Differential geometry theory is used to show how an ideal aligned fiber composite (incompressible, inextensible fibers, constant uniform spacing between fibers) must be deformed in order to make a part of complex curvature. Three fundamental results are obtained: the first two relate the required shears to the fiber curvatures (normal and geodesic), and the third, called the Gauss-Bonnet theorem, relates the shears to the Gaussian curvature of the part and the fiber orientation. Finally, it is shown how these results can be used to simplify experimental data. © 1991 CIRP.
Gutowski, T., Tam, A., Dillon, G., Stoller, S., & Suh, N. (1991). Forming Aligned Fiber Composites into Complex Shapes. CIRP Annals - Manufacturing Technology, 40(1), 291–294. https://doi.org/10.1016/S0007-8506(07)61989-1