Analytical solutions of the cylindrical bending problem for the relaxed micromorphic continuum and other generalized continua

We consider the cylindrical bending problem for an infinite plate as modeled with a family of generalized continuum models, including micromorphic approach. The models allow to describe length scale effects in sense that thinner specimens are comparatively stiffer. provide analytical solution each case and exhibits predicted stiffness. relaxed shows bounded stiffness arbitrary thin specimens, while classical or gradient elasticity well Cosserat (Neff et al. Acta Mechanica 211(3–4):237–249, 2010) exhibit unphysical unbounded specimens. This finding highlights advantage using model, which has definite limit small samples aids identifying relevant material parameters.