New trends in couple-stress hyperelasticity

This communication reconsiders and reorganises parts of existing knowledge that refers to Cosserat-type hyperelasticity formulations in a manner respects pays tribute the early development pattern couple-stress theory and, also, associates with it more recent findings relevant discoveries related certain type polar hyperelastic behaviour fibrous composites. It further shows these different branches can both emanate, as special cases, from common, general, advanced theoretical framework. thus reveals proper completion any formulation requires advance specification pair kinematic parameters, each which (1) is related, virtual or actual manner, observed global, macroscopic elastic deformation material, but (2) principally part material response. The first parameters represents pseudovector field whose gradient energetically reciprocal emerging field, while second either vector serves specific constitutional needs characterising source anticipated Different versions formulations, thus, are obtained by appropriately choosing suitably tuning parameters. also seen that, regardless employed model, full solution well-posed boundary value problem generally achievable use two-step process. step includes determination deviatoric spin global deformation. In step, initial enable formation an additional differential equation leads spherical couple-stress.