Statistical theory of dislocations in two-dimensional elastic bodies

Rendiconti di Matematica e delle Sue Applicazioni

H. Zorski¹ 

[1] Polish Academy of Sciences;

关键词: elastic body;    dislocation field;    waves in mixture;   

DOI  :  

来源: DOAJ

【 摘 要 】

We derive in this paper equations of continuously distributed dislocations in linear elastic media, starting from a finite number of dislocation lines perpendicular to the plane of the solid. Thus, dislocations are points with a structure and the non-material (but possessing field mass) dislocation “gas” is constructed by statistical means, following known procedures of the kinetic theory. A constitutive law for the kinetic stress tensor is postulated - the only one required in this theory. The result is a mixture of two interacting continua, governed by a system of 6 partial differential equations, for 3 displacements, 2 dislocation gas velocities and the dislocation density. Energy balance law is derived from the system of equations and some general properties of the latter are examined. One particular case is examined in more detail, namely screw dislocations.

【 授权许可】

Unknown