Fundamental Role of Local Crystal Structure Curvature in Nonlinear Behavior of Solids in External Effective Fields

摘要

The behavior of solids in external effective fields is conventionally described in Euclidean geometry. However, the generation of any defects in solids changes the local space metric and gives rise to local curvature. So, as shown in the non-Euclidean model [1,2], the vortex-free displacement field for points of a medium comprises an elastic displacement field with no defects and a field which characterizes the difference of model geometry from Euclidean geometry. The internal stress components are thus the sum of elastic stresses and self-balanced stresses defined by scalar curvature. This means that in non-Euclidean geometry, all types of defects in a crystal are curvature solitons of different structural scales.