Problem Of Plasticity Theory Research Articles

Weak solutions to Dirichlet problems in the Hencky deformation theory of plasticity

A minimum problem for a class of functionals defined in Orlicz-Sobolev spaces is studied. As application, the existence and uniqueness of the weak solutions to Dirichlet problems for the Hencky deformation operator are obtained.

A general method of stress analysis for a generalized linear yield criterion under plane strain and plane stress

The present paper deals with the system of equations comprising a yield criterion together with the stress equilibrium equations under plane strain and plane stress conditions. This system of equations can be studied independently of any flow rule, and its solution supplies the distribution of stress. It is shown that this problem of plasticity theory is reduced to a purely geometric problem. The stress equilibrium equations are written relative to a coordinate system in which the coordinate curves coincide with the trajectories of the principal stress directions. The general solution of the system is constructed giving a relation connecting the two scale factors for the coordinate curves. This relation is used for developing a method for finding the mapping between the principal lines and Cartesian coordinates with the use of a solution of a hyperbolic system of equations. In particular, the mapping between the principal lines and Cartesian coordinates is given in parametric form with the characteristic coordinates as parameters. Finally, a boundary value problem for the region adjacent to an external boundary which coincides with a principal stress trajectory is formulated and its general solution is given.

Riemann method for the plane strain of a homogeneous porous plastic material

The system of static equations describing the stress state in a homogeneous porous plastic material obeying the pyramidal yield criterion is studied under plane strain conditions. It is shown that determining the curvature radii of the characteristics amounts to solving the telegraph equation. Thus, it is expedient to construct the net of characteristics by the Riemann method, which is widely used to solve boundary value problems in the classical theory of plasticity of incompressible materials. These solutions can directly be generalized to the considered porous material model.

Theoretical aspects of technological mechanics. 8. Plane problems in plasticity theory. Part 2

The stress and kinematic state of rectangular strip in upsetting with friction is considered.

Theoretical aspects of technological mechanics. 8. Plane problems in plasticity theory. Part 1

Theoretical aspects of technological mechanics. 8. Plane problems in plasticity theory. Part 1

Theoretical aspects of technological mechanics. 7. Axisymmetric problems in plasticity theory. Part 3

Theoretical aspects of technological mechanics. 7. Axisymmetric problems in plasticity theory. Part 3

Theoretical aspects of technological mechanics. 7. Axisymmetric problems in plasticity theory. Part 2

Theoretical aspects of technological mechanics. 7. Axisymmetric problems in plasticity theory. Part 2

Theoretical aspects of technological mechanics. 7. Axisymmetric problems in plasticity theory. Part 1

Theoretical inconsistencies in existing methods of calculating the force in the upsetting and drawing of cylindrical blanks are analyzed.

Axisymmetric extrusion and drawing through a die of arbitrary form

Axisymmetric extrusion and drawing through a die of arbitrary shape is analyzed by the Orowan method. The stress state in a representative element is determined by solving a boundary value problem of plasticity theory.

Regularity for minimizers of some variational problems in plasticity theory

A variational problem for a functional depending on the symmetric part of the gradient of the unknown vectorvalued function is considered. We assume that the integrand of the problem has power growth with exponent less than two. We prove the existence of summable second derivatives near a flat piece of the boundary. In the two-dimensional case, Holder continuity up to the boundary of the strain and stress tensors is established. Bibliography: 6 titles.

Remarks on regularity up to the boundary for solutions to variational problems in plasticity theory

We discuss the problem of the global W 12 -regularity for the stress tensor of a perfect elastic-plastic body at equilibrium. In particular, we construct an example showing that the method proposed by the author to establish the local W 12 -regularity, in general, does not work in investigations of regularity up to the boundary if the given body is nonconvex. Bibliography: 3 titles.

On a class of variational problems related to plasticity with polynomial hardening

For 1 < p < 2 and regions we consider local minimizers of the energy denotes the strain deviator. We obtain local Holder continuity of u by showing that u has second generalized derivatives in the space . Functionals of the above type arise naturally from the study of problems in plasticity theory with polynomial hardening.

Analytical solutions of mixed mode plane strain crack problems in elastic perfectly plastic materials

Abstract In the present paper analytical solutions concerning the stress state at the tip of a crack in an elastic-perfectly plastic body, subjected to mixed mode loadings under plane strain conditions, are presented. Analytical solutions of the nonlinear ordinary differential equations are obtained and the dominant singularity is completely determined with the aid of suitable boundary conditions. The obtained results are in perfect agreement with those given by other investigators, both analytical and numerical. The novel aspect here is the methodology used for the solution, as well as the direct determination of the plastic zones. As a consequence, the resulting analytical solutions cover many more problems in the mathematical theory of plasticity compared to similar existing methods and they may be proved of importance in various applications.

Closed form solutions of the differential equations governing the plastic fracture field in a power-law hardening material with low strain-hardening exponent

In this paper closed form solutions for the evaluation of the stress and strain-fields are estimated for a power-law hardening, plastically incompressible material, cracked under plane-strain conditions. A convenient decoupling methodology, concerning a strongly non-linear ordinary differential system given by Rice and Rosengren [1], leads to a modified higher-order non-linear differential equation which for the case of low strain-hardening behaviour, using appropriate analytical treatments, is integrated in a closed form. Applications of the derived solutions for low hardening exponents yield results which are in excellent agreement with those derived numerically by other investigators. The solutions obtained herein cover a large class of problems in the mathematical theory of plasticity and fracture mechanics, and may be proved powerful in application .

Boundary value problems in plasticity theory

Boundary value problems in plasticity theory

Postlimiting state of rocks and its relation with problems in the inhomogeneous theory of plasticity

Postlimiting state of rocks and its relation with problems in the inhomogeneous theory of plasticity

Analysis of Contained Plastic Flow in Plane Solids

Quantitative analysis of general contained plastic flow in solids is an extremely difficult and analytically unsolved problem of plasticity theory. A numerical approach, involving the use of a lumped-parameter model, for such problems in plane solids is described. With the use of the lumped-parameter model, contained plastic flow in a solid is characterized by the plastic flow of a finite number of stress points in the model. By a recursive numerical process a set of displacements that induces a compatible set of stresses satisfying the stress equations of equilibrium is determined for each applied load level. Thus, a complete history of stress and strain corresponding to a given loading history can be obtained. The proposed method of analysis is demonstrated for problems involving increasing external loads.