Elastoplastic law of Cosserat type in shell theory with drilling rotation

Abstract

Within the framework of six-parameter non-linear shell theory, with strain measures of the Cosserat type, we develop small-strain J2-type elastoplastic constitutive relations. The relations are obtained from the Cosserat plane stress relations assumed in each shell layer, by through-the-thickness integration employing the first-order shear theory. The formulation allows for unlimited translations and rotations. The constitutive relations are expressed in terms of the following material data: Young’s modulus, Poisson’s ratio, Cosserat shear modulus, characteristic length and material parameters pertaining to plasticity. Numerical examples are presented to show the correctness of the proposed model and capacity to analyze regular and irregular shells.