Morphogenesis in Constrained Spaces
How does a spherical shell fold when it grows inside a hollow sphere? The scientiﬁc interest of our project lies in a theoretical understanding of two crucial aspects of this problem:
First, we investigate how symmetry is broken, in particular from the initially spherical shell to a buckled one. First-principle simulations and analytical considerations show that this question is entirely different from the well-studied O(3) bifurcation buckling of a sphere under homogenous pressure.
Second, the inﬂuence of physical material parameters such as shell thickness, friction and plasticity on the buckling and folding patterns is studied in detail. A mechanically accurate simulation has to take into account the strong non-linear character of the governing elastic equations. Additionally, the associated energy landscape is very complex, which renders it difficult and computationally demanding to ﬁnd the lowest energy solution. Using recent advances in ﬁnite element research, we approach this problem with an adaptive mesh and iterative, high performance parallel solvers.