Two versions of the extended Hill’s lemma for non-Cauchy continua based on the couple stress theory

Two versions of the extended Hill’s lemma for non-Cauchy continua satisfying the couple stress theory are proposed. Each version can be used to determine two effective elasticity (stiffness) tensors: one classical and the other higher order. The classical elasticity tensor relates the symmetric part of the force stress to the symmetric strain, whereas the higher-order elasticity tensor links the deviatoric part of the couple stress to the...