Interaction of a one-dimensional unloading wave with an elastoplastic boundary in an elastoviscoplastic medium

This paper presents a solution of the boundary-value problem of the theory of large elastoviscoplastic strains for the development of viscoplastic flow in a heavy layer of material located on an inclined plane and subjected to loading at the free surface with subsequent instantaneous removal of the load. This discontinuous change in the boundary conditions gives rise to a surface of strain discontinuity propagating in the medium and called an unloading wave. The reflection of the wave from the elastoviscoplastic boundary and its motion after reflection from the fixed plane and the free surface are considered.     

Penetration of a body of revolution into an elastoplastic medium

We consider a model of spatial motion of a body of revolution in a weak soil-type medium with nonsymmetric flow separation taken into account. We obtain a system of equations describing the entry and penetration of a thin body into a half-space. We calibrate the model by comparing it with experiments on penetration of thin cones into plasticine. Test computations show that the model describes complex body motion trajectories for various angles of entry into the target with adequate accuracy.     

Reliable solutions to the problem of periodic oscillations of an elastoplastic beam

We consider time-periodic oscillations of a beam with a spatially inhomogeneous Prandtl–Ishlinskii constitutive law describing the elastoplastic hysteresis. The data (mass density, Prandtl–Ishlinskii distribution, external load) are assumed to be uncertain. It is shown that a unique solution exists and is stable with respect to the data variation. Considering the total dissipated energy as a measure for the accumulated material fatigue, we identify and estimate from above the ‘worst scenario’ case, where the dissipation over one period is maximal within an admissible set of data obtained from inaccurate measurements.     

Spectrum of normal oscillations of a dislocation ensemble in a viscoplastic medium

Dynamic equations of a dislocation ensemble are derived within the framework of the gauge model of an elastic body with defects. The governing relation between the defect field and the material continuum is obtained with allowance for the analogy between the equations obtained and Maxwell's electrodynamic equations. In the phenomenological theories of plasticity, this relation corresponds to the definition of a viscoplastic body. The dispersion relations and configurations of the normal oscillations of a dislocation ensemble in a viscoplastic medium are calculated. Institute of the Physics of Strength and Materials Science, Siberian Division, Russian Academy of Sciences, Tomsk 634821. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1. pp. 182–185, January–February, 2000.     

A geometrical model of the defect structure of an elastoplastic continuous medium

We consider a new class of elastoplastic models which are based on the assumption that internal interaction between the continuum particles has affine-metric geometrical structure. From the physical viewpoint, the affine-metric objects are intrinsic thermodynamic variables which describe the evolution of various defect structures in a deformable material and also interaction between themselves and with the field of reversible strains. The analysis performed allows one to establish a relation between the classical mechanical characteristics of elastoplastic materials and the field of dislocation density and other types of defects. Institute of Automatics and Control Processes, Far-Eastern Division, Russian Academy of Sciences, Vladivostok 690041. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 163–173, March–April, 1999.     

Stability of spatial motion of a body of revolution in an elastoplastic medium

A previously constructed model that describes the spatial motion of a body of revolution in an elastoplastic medium (without flow separation and with nonsymmetric separation of the medium flow taken into account) is used to study the Lyapunov stability of rectilinear motion of a body in the case of frozen axial velocity on a half-infinite time interval. Some stability criteria are obtained and the influence of tangential stresses is analyzed.     

Direct and inverse problems of oscillations of an elastoliquid layered medium

A plane problem of forced oscillations of an ideal compressible liquid bounded from above by an elastic layer with a rough lower surface and an inverse geometric problem of determining the shape of the rough lower surface of an elastic layer from the wave characteristics on the upper surface are considered. Three methods are used to solve the direct problem: the small parameter method, the boundary element method, and the Born approximation. Solving the inverse problem is reduced to solving the integral Fredholm equation of the first kind. Results of a numerical experiment are presented.     

The biaxial tension of an elastoplastic space with a prismatic inclusion

The problem on the elastoplastic state of a thick isotropic plate (the case of plane deformation) is solved. A larger prismatic inclusion is made a close fit in a polygonal hole in the plate. The plate is stretched at infinity by constant mutually perpendicular forces. The problem is solved by the small-parameter method and by the theory of ideal plasticity. The axisymmetric state of the plane with a circular hole stiffened by a round ring with a constant force applied to its inner contour is considered as a zero approximation. Some specific shapes of the hole and reinforcing elastic rigid ring are considered. Voronezh University, Russia. Translated from Prikladnaya Mekhanika, Vol. 36, No. 6, pp. 114–120, June, 2000.     

Buckling of an elastoplastic bar

Buckling of a bar of an elastoplastic material is studied. It is shown that for any (σ-?) diagram of the bar material, the limit load (the longitudinal external force) in dimensionless variables that the bar can withstand does not exceed the current bending stiffness of the most loaded (in terms of the bending moment) section.     

Hardening of an elastoplastic body

The purpose of the experimental investigations whose results are described here is to study plastic states in which loading occurs in some directions and unloading in others, and also to verify the applicability of the plastic strain schemes proposed in [1,2] for these states. The existence of an angular point on the loading surface is detected. The influence of the loading path on the development of this point is investigated. A load of biaxial tension type was produced in a 45KhN steel-pipe specimen subjected to internal pressure and an axial force. The ratio between the principal stresses hence varied, but the principal directions of the stress tensor remained fixed in the body of the specimen.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 144–148, May–June, 1976.The author is grateful to E. I. Shemyakin for supervising the research, and to V. M. Zhigalkin, G. F. Bobrov, and N. S. Adigamov for taking part in performing the tests.     

Mechanical model of an elastoplastic body

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 136–144, September–October, 1989.