Institute of Fundamental Technological Research
Polish Academy of Sciences

Partners

P.A. Gourgiotis

University of Trento (IT)

Recent publications
1.  Gourgiotis P.A., Stupkiewicz S., Macroscopic stress and strain in a doubly periodic array of dislocation dipoles, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, ISSN: 1364-5021, DOI: 10.1098/rspa.2014.0309, Vol.470, pp.20140309-1-16, 2014

Abstract:
It is known that in two-dimensional periodic arrays of dislocations the summation of the periodic image fields is conditionally convergent. This is due to the long-range character of the elastic fields of dislocations. As a result, the stress field obtained for a doubly periodic array of dislocation dipoles may contain a spurious constant stress that depends on the adopted summation scheme. In the present work, we provide, based on micromechanical considerations, a simple physical explanation of the origin of the conditional convergence of lattice sums of image interactions. In this context, the spurious stresses are found in a closed form for an arbitrary elastic anisotropy, and this is achieved without using the stress field of an individual dislocation. An alternative procedure is also developed where the macroscopic spurious stresses are determined using the solution of the Eshelby's inclusion problem.

Keywords:
dislocation dynamics, conditional convergence, micromechanics, Eshelby’s inclusion problem

Affiliations:
Gourgiotis P.A. - University of Trento (IT)
Stupkiewicz S. - IPPT PAN

Category A Plus

IPPT PAN

logo ippt            Pawińskiego 5B, 02-106 Warsaw
  +48 22 826 12 81 (central)
  +48 22 826 98 15
 

Find Us

mapka
© Institute of Fundamental Technological Research Polish Academy of Sciences 2021