Linear Cosserat Elasticity, Conformal Curvature and Bounded Stiffness

Abstract

We describe a principle of bounded stiffness and show that bounded stiffness in torsion and bending implies a reduction of the curvature energy in linear isotropic Cosserat models leading to the so called conformal curvature case $\frac{1}{2}\mu L_{c}^{2}\Vert{\operatorname{dev}\operatorname{sym}\nabla \operatorname{axl}\overline{A}}\Vert^{2}$ where $\overline{A}\in\mathfrak{so}(3)$ is the Cosserat microrotation. Imposing bounded stiffness greatly facilitates the Cosserat parameter identification and allows a well-posed, stable determination of the one remaining length scale parameter L _c and the Cosserat couple modulus μ _c .