a b s t r a c tWe present a micromechanically motivated form of the curvature energy in infinitesimal isotropic gradient elasticity. The basis is a homogenization/averaging scheme using a micro-randomness assumption imposed on a directional higher gradient interaction term. These directional interaction terms are matrixvalued allowing to apply the standard orthogonal Cartan Lie-algebra decomposition. Averaging over all (subgrid) directions leads to three quadratic curvature terms, which are conformally invariant when neglecting volumetric effects. Restricted to rotational inhomogeneities we motivate thereby a symmetric couple stress tensor in the infinitesimal indeterminate couple stress model of Koiter-Mindlin-Toupintype. Relations are established to a novel conformally invariant linear Cosserat model.

We investigate the numerical response of the linear Cosserat model with conformal curvature. In our simulations we compare the standard Cosserat model with a novel conformal Cosserat model in torsion and highlight its intriguing features. In all cases, free boundary conditions for the microrotations overline A are applied. The size‐effect response is markedly changed for the novel curvature expression. Our results suggest that the Cosserat couple modulus µc > 0 remains a true material parameter independent of the sample size which is impossible for stronger, pointwise positive curvature expressions.