Computational aspects of morphological instabilities using isogeometric analysis

Abstract

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.

Mathematical and computational modelling of skin biophysics: a review

“…Isogeometric finiteelement formulations [192][193][194] are therefore superior to those based on Lagrange polynomial interpolation. Identifying critical conditions that trigger surface instabilities is also a challenging endeavour but progress in this area is steadily moving forward [195].…”

Quantifying the relationship between cell division angle and morphogenesis through computational modeling

“…This work is only just the beginning of serious consideration of the macroscale implications of the probability distribution of cell division angle. Future work with this framework may address topics such as alternative growth and division laws, how individual cell anisotropy may influence macroscale growth, or how cell division behavior may connect to other forms of mechanically driven emergent behavior such as buckling and wrinkling (Dortdivanlioglu et al, 2016). Overall, our results indicate that the distribution of cell division angle emerges as a critical factor in morphogenesis and presents a basis for further investigation of the topic.…”

Mixed isogeometric analysis of strongly coupled diffusion in porous materials

“…In addition, we provided a mathematical proof to show that the inf‐sup condition in mixed elasticity and Stokes flow is sufficient to prove stability in poromechanics problems. This work is expected to provide a framework for more application‐based problems such as geometrical instabilities() observed in swelling hydrogels due to coupled diffusion() or a diffusion‐induced fracture. ()…”

“…To this purpose, IGA and computer‐aided design systems commonly adopt B‐splines and nonuniform rational B‐splines (NURBS) as underlying basis functions, leading to an exact representation of computational geometry for analyses. Consequently, the high‐order continuity of NURBS elements eases the use of higher‐order basis functions in the analysis process and offers significant computational benefits such as robustness,() vastly improved accuracy per degree of freedom,() and exact representation of complex geometries. () These unique features of IGA have been further exploited for various applications.…”