Existence theorem for geometrically nonlinear Cosserat micropolar model under uniform convexity requirements

Abstract

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 $\bar{\mathbf{K}}={\bar{\mathbf{R}}}^T\mathrm{Curl}\bar{\mathbf{R}}$ as a suitable Cosserat curvature measure.

References in corpus (4)

• A unifying perspective: the relaxed linear micromorphic continuum
• A Riemannian approach to strain measures in nonlinear elasticity
• Existence theorems in the geometrically non-linear 6-parametric theory of elastic plates
• Soliton-like solutions based on geometrically nonlinear Cosserat micropolar elasticity