Abstract
The non-homogeneous Föppl-von Kármán 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.
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Notes
The incompatibility measures written here are corrected version of the Eqs. (59)–(62) in [13].
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Acknowledgement
The authors acknowledge the financial support from SERB (DST) Grant No. CRG/2018/002873 titled “Micromechanics of Defects In Thin Elastic Structures”.
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Roychowdhury, A., Gupta, A. Growth and Non-Metricity in Föppl-von Kármán Shells. J Elast 140, 337–348 (2020). https://doi.org/10.1007/s10659-020-09766-9
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DOI: https://doi.org/10.1007/s10659-020-09766-9