A computational framework for the morpho-elastic development of molluskan shells by surface and volume growth
Fig 4
Mathematical model of molluskan shell growth over (tk, tk+1] through a sequence of surface growth, volume growth, secretion and calcification.
Beginning with a calcified mantle current configuration , growth over (tk, tk+1] is modelled via the following sequence of steps: (1) Surface growth—leading surface
is displaced due to mantle extension by v1Δt s1 to a new reference surface
defining a strip of the mantle in its reference configuration
. (2) Volume (morphoelastic) growth—
is imposed on the mantle strip
over Δt = tk+1 − tk, driving its nonlinear deformation into the current configuration
. (3) Shell growth occurs by secretion on the mantle strip
, followed by (4) calcification of the mantle strip
at tk+1. During the volume growth of the mantle strip from its reference configuration
to its current configuration
, boundary conditions are applied on the trailing surface (highlighted in red) and the lateral surfaces (highlighted in yellow) of the mantle strip. The front surface of the mantle strip is highlighted in green.