Non‐isometric deformation in double curvature and symmetric composite laminates due to shrinkage.

Application of the global Gauss–Bonnet theorem for the prediction of changes in Gaussian curvature for double curvature laminate geometries due to shrinkage is developed for non‐isometric deformation states where in surface area change accompanies changes in curvature. The transition between isometric and non‐isometric deformation is strongly influenced by the ratio of the principal radii of curvature of the double curved surface and a relationship is proposed by the authors to accommodate the transition. Examples for the radii of curvature ratios of 2, 3, and 4 are compared to results from finite‐element simulations and the developed relationship is shown to be accurate within 0.55%. Furthermore, these results demonstrate that isometric deformation state can be taken as an adequate representation for double curvature toroidal laminate geometries of ρ2/ρ1 >10 and the class of materials studied in this work. Highlights: Shrinkage induced deformation in multi‐curvature composite laminates is a recurring issue in polymer composite manufacturing.Thermal, crystallization and cure shrinkage are the dominant sources of shrinkage deformation in polymer composite systems.Isometric deformation of multi‐curvature, symmetric laminates composite is defined by the absence of membrane strain.The Gauss–Bonnet theorem provides a platform for determining radii of curvature changes in multi‐curvature symmetric laminates,Non‐isometric deformation of symmetric laminates can be treated by the Gauss–Bonnet theorem for radii of curvature ratios that correspond to geometric self‐constraint. The above highlights yield insight into the anticipated geometric distortions due to shrinkage in polymer composites. [ABSTRACT FROM AUTHOR]