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.

中文翻译：

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Föppl-von Kármán Shells 的增长和非度量

通过直接从与生长相关的非度量张量导出非均匀性源项，重新审视了用于生长薄弹性浅壳的非齐次 Föppl-von Kármán 方程。这与现有文献相反，在现有文献中，源项是在利用总应变的加法分解为其弹性和增长对应物后使用拉伸和曲率增长应变获得的。我们的框架不仅建立了加法分解，而且根据非度量张量给出的真正材料不均匀性度量提供了增长的几何性质的明确说明。