A computational framework for the morpho-elastic development of molluskan shells by surface and volume growth
Fig 14
Spatially varying volume growth.
We impose volume growth strain increments that vary along the ΞΎ1 direction that is the curvilinear coordinate defining s1, with an increasing gradient toward the leading edge, as shown in (a). The result appears in (b), displaying large, negative Gaussian curvature, mimicking the strongly backward arching morphology observed in a number of shell species, for example as seen also in (c) Hexaplex chicoreum. Dirichlet boundary conditions, u = 0, are applied on the trailing surface (boundary) and the lateral surfaces (boundaries) of the mantle, which are perpendicular to s1, and traction-free Neumann conditions, PN = 0, are applied on the front surface (boundary). Also see S6 Movie for the evolution of deformation leading to a morphology with strongly negative Gaussian curvature.