Subdivision Shell Elements with Anisotropic Growth
For computational mechanics researchers, it provides a computationally efficient tool for simulating anisotropic growth in thin shells, though the approach is incremental.
The paper presents a thin shell finite element method based on Loop's subdivision surfaces that handles large deformations and anisotropic growth, demonstrating its efficiency on benchmarks and applications including growth-induced instabilities.
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.