Computational aspects of morphological instabilities using isogeometric analysis

Morphological instabilities play a crucial role in the behavior of living systems as well as advanced engineering applications. Such instabilities initiate when a thin stiff film on a compliant substrate is subject to compressive stresses. For bilayer systems, the first mode of instability is sinusoidal wrinkling. While the critical conditions to induce wrinkling are extensively studied, the more complex patterns formed beyond wrinkling remain elusive and poorly understood. The objective of this contribution is to establish a generic computational framework capable of capturing various instabilities, using isogeometric analysis (IGA) enhanced with a concurrent eigenvalue analysis. It is shown that the eigenvalue analysis provides quantitatively accurate predictions for the onset of instabilities. In addition, the results are compared with the standard finite element analysis (FEA) and it is clearly observed that IGA furnishes significantly more accurate results compared to FEA, for the same number of degrees of freedom. We believe that this generic framework is widely applicable to advance our understanding of emergence and evolution of morphological instabilities for a rich variety of applications in soft materials and living systems.