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Existence theorem for geometrically nonlinear Cosserat micropolar model under uniform convexity requirements. (English) Zbl 1327.74035

Summary: We reconsider the geometrically nonlinear Cosserat model for a uniformly convex elastic energy and write the equilibrium system 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 \(\overline{\boldsymbol{K}}= \overline{\boldsymbol{R}}^{T}\operatorname{Curl}\overline{\boldsymbol{R}}\) as a suitable Cosserat curvature measure.

MSC:

74B20 Nonlinear elasticity
49J40 Variational inequalities
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