Subdivision Shell Elements with Anisotropic Growth

Abstract

A thin shell finite element approach based on Loop's subdivision surfaces is proposed, capable of dealing with large deformations and anisotropic growth. To this end, the Kirchhoff-Love theory of thin shells is derived and extended to allow for arbitrary in-plane growth. The simplicity and computational efficiency of the subdivision thin shell elements is outstanding, which is demonstrated on a few standard loading benchmarks. With this powerful tool at hand, we demonstrate the broad range of possible applications by numerical solution of several growth scenarios, ranging from the uniform growth of a sphere, to boundary instabilities induced by large anisotropic growth. Finally, it is shown that the problem of a slowly and uniformly growing sheet confined in a fixed hollow sphere is equivalent to the inverse process where a sheet of fixed size is slowly crumpled in a shrinking hollow sphere in the frictionless, quasi-static, elastic limit.

20 pages, 12 figures, 1 table

References in corpus (8)

• Elastic theory of unconstrained non-Euclidean plates
• Morphogenesis of growing soft tissues
• Viscous regularization and r-adaptive remeshing for finite element analysis of lipid membrane mechanics
• Conical defects in growing sheets
• Packing of elastic wires in spherical cavities
• Self-contact and instabilities in the anisotropic growth of elastic membranes
• Finite Element Simulation of Dense Wire Packings
• Morphogenesis of membrane invaginations in spherical confinement

Cited by in corpus (15)

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• Computational modeling of active deformable membranes embedded in 3D flows
• Kibble-Zurek mechanism in curved elastic surface crystals
• Collapse of orthotropic spherical shells
• Simulating Thin Sheets: Buckling, Wrinkling, Folding and Growth
• Packing of elastic wires in flexible shells
• Fluid structure interaction with curved space lattice Boltzmann
• Semi-implicit methods for the dynamics of elastic sheets
• Distributed branch points and the shape of elastic surfaces with constant negative curvature
• Orthotropic rotation-free thin shell elements
• A Geometric Mapping from Rectilinear Material Orthotropy to Isotropy: Insights to Plates and Shells
• A Non-intrusive Approach for the Imposition of Strong Dirichlet Boundary Conditions in Unfitted Boundary Meshes