  A state-based peridynamic formulation for linear elastic shells is presented.
The emphasis is on introducing, possibly for the first time, a general surface
based peridynamic model to represent the deformation characteristics of
structures that have one physical dimension much smaller than the other two. A
new notion of curved bonds is exploited to cater for force transfer between the
peridynamic particles describing the shell. Starting with the three dimensional
force and deformation states, appropriate surface based force, moment and
several deformation states are arrived at. Upon application on the curved
bonds, such states beget the necessary force and deformation vectors governing
the motion of the shell. Correctness of our proposal on the peridynamic shell
theory is numerically assessed against static deformation of spherical and
cylindrical shells and flat plates.
