Existence theorem for geometrically nonlinear Cosserat micropolar model   under uniform convexity requirements
  We reconsider the geometrically nonlinear Cosserat model for a uniformly convex elastic energy and write the equilibrium problem as a minimization problem. Applying the direct methods of the calculus of variations we show the existence of minimizers. We present a clear proof based on the coercivity of the elastically stored energy density and on the weak lower semi-continuity of the total energy functional. Use is made of the dislocation density tensor $\bar{\boldsymbol{K}}=\bar{\boldsymbol{R}}^T\,\mathrm{Curl}\,\bar{\boldsymbol{R}}$ as a suitable Cosserat curvature measure. 
Patrizio Neff, Mircea B\^irsan and Frank Osterbrink
math.AP math-ph math.MP