Incompatibility of strains and its application to mesoscopic studies of plasticity

0348736 - ÚFM 2011 RIV US eng J - Journal Article
Gröger, Roman - Lookman, T. - Saxena, A.
Incompatibility of strains and its application to mesoscopic studies of plasticity.
Physical Review. B. Roč. 82, č. 14 (2010), Art. No. 144104. ISSN 1098-0121
Institutional research plan: CEZ:AV0Z20410507
Keywords : incompatibility * dislocation * mesoscopic
Subject RIV: BM - Solid Matter Physics ; Magnetism
Impact factor: 3.772, year: 2010

Structural transitions are invariably affected by lattice distortions. If the body is to remain crack free, the strain field cannot be arbitrary but has to satisfy the Saint-Venant compatibility constraint. Equivalently, an incompatibility constraint consistent with the actual dislocation network has to be satisfied in media with dislocations. We provide a systematic analysis of this constraint in three dimensions and show how three incompatibility equations accommodate an arbitrary dislocation density. This approach allows the internal stress field to be calculated for an anisotropic material with spatially inhomogeneous microstructure and distribution of dislocations by minimizing the free energy. This is illustrated by calculating the stress field of an edge dislocation and comparing it with that of an edge dislocation in an infinite isotropic medium. We outline how this procedure can be utilized to study the interaction of plasticity with polarization and magnetization.
Permanent Link: http://hdl.handle.net/11104/0189175