Soliton solutions in geometrically nonlinear Cosserat micropolar elasticity with large deformations

This is the authors' abstract. We don't add key points for this paper.

We study the fully nonlinear dynamical Cosserat micropolar elasticity problem in three dimensions with various energy functionals dependent on the microrotation R¯ and the deformation gradient tensor F. We derive a set of coupled nonlinear equations of motion from first principles by varying the complete energy functional. We obtain a double sine–Gordon equation and construct soliton solutions. We show how the solutions can determine the overall deformational behaviours and discuss the relations between wave numbers and wave velocities thereby identifying parameter values where the soliton solution does not exist.