Static-geometric analogy in the micropolar theory of elasticity

Abstract

For a micropolar elastic medium with distributed dislocations and disclinations, an analogy has been established between the equilibrium equations for force and couple stresses and the reduced incompatibility equations for metric and bending strains. The strain boundary conditions have been derived. The physically different but mathematically equivalent boundary-value problems of the three-dimensional micropolar theory of elasticity have been formulated.