This paper presents a general, nonlinear finite element formulation for
rotation-free shells with embedded fibers that captures anisotropy in
stretching, shearing, twisting and bending -- both in-plane and out-of-plane.
These capabilities allow for the simulation of large sheets of heterogeneous
and fibrous materials either with or without matrix, such as textiles,
composites, and pantographic structures. The work is a computational extension
of our earlier theoretical work (Duong et al., 2021) that extends existing
Kirchhoff-Love shell theory to incorporate the in-plane bending resistance of
initially straight or curved fibers. The formulation requires only displacement
degrees-of-freedom to capture all mentioned modes of deformation. To this end,
isogeometric shape functions are used in order to satisfy the required
C1-continuity for bending across element boundaries. The proposed
formulation can admit a wide range of material models, such as surface
hyperelasticity that does not require any explicit thickness integration. To
deal with possible material instability due to fiber compression, a
stabilization scheme is added. Several benchmark examples are used to
demonstrate the robustness and accuracy of the proposed computational
formulation.Comment: This version updates the paper format and adjust the units in figure
axes, results unchange