Elastoplastic Space Research Articles

ПРИБЛИЖЕННОЕ ОПРЕДЕЛЕНИЕ ГЕОМЕТРИЧЕСКИХ ПАРАМЕТРОВ НАПЛЫВА ПРИ ВНЕДРЕНИИ ПАРАБОЛОИДНОГО ИНДЕНТОРА В ПОЛУПРОСТРАНСТВО

The problem of the indenter embedding into a half-space is formulated and solved. A concept of the elastic contact is used, which implies the uniformity of the stress-strain state in a surface layer. The process of the surface layer formation after mechanical treatment is studied. Based on the general theory of indenter penetration into a half-space, numerical and analytical solutions, determining the length and depth of penetration of a paraboloid into elastoplastic space, are obtained. According to the theory of indentation, the problem is reduced to the use of the method of approximate determination of geometric parameters of a bead, when a paraboloid is being embedded into elastoplastic space. An exact solution to the formulated problem allows one to obtain analytical dependences for calculating the velocities and to study the stress-strain state of the material in the half-space surface layer during the processing. The reliability of the obtained analytical solution is confirmed by numerical calculations without introducing additional hypotheses. Based on the analytical solution, the geometric parameters of the influx from the penetration depth are determined. Calculations can be performed at any embedding depth. Sag formation during the indenter embedding by 18 mm into plasticine specimens is considered as an example. It is shown that the rigid zone is insignificant or absent.

Logarithmic strain measure applied to the nonlinear positional formulation for space truss analysis

The logarithmic strain measure is used to obtain a consistent geometric nonlinear finite element formulation to deal with large strains on space trusses. The formulation is based on the positional formulation and no local system of coordinates on the elements is needed to describe its kinematics. Three numerical examples are presented, including a tensegrity tower and a double layer elastoplastic space truss. The paper proves that the positional nonlinear formulation is valid for other objective strain measures used in the classical nonlinear formulations, i.e. logarithmic strain measure.

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.

A conservative integral in elastoplastic space with a steady growth crack

In the study of crack growth, the region near the crack tip is divided into several different sectors of loading and unloading as in [1][2]. Now, let us define a stress work function W --=~e'" Of course, for an elastic body, it is the well known ~j lJoijdeij" density of strain energy, and it is a single valued 0 function of strain s. • But for an elastoplastic body, it is neither the density of strain e~rgy nor a single valued function of strain. It is only known that W = f(x],xv,x.,t)o For a material point, at the interval of loading (or unloading), however, it is still a single valued function of s.,. ij For a material point, x~,x_,x_ are fixed but t is a variable. Thus, i z 3 for a material point, in the interval of loading (or unloading), one has