A new paradigm: the linear isotropic Cosserat model with conformally invariant curvature energy

摘要

We discuss a linear Cosserat model with weakest possible constitutive assumptions on the curvature energy still pro-viding for existence, uniqueness, and stability. The assumed curvature energy is the conformally invariant expressionit L2 dev sym V ax1A112, where axl A is the axial vector of the skewsymmetric microrotation A E so (3), dev is theorthogonal projection on the Lie-algebra .61(3) of trace free matrices and sym is the orthogonal projection onto symmetricmatrices. It is observed that unphysical singular stiffening for small samples is avoided in torsion and bending while size ef-fects are still present. The number of Cosserat parameters is reduced from six to four: in addition to the (size-independent)classical linear elastic Lame moduli p, and A only one Cosserat coupling constant p, > 0 and one length scale parameterL0 > 0 need to be determined. We investigate those deformations not leading to moment stresses for different curvatureassumptions and thereby hypothesize a novel invariance principle of linear, isotropic Cauchy elasticity which is extendedto the Cosserat and couple-stress (Koiter-Mindlin) model with conformal curvature.