Growth and Non-Metricity in Föppl-von Kármán Shells

Abstract

The non-homogeneous Foppl-von Karman equations for growing thin elastic shallow shells are revisited by deriving the inhomogeneity source terms directly from the non-metricity tensor associated with growth. This is in contrast with the existing literature where the source terms are obtained using the extensional and curvature growth strains after exploiting the additive decomposition of the total strain into its elastic and growth counterpart. Our framework not only establishes the additive decomposition but provides an unambiguous illustration of the geometric nature of growth in terms of a genuine material inhomogeneity measure given by the non-metricity tensor.