  In this work we present a generalized Kirchhoff-Love shell theory that can
capture anisotropy not only in stretching and out-of-plane bending, but also in
in-plane bending. This setup is particularly suitable for heterogeneous and
fibrous materials such as textiles, biomaterials, composites and pantographic
structures. The presented theory is a direct extension of existing
Kirchhoff-Love shell theory to incorporate the in-plane bending resistance of
fibers. It also extends existing high gradient Kirchhoff-Love shell theory for
initially straight fibers to initially curved fibers. To describe the
additional kinematics of multiple fiber families, a so-called in-plane
curvature tensor - which is symmetric and of second order - is proposed. The
effective stress, in-plane and out-of-plane moment tensors are then identified
from the mechanical power balance. These tensors are all second order and
symmetric for general materials. The constitutive equations for hyperelastic
materials are derived from different expressions of the mechanical power
balance. The weak form is also presented as it is required for computational
shell formulations based on rotation-free finite element discretizations.
