On the Force Exerted upon Continuously Distributed Dislocations in a Cosserat Continuum

✍ Scribed by S. Minagawa

• Book ID: 104539471
• Publisher: John Wiley and Sons
• Year: 1970
• Tongue: English
• Weight: 339 KB
• Volume: 39
• Category: Article
• ISSN: 0370-1972
• DOI: 10.1002/pssb.19700390123

✦ Synopsis

Abstract

The force acting on distributed dislocations in a Cosserat continuum is studied and the expressions for the force and force density are given in tensorial form. The increase in the potential energy of the material body, caused by a displacement of distributed dislocations in a certain region of the body, is obtained. The force acting on those dislocations is deduced by differentiating it with respect to the distance through which the dislocations are displaced. The expression for the density of forces is given as follows:
equation image

where s~jni~ is the tensor of dislocation density, ∑^ij^ the symmetric part of stresses, M~jni~ the couple‐stress tensor, and η^ij^ the incompatibility tensor.