Theory Of Ideal Plasticity Research Articles

Modelling of a production process of irreversible strains in a material of a thick-walled cylindrical tube under the influence of inner pressure

This article considers the processes of the accumulation of irreversible strains in an elastoviscoplastic material of a thick-walled cylindrical tube in the framework of small strains. The material is deformed under the action of uniform inner pressure changing with time. Irreversible strains accumulate in the material by means of two different mechanisms, namely creep and plastic flow. Initially, whereas stresses increase in the deformed body due to mechanical influence, irreversible strains are produced as creep strains because of the viscous material properties. When the stress state reaches a loading surface, the production mechanism of irreversible strains becomes plastic. When unloading, this sequence in the production mechanisms is opposite, i.e. the fast plastic mechanism is replaced by the slow viscous one. The continuity in the growth of irreversible strains is provided by the corresponding setting of creep and plastic potentials. The possibility of the use of these potentials in the form of piecewise linear functions is investigated. It makes possible to use the developed mathematical formalism of the ideal plasticity theory. The creep and plastic flow processes under increasing and constant inner pressures are considered. The unloading process and repeated plastic flow under decreasing inner pressure, the stress relaxation after the full removal of a loading force are investigated. The reversible and irreversible strains, stresses and displacements in the medium are calculated. The laws of the motion of elastoplastic boundaries in the cylindrical layer are determined.

The Ideal Plasticity Theory Usage Peculiarities to Concrete and Reinforced Concrete

The usage aspects of ideal plasticity theory for concrete and reinforced concrete are investigated. The plastic deformation is considered to be localized n thin layers on the failure plane which divides the element into rigid parts. The variation method is used and the solutions in discontinuous functions are received. The functional of virtual velocities principle is investigated to stationary condition, the minimal capability of plastic deformation is found with which the solid changes into the mechanism. The limit and realization criterion of concrete failure under shear are set. The reinforcement influence on the element load-carrying capacity is taken into account.

The design of concrete elements strength under local compression based on the variational method in the plasticity theory

The two-dimensional concrete elements under the action of one-sided central crushing often occurs. For them, the strength problems are solved on the basis of the concrete ideal plasticity theory variational method with application of discontinuous velocities functions. The method takes into account the influence on concrete elements strength the compressive strength and tensile strength of concrete. It also takes the ratio of a sample height to the crushing platform length and friction coefficient between a surface of element and a load punch if it’s necessary. The results of experimental researches were confirmed the assumed in the theoretical solution the kinematical schemes of elements failure. Higher convergence of theoretical strength with tested is received. The calculation sequence of the concrete element under one-sided central crushing is described. The joint calculation of all factors that determine the strength opens the possibility of more accurate assessment and improvement on its basis of structural solutions of concrete elements under the local compressive load.

Vibration of a prestressed tube in the presence of plastic zone

The paper is devoted to a problem of radial steady state vibrations for a tube taking into account the inhomogeneous residual stress (RS) field. According to the theory of ideal plasticity the RS field is caused by elastoplastic deformation due to the internal pressure and the further unloading process. Various RS distributions inside both elastic and plastic zones are described. A finding of displacement function is reduced to the numerical solving of the first-order differential equations. Within the framework of the acoustical method, the inverse problem for RS field identification is stated. On the basis of the free radial vibration problem for tube, we derived the formula for a dependency of eigenfrequency on RS distribution by using the linearization method. By using this formula for two different values of eigenfrequencies, we state the system of two equations to identify the plasticity zone radius and RS level. Examples of numerical solution of this system for different values of parameters (RS level and tube thickness) are demonstrated. The estimation accuracy of eigenfrequencies measurement for successful implementation of the proposed approach is given.

TASK ON INDENTATION OF SMOOTH PUNCH OF AN ARBITRARY FORM IN PLANE VIEW IN HARD PLASTIC HALF-SPACE

In the work the general properties of equations of spatial problem of the theory of ideal plasticity in the condition of Treska plasticity and stressed state that correspond to the ridge of surface of fluctuation are viewed. Singular lines in hard plastic space and solutions in the neighborhood of a singular line that are similar to the expansion in beam series are viewed. On the basis of the developed theory the boundary problem appearing at indentation of punch with smooth basis in a certain plastic body which in the simplest case is a half-space is solved.

On a mechanical analogy in the ideal plasticity theory

The Cauchy problem of propagation of plastic state zones in a boundless medium from the boundary of a convex surface, along which normal pressure and shear forces act, is considered. In the case of complete plasticity, the Tresca system of quasi-static equations of ideal plasticity, which describes the stress-strain state of the medium, is known to be hyperbolic and to be similar to a system that describes a steady-state flow of an ideal incompressible fluid. This system is numerically solved with the use of a difference scheme applied for hyperbolic systems of conservation laws. Results of numerical calculations are presented.

Analyticity of the solution of a plane elastoplastic problem

Elastoplastic problems of the theory of ideal plasticity were studied numerically by the method of small parameter in the monographs [1–3], and strengthening elastoplastic problems were studied in the monograph [4], where a rather complete bibliography of studies in this direction is given. The conditions for the continuous dependence of the the stress-strain state characteristics on the boundary conditions and the material inhomogeneity are defined using the implicit function theorem in [5, 6].

Linearized equations of spatial statically determinate states in the theory of ideal plasticity

In the present paper, we consider linearized statically determinate relations in the theory of ideal plasticity for the case in which the full plasticity condition does not hold. We analyze the type of the equations under study. We note that the linearized equations under the full plasticity condition were considered in [1–3].

Statically definable relationships in ideal-plasticity theory

Statically definable relationships in ideal-plasticity theory

On statistically definable relationshpis in ideal-plasticity theory

On statistically definable relationshpis in ideal-plasticity theory

On linearized equations of statically definable relationships in ideal-plasticity theory

On linearized equations of statically definable relationships in ideal-plasticity theory

The indentation of a flat punch into an ideal rigid-plastic half-space under the action of shear contact stresses

A general plane problem of the impression of a flat punch into a rigid-plastic half-space under the action of transverse and longitudinal shear contact stresses is considered. The condition of complete plasticity and the hyperbolic equations of the general plane problem of the theory of ideal plasticity [1] are used. The reduction of the limit pressure on the punch is determined as a function of the shear contact stresses.

A GENERALIZATION OF GALIN'S PROBLEM IN THE THEORY OF IDEAL PLASTICITY

A perturbation method with a non-axially symmetric initial approximation is used to solve the problem of ideal plasticity theory involving the stretching-compression of a medium with a circular hole when the plastic subregions partially span the contour of the hole and are not in contact with one another.

On features of relations for a general two-dimensional problem in the ideal-plasticity theory

On features of relations for a general two-dimensional problem in the ideal-plasticity theory

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.

Effective field method in ideal plasticity theory for composite materials

Effective field method in ideal plasticity theory for composite materials

Application of structural representations to the solution of boundary-value problems of ideal plasticity

The method of successive approximations is proposed for solving plane problems of the theory of ideal plasticity, based on structural representations. By using this method the state of stress is determined in an infinite plane with a circular hole for an arbitrary change in the forces applied at infinity. It is shown that for a certain constraint on the asymmetry of the loads, the solution of the problem considered is independent of the loading trajectory. When the mentioned constraint is violated, the plasticity domain will be different depending on the history of the load change.

Some properties of equations and the method of the small parameter in two-dimensional spatial problems of the theory of ideal plasticity

6. V. M. Finkel', Physics of Fracture [in Russian], Metallurgiya, Moscow (1970). L. I. Sedov, Mechanics of Continuous Media [in Russian], Nauka, Moscow (1970), Vol. 2. F. I. Kucheryavyi, A. V. Mikhalyuk, and Yu. I. Voitenko, "Control of the pressure threshold in hydrofracture of rock," Izv. Vyssh. Uchebn. Zaved., Gorn. Zh., No. 4 (1983). N. M. Bezukhov, Foundations of the Theory of Elasticity, Plasticity, and Creep [in Russian], Vyssh. Shkola, Moscow (1968).

Methods of structural systems reliability

In a condensed form this report presents the last five to ten years of development within the field of structural reliability theory with particular attention to structural systems. Besides dealing with effective specific methods of probability calculation it reflects one school of thought with respect to the interpretation of structural reliability measures. This school supports the pragmatic decision model point of view rather than the ideal of a strict physical theory. Since such thinking may not have gained general consensus the approval of the report by the committee does not commit its members to agree either on the general philosophy or on the details of the report. The main chapters are: Single Element Reliability; Series Systems Reliability; Parallel Systems and General Systems Reliability; Large Redundant Idealized Structural Systems; Modifications Needed to Deal with Variations in Time. Special emphasis is put to the often suppressed problem of formulating realistic limit state models for structural systems when considered in the night of the load history dependency problem. Attention is given to the ideal plasticity theory because it allows substantial simplifications of this problem. In fact, it seems to be the only constitutive model that can justify the time independent stable configuration type of model. Also ideal brittle systems subject to proportional random loading are analysed in some detail.

Singular approximation in ideal plasticity theory of microinhomogeneous media

Singular approximation in ideal plasticity theory of microinhomogeneous media