On deformational and configurational mechanics of micromorphic hyperelasticity – Theory and computation

A micromorphic continuum formulation is presented in the context of both, the spatial- and the material-motion problem. For both approaches the kinematics as well as the balance relations together with the various representations of the occurring stress fields are derived. The relations between the spatial-motion problem and the material-motion problem quantities are examined in detail. Upon a hyperelastic constitutive assumption a finite-element approximation is derived and the material–force method, which is especially suited for defect-mechanics problems, is successfully applied to the present micromorphic continuum theory.