Fig. 2: Archetypal wrinkling behavior of a biofilm under constant nutrient supply.

a Radial (\({{\rm{\sigma }}}_{{\rm{r}}}\)) and circumferential (\({{\rm{\sigma }}}_{{\rm{\theta }}}\)) stress distributions, and (b) radial (\({{\rm{\varepsilon }}}_{{\rm{r}}}\)) and circumferential (\({{\rm{\varepsilon }}}_{{\rm{\theta}}}\)) strain distributions, both plotted just prior to buckling as a function of normalized radial distance (r/R), where R is the biofilm radius. c Time evolution of the maximum compressive principal stress (\({{\rm{\sigma }}}_{\max }\)). d Biofilm expansion rate (R) over time. Hollow circles in panels (c, d) mark the onset of buckling. (e–h) Snapshots illustrating the formation and evolution of wrinkles. Color bars indicate the height of the biofilm above the plane of the substrate. All results shown correspond to a simulation with intermediate friction and adhesion values within the studied ranges (\({D}_{{\rm{b}}}^{\mathrm{on}}=36\,{\mathrm{nm}}^{2}\,{{\rm{h}}}^{-1}\) and \({\rm{\gamma }}=5\,{\rm{\mu }}{\rm{J}}\,{{\rm{m}}}^{-2}\)).