The Gamma limit of the simple shear problem in nonlinear Cosserat elasticity

TL;DR

This paper investigates the asymptotic behavior of the mechanical energy in nonlinear Cosserat elasticity as the internal length scale approaches zero, establishing convergence of minimizers and characterizing the limit functionals.

Contribution

It provides the first rigorous analysis of the Gamma-limit in nonlinear Cosserat elasticity for shear problems, revealing the effective behavior as the internal length scale vanishes.

Findings

Convergence of minimizers as the internal length scale tends to zero.

Explicit characterization of the Gamma-limit functionals.

Insights into the effective behavior of Cosserat materials in the limit.

Abstract

The zero and first order Gamma-limit of vanishing internal length scale are studied for the mechanical energy of a shear problem in geometrically nonlinear Cosserat elasticity. The convergence of the minimizers is shown and the limit functionals are characterized.