A new deformation measure for the nonlinear micropolar continuum

The possibility to introduce a new relative rotation tensor in the field of nonlinear micropolar continua is discussed in the present paper. The proposed deformation tensor is able to uncouple the classic energetic contribution, related to the material particles translation, and the non-classic ones due to the material particles microrotation. The two main used tool are the least action principle and Levi–Civita absolute tensor calculus which allow to derive the new Euler–Lagrange equations. Some numerical applications are made to investigate the mathematical and mechanical implications of the proposed theoretical model. Axial, bending and torsion numerical tests are performed on structural elements typical of a pantographic structure. Interesting behaviours have been obtained which cannot be forecasted by classical elasticity. In addition of predicting new phenomena, it follows that the new relative rotation tensor could help in the description of granular materials and in the design of novel metamaterials that could be macroscopically described by means of the proposed tensor itself.