Subdivision shell elements with anisotropic growth

• Published in: International journal for numerical methods in engineering 2013-08, Vol.95 (9), p.791-810
• Main Authors: Vetter, Roman, Stoop, Norbert, Jenni, Thomas, Wittel, Falk K., Herrmann, Hans J.
• Format: Article
• Language: English
• Subjects: Anisotropy; Dealing; elasticity; Exact sciences and technology; finite element methods; Fundamental areas of phenomenology (including applications); Instability; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); nonlinear dynamics; Numerical analysis; Numerical analysis. Scientific computation; Physics; Reproduction; Sciences and techniques of general use; shells; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; structures; Subdivisions; Thin walled shells
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.4536

SUMMARYA 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, quasistatic, elastic limit. Copyright © 2013 John Wiley & Sons, Ltd.