Beltrami stress fields in an elastic body

Abstract

It is proposed to search for solutions to the equation of continuum equilibrium satisfying additionally the Beltrami tensor equation, which describes self-transformation of a solenoidal field and is well-known in hydrodynamics for the velocity vector field; however, it has apparently still not been considered for tensor fields. A series of localized stress distributions twisting the material continuum are obtained as well as the stress distribution in the form of periodic structures in the space caused by the regular distribution of incompatible plastic deformation in an elasto-plastic solid. The obtained solutions are not known in the theory of elasticity and represent a certain interest in connection with the description of defects in a solid.