     

Some geometrically nonlinear problems of deformation of inelastic plates and shallow shells

This paper considers geometrically nonlinear problems of deformation of elastoplastic shallow shells and viscoelastoplastic plates where it is required to find kinematic loads for a given time interval such that a shell (plate) acquires prescribed residual deflections after these loads are applied and then removed. For some constraints, the correctness of the corresponding formulations (uniqueness of the solution and its continuous dependence on the problem data) is shown and iterative solution methods are justified.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 151–157, March–April, 2005.     

On two-scale homogenized equations of the Ishlinskii type viscoelastoplastic body longitudinal vibrations with rapidly oscillating nonsmooth data

We study the initial-boundary value problems for a system of operator-differential equations describing Ishlinskii type viscoelastoplastic body longitudinal vibrations with rapidly oscillating nonsmooth coefficients and initial data. The main feature is an presence of hysteresis Prandtl–Ishlinskii operator. We rigorously justify the passage to the corresponding limit initial-boundary value problems for a system of two-scale homogenized operator-integro-differential equations, including the existence theorem for the limit problems. The results are global with respect to the time interval and the data. To cite this article: A. Amosov, I. Goshev, C. R. Mecanique 334 (2006).     

Defect nucleation in SOI wafers due to hydrogen ion implantation

Hydrogen ion implantation in the Smart-Cut production process leads to fracture of Si–Si bonds, formation of microcavities and splitting of a single-crystal silicon wafer. In the present paper, an analysis model for defect nucleation induced by hydrogen ion implantation is established based on the continuum mechanics theory accounting for the crystal structure of silicon. Using this model and probability theory, an analytical expression is derived to calculate the defect density as a function of the hydrogen ion implantation dose and the temperature.     

Nonlinear Antiplane Deformation of an Elastic Body

The antiplane elastic deformation of a homogeneous isotropic prestretched cylindrical body is studied in a nonlinear formulation in actual–state variables under incompressibility conditions, the absence of volume forces, and under constant lateral loading along the generatrix. The boundary–value problem of axial displacement is obtained in Cartesian and complex variables and sufficient ellipticity conditions for this problem are indicated in terms of the elastic potential. The similarity to a plane vortex–free gas flow is established. The problem is solved for Mooney and Rivlin—Sonders materials simulating strong elastic deformations of rubber–like materials. Axisymmetric solutions are considered.     

Elastic–plastic and elastic anti-plane shear of two parallel cracks

Two infinite interacting parallel cracks in an elastic–plastic and in an elastic body under anti-plane strain (mode III) loading conditions are considered. The body is subjected to vanishing remote loading and the cracks are traction free. Closed-form solution is found for the elastic–plastic problem in terms of elementary functions, where the shape of the plastic boundary is obtained. The complete stress distribution is obtained in an inverse form i.e. physical coordinates are functions of stresses.     

A penny-shaped cohesive crack model for material damage

A novel micromechanics based damage model is proposed to address failure mechanism of defected solids with randomly distributed penny-shaped cohesive micro-cracks (Barenblatt–Dugdale type). Energy release contribution to the material damage process is estimated in a representative volume element (RVE) under macro hydrostatic stress state. Macro-constitutive relations of RVE are derived via self-consistent homogenization scheme, and they are characterized by effective nonlinear elastic properties and a class of pressure sensitive plasticity which depends on crack opening volume fraction and Poisson’s ratio. Several distinguished features of the present model are compared with Gurson model and Gurson–Tvergaard–Needleman (GTN) model, showing that the proposed model can better capture material degradation and catastrophic failure due to cohesive micro-crack growth and coalescence.     

Study of the Effects of Thermomechanical Coupling Near Stress Concentrators in Viscoelastoplastic Bodies

A model is developed to investigate thermal effects in elastoviscoplastic bodies. It allows us to obtain some quantitative and qualitative information on the stress–strain state of a body and to carry out a nondestructive diagnostics of internal defects, which are stress and strain concentrators. The problem on the plane stress state of a rectangle with a hole is considered as an example. The plate is made of steel and aluminum alloy. The variation in the temperature on the external contour of the body under monotonous and cyclic tension in the elastic and plastic domains is studied     

Mesoscale plastic flow generation and development for polycrystals

The traditional yield criteria of plasticity such as Mises, Tresca, etc. make use of averaged macroparameters while mesomechanics consideration is based on the physical notion of plastic deformation mechanisms. They may involve the development of plastic shears on the surfaces and interfaces of internal structure elements involving stress concentration and relaxation. A criterion of plastic flow is proposed; it is based on the stress–strain state in a cell of computational grid as well as in the neighboring cells. An algorithm of plastic shear generation is developed for the progressive propagation of the plastic shears over the crystal. Test calculations of the crystal behavior under tension are made and the results are presented.     

Deformation of a flowing powder with nonviscous friction

A model for an ideally plastic body is extended to a powder medium with nonorthogonal slip lines; it is shown that some properties of the ideal-plasticity model are not essential and should not be generalized, namely, the coincidence between the characteristics for the velocity and stress distributions, and independence of the velocity distribution from the possible differences in the shears on the areas, A closed system of equations is derived, and the properties of the discontinuous solutions are discussed; boundary-value problems are formulated. It is shown that the stability-loss lines are arcs of circles (surface of a circular cylinder) in the case of bank stability.Translated from Zhurnal Prikladnoi Matematiki i Tekhnicheskoi Fiziki, No. 4, pp. 119–124, July–August, 1974.     

Deformation, stress state and thermodynamic force for a growing void in an elastic–plastic material

The growth of a spherical void in an elastic–plastic body, subjected to external pressure or tension and a gas pressure as well as a surface stress at the void surface, is investigated. The deformation, strain and stress state in the full body is presented. In addition, the local and global energy terms are calculated. Finally the total thermodynamic force on the void surface as well as the total dissipation are evaluated and compared allowing the calculation of the mechanical contribution to void growth due to diffusion of vacancies generated by plastification or irradiation.     

Calculating the calibration curves of high-pressure devices with profiled anvils

A determination of the calibration curves of high-pressure devices is presented on the basis of an approximate calculation of the stressed state of points in the median plane (with respect to height) of a thin layer of an ideal generalized plastic material, compressed between rigid profiled anvils. A specific relationship is derived for the angle between the greatest principal stress and the median plane as a function of height and it is assumed that slip, retardation, and stagnation zones occur in the contact region. Recommendations are made in order to determine the boundaries of the stagnation zone for the case of profiled anvils. The difference between the results of the calculation and experimental data is no greater than 8%.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 149–154, May–June, 1976.     

Perfect Plasticity Theory: State of the Art and Development Trends

The state of the art and development trends of model conceptions in perfect plasticity theory are overviewed. The paper does not consider limit equilibrium theorems, theory of optimum design and adaptability, flow problems in metal forming, dynamic behavior of rigid–plastic and elastic–plastic bodies, etc