Allowance for complex loading in transversely isotropic solids

A model of plasticity for a transversely isotropic material with allowance for complex loading is developed, based on results of experiments with homogeneous cylindrical specimens of isotropic materials. An empirical model of plasticity for isotropic metals is constructed with allowance for vector properties of the material. The model is extended to a particular case of anisotropy. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 128–133, January–February, 2009.     

Axisymmetric thermoelastoplastic stress-strain state of transversely isotropic laminated shells

The method of successive approximations is used to determine the thermoelastoplastic stress-strain state of isotropic and transversally isotropic laminated shells of revolution under axisymmetric loading. Hill’s theory of plasticity with isotropic hardening is used to describe the deformation of transversely isotropic materials, while the theory of deformation along paths of small curvature is used to describe the deformation of isotropic materials. The elastoplastic stress-strain state of a two-layer cylindrical shell under mechanical and thermal loads is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 71–80, June 2006.     

Deformation model for brittle materials and the structure of failure waves

Constitutive equations that describe the experimentally observed failure waves are proposed to model inelastic strains of brittle materials. The complete system of equations is hyperbolic, each equation of this system has divergent form. The model is based on the assumption that continual failure is the process of transition from an intact state to a “fully damaged” state described by the kinetics of the order parameter. The structure of stationary traveling compressive waves is analyzed using a simplified model. It is shown that in a certain range of amplitudes, the wave splits into an elastic precursor and a failure wave. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 164–172, May–June, 2007.     

Ovsyannikov plane vortex: The equations of the submodel

A submodel of the equations of ideal magnetohydrodynamics is constructed that generalizes the classical motion of an ideal continuous medium with plane waves. It is shown that, in contrast to classical motion, in this submodel the velocity and magnetic-field vectors can change direction in a plane orthogonal to a distinguished spatial direction. The submodel is described by a system of equations with two independent variables and a finite relation specifying the orientation of the vector fields in space. The solutions of the submodel define substantially spatial processes and singularities in the motion of continuous media which cannot be studied in the classical one-dimensional formulation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 27–40, September–October, 2008.     

On the choice of coordinates in the analysis of plane plastic strain

The plane strain of an ideal rigid-plastic medium is studied in curvilinear coordinates. The methods used to solve the equations of plasticity were considered in [1–3]. Curvilinear orthogonal coordinates with the introduction of a metric function were used in [4, 5].     

Radial expansion of a granular medium in spherical and cylindrical layers

An exact solution that describes the fields of displacements and stresses in an expanding spherical layer is constructed within the framework of the theory of small strains of a granular medium with rigid particles. For finite strains, the problem reduces to a nonlinear system of ordinary differential equations, which is solved by numerical methods. Similar solutions are found in the problem for a cylindrical layer. Based on these solutions, the effect of the dilatancy of the granular medium on the stress-strain state near expanding cavities is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 190–196, May–June, 2009.     

Gas-dynamic analogy for vortex free-boundary flows

The classical shallow-water equations describing the propagation of long waves in flow without a shear of the horizontal velocity along the vertical coincide with the equations describing the isentropic motion of a polytropic gas for a polytropic exponent γ = 2 (in the theory of fluid wave motion, this fact is called the gas-dynamic analogy). A new mathematical model of long-wave theory is derived that describes shear free-boundary fluid flows. It is shown that in the case of one-dimensional motion, the equations of the new model coincide with the equations describing nonisentropic gas motion with a special choice of the equation of state, and in the multidimensional case, the new system of long-wave equations differs significantly from the gas motion model. In the general case, it is established that the system of equations derived is a hyperbolic system. The velocities of propagation of wave perturbations are found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 8–15, May–June, 2007.     

Qualitative Distinctions in the Solutions Based on the Plasticity Theories with the Mohr-Coulomb Yield Criterion

The following two models of the plasticity theory are considered: the model with the Mohr-Coulomb yield criterion and the classical model of the plasticity theory with a yield criterion independent of the mean stress. The deformation problem of a plastic layer enclosed between two rotating plates is studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 136–145, November–December, 2005.     

Plastic macrodeformation of polycrystalline and submicrocrystalline titanium for biomedical applications

The deformation behavior of commercially pure submicrocrystalline and coarse-grained titanium was studied at the macroscopic level. Stress-strain curves of the materials were analyzed. Time-space distributions of local strains were studied at all stages of strain hardening using speckle interferometry. The life time of test specimens of the materials and the coordinates of the fracture region were calculated theoretically and confirmed experimentally. The motion of the zones of localized plasticity was studied. The prefracture stage was shown to involve “condensation” of the zones of localized plasticity and migration of deformation to the fracture neck. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 164–172, May–June, 2008.     

Biaxial Testing of Sheet Materials at High Strain Rates Using Viscoelastic Bars

A dynamic bulge testing technique is developed to perform biaxial tests on metals at high strain rates. The main component of the dynamic testing device is a movable bulge cell which is directly mounted on the measuring end of the input bar of a conventional split Hopkinson pressure bar system. The input bar is used to apply and measure the bulging pressure. The experimental system is analyzed in detail and the measurement accuracy is discussed. It is found that bars made of low impedance materials must be used to achieve a satisfactory pressure measurement accuracy. A series of dynamic experiments is performed on aluminum 6111-T4 sheets using viscoelastic nylon bars to demonstrate the capabilities of the proposed experimental technique. The parameters of the rate-dependent Hollomon–Cowper–Symonds J2 plasticity model of the aluminum are determined using an inverse analysis method in conjunction with finite element simulations.     

Isotropic hardening in micropolar plasticity

Experimental evidence for length scale effects in plasticity has been provided, e.g., by Fleck et al. (Acta Metall. Mater. 42:475–487, 1994). Results from torsional loadings on copper wires, when appropriately displayed, indicated that, for the same shear at the outer radius, the normalized torque increased with decreasing specimen radius. Modeling of the constitutive behavior in the framework of micropolar plasticity is a possibility to account for length scale effects. The present paper is concerned with this possibility and deals with the theory developed by Grammenoudis and Tsakmakis (Contin. Mech. Thermodyn. 13:325–363, 2001; Int. J. Numer. Methods Eng. 62:1691–1720, 2005; Proc. R. Soc. 461:189–205, 2005). Both isotropic and kinematic hardening are present in that theory, with isotropic hardening being captured in a unified manner. Here, we discuss isotropic hardening composed of two parts, responsible for strain and gradient effects, respectively.     

Dynamic compaction model for a granular medium

A model for dynamic compaction of granular medium is proposed for the case in which the external action far exceeds the yield strength of the material. A radial axisymmetric compaction problem is solved for a granular medium with nanosize structure in the presence of a rigid rod at the symmetry axis. Simulated data are compared with experimental data on magnetic pulsed compaction of oxide nanopowders. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 211–215, March–April, 2008.     

Plastic Constants of Fracture

Based on the theory of an ideal rigid-plastic body, an approach is formulated for determining fracture constants on the basis of standard mechanical tests on uniaxial extension of plane and cylindrical samples. Instead of the experimentally determined characteristics of fracture of materials (dimensionless elongation and constriction of the sample during its fracture), two invariant tensor characteristics of the degree of sample deformation are introduced, which correspond to the moment of origination of a macrocrack and critical strain at the crack tip determining the process of crack propagation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 147–155, March–April, 2006.     

Modeling non-equilibrium traffic dynamics in a Lagrangian framework

In this paper, we propose a formulation for modeling macroscopic traffic flow using a modified speed–density relationship. The flow model consists of a nonlinear hyperbolic system of conservation laws. The proposed modification distinguishes between acceleration and deceleration by assuming a different equilibrium velocity for a given traffic density based on whether a platoon of vehicles is accelerating or decelerating. We examine the appropriateness of this modification to two prominent traffic flow models in a Lagrangian reference frame, which we solve computationally. We show that a Lagrangian coordinate system is ideal for the incorporation of the proposed modification due to its ability to track the behavior of moving vehicles. We see that the modification is particularly well suited to “second order” models.     

Plane waves in a heavy two-layer liquid excited by a cylinder moving at an angle to the horizontal

A solution of an initial-boundary-value problem for a system of integrodifferential equations which describes the plane waves excited in an initially stationary heavy two-layer ideal fluid by a cylinder moving at an angle to the horizontal is investigated. The homogeneous fluid fractions of different densities are assumed to be separated by an evolving fluid interface (horizontal plane, if the liquid is at rest). An approximate solution of two problems for the waves excited by a cylinder moving with a constant acceleration and an oscillating cylinder is constructed analytically. Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–152, July–August, 1998.     

Theories of ideal plasticity with a singular yield surface

Specific features of the theories of ideal plasticity which are based on the Tresca yield criterion and the maximum reduced stress criterion are discussed. An analysis is carried out in terms of the canonical basis of the deviatoric stress tensor. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 181–188, March–April, 1999.     

One plasticity model for problems of plastic metal working

Scalar and tensor models of plastic flow of metals extending plasticity theory are considered over a wide range of temperatures and strain rates. Equations are derived using the physico-phenomenological approach based on modern concepts and methods of the physics and mechanics of plastic deformation. For hardening and viscoplastic solids, a new mathematical formulation of the boundary-value plasticity problem taking into account loading history is obtained. Results of testing of the model are given. A numerical finite-element algorithm for the solution of applied problems is described. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 159–169, November–December, 2008.     

Shallow-water equations with dispersion. Hyperbolic model

A hyperbolic shallow-water model is constructed with allowance for nonlinear and dispersive effects. The model describes solitonlike solutions in a range of wave velocities and predicts the breaking of smooth waves when the limiting amplitude is attained. The model is found to be adequate by comparison with experimental data on the evolution of a wave packet generated by the moving lateral wall of a channel. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 40–46, March–April, 1998.     

Stability of tribotechnical laminated coatings subjected to tracing loads

The problems of surface stability of laminated coatings subjected to the combined effect of tracing surface loads and a stationary temperature field is considered. The material of the layer and the base are considered linearly elastic and trasversally isotropic. Fulfillment of conditions of absolutely rigid force and ideal contacts are assumed between the individual elements of the laminar medium. The subcritical stress state of the laminar medium under consideration is piecewise-homogeneous. Interbranch Engineering Center “Tribotekhnika”, Dnepropetrovsk, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 6, pp 32–38, June, 1999.     

Differential constitutive equations of incompressible media with finite deformations

A method is proposed for constructing a system of constitutive equations of an incompressible medium with nonlinear dissipative properties with finite deformations. A scheme of the mechanical behavior of a material is used, in which the points are connected by horizontally aligned elastic, viscous, plastic, and transmission elements. The properties of each element of the scheme are described with the use of known equations of the nonlinear elasticity theory, the theory of nonlinear viscous fluids, and the theory of plastic flow of the material under conditions of finite deformations of the medium. The system of constitutive equations is closed by equations that express the relation between the deformation rate tensor of the material and the deformation rate tensor of the plastic element. Transmission elements are used to take into account a significant difference between macroscopic deformations of the material and deformations of elements of the medium at the structural level. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 158–170, May–June, 2009.