Continuum theory of dislocations and disclinations in nonlinearly elastic micropolar media

摘要

A nonlinear theory of continuously distributed dislocation and disclination type defects in elastic media with intrinsic rotational degrees of freedom and couple stresses is proposed. The mediumstrains are assumed to be finite. The solving equations of the continuum theory of defects are obtained by passing to the limit from a discrete set of isolated dislocations and disclinations to their continuous distribution. The notions of dislocation and disclination densities in a micropolar body under large deformations are introduced. Incompatibility equations are obtained and a boundaryvalue problem of equilibriumis posed for an elastic micropolar body with a given density of distributed defects. A nonlinear problem of determining the intrinsic stresses in a hollow circular cylinder due to a given distribution of disclinations is solved. A mathematical model of moment (micropolar) media can be used to describe the deformations of structurally inhomogeneous bodies [1], liquid crystals, composites, nano-structural and magnetic materials. Earlier [2], continuously distributed dislocations were studied in the framework of the model of a simple nonlinear elasticmediumwithout thematerialmicrostructure taken into account. A nonlinear theory of isolated dislocations and disclinations in micropolar media is presented in [3].