Instabilities in Concave Surfaces

The brain is a highly complex organ that contains folds due to material instability. Previous idealized convex models of the brain don’t fully represent anatomy therefore requiring the simulation of concave surfaces. The purpose of this paper is to determine how instability characteristics change on concave geometries. The model used represents a soft bilayered material of a circular geometry inspired by the bronchi in the lungs which also experience instabilities. The usage of symmetry boundary conditions allow for the model to be quartered and run over varying degrees of concavity and stiffness ratios. The degree of concavity was varied by changing the radius of the model in the range of 1-10mm and the stiffness ratio was varied between 10-50. These simulations suggest that the concave model’s buckling point and wavelength trends are similar to those of flat and convex models. The thickness ratio trends appear to also follow trends of previous flat and convex models if these models presented data within a larger range of stiffness ratios comparable to the ones in this study. Refinement of our simulations to lower stiffness ratios comparable to anatomy would further confirm all results found within this study. The results from our simulations represent similar instability characteristics between flat, convex, and concave geometries which presents progress for the hope to find a unifying theory of instability between varying geometries under similar conditions.