A framework for the nonlocal analysis of inelastic deformations and defect evolution in shells

In this paper a thermodynamically consistent framework is developed to analyze inelastic deformations of shells taking into account the defect evolution in the material of which the shell is made of. The framework is based on the three-dimensional, weakly-nonlocal theory developed by the authors for 3D continua and on the exact derivation of the resultant 2D balance laws initiated by Simmonds (1984) for elastic shells. The theory is formulated in stress resultants obtained by through-the-thickness integration. The framework consists of three parts. First a weakly-nonlocal theory of inelastic shells is formulated, which is based on the resultant Cosserat-type balance laws of forces and couples in the physical space. Next, the weakly-nonlocal balance laws of forces and couples caused by fields of microdefects in the material space is derived. Finally, the general structure of the 2D constitutive equations and their approximate nature is carefully studied.