Stress and couple-stress invariance in non-centrosymmetric micropolar planar elasticity

Abstract

The stress-invariance problem for a chiral (non-centrosymmetric) micropolar material model is explored in two different planar problems: the in-plane and the anti-plane problems. This material model grasps direct coupling between the Cauchy-type and Cosserat-type (or micropolar) effects in Hooke's law. An identical strategy of invariance is set for both problems, leading to a remarkable similarity in their results. For both problems, the planar components of stress and couple-stress undergo strong invariance, while their out-of-plane counterparts can only attain weak invariance, which restricts all compliance moduli transformations to a linear type. As an application, when heterogeneous (composite) materials are subjected to weak invariance, their effective (volume-averaged) compliance moduli undergo the same linear shift as that of the moduli of the local phases forming the material, independently of the microstructure, geometry and phase distribution. These analytical results constitute a valuable means to validate computational procedures that handle this particular type of material model.