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Elastic objects across a wide range of scales deform under local changes oftheir intrinsic properties, yet the shapes are ${\it glocal}$, set by acomplicated balance between local properties and global geometric constraints.Here, we explore this interplay during the inversion process of the green alga${\it Volvox}$, whose embryos must turn themselves inside out to complete theirdevelopment. This process has recently been shown [S. H\"ohn ${\it et~al}.$,${\it Phys. Rev. Lett.}$ $\textbf{114}$, 178101 (2015)] to be well described bythe deformations of an elastic shell under local variations of its intrinsiccurvatures and stretches, although the detailed mechanics of the process haveremained unclear. Through a combination of asymptotic analysis and numericalstudies of the bifurcation behavior, we illustrate how appropriate localdeformations can overcome global constraints to initiate inversion.

Elasticity and Glocality: Initiation of Embryonic Inversion in ${\it Volvox}$