Multilevel, subdivision-based, thin shell finite elements: development and an application to red blood cell modeling

Abstract

This work focuses on efficient hierarchical, numerical simulation of the deformation of thin walled structures. We address the need to characterize and improve the performance of the subdivision thin shell finite element for practical applications in engineering design and analysis. The contribution of this document is to provide a thorough investigation of thin shell simulation using the subdivision shell element, focusing on novel element design and implementation, accurate boundary conditions, efficient multilevel solution strategies, and applications to the current engineering problem of blood cell membrane simulation.We describe a unified framework for the simulation of thin bodies via hierarchical, rotation-free thin shell finite elements for meshes with both quadrilateral (Catmull-Clark scheme) and triangular connectivity (Loop's scheme). A corresponding planar beam element is also presented. We present an algorithm that exploits the hierarchical structure of subdivision surfaces to accelerate solution convergence. Our examples show that the run time of the algorithm presented scales nearly linearly with problem size.We present a new method for enforcing boundary conditions within subdivision finite element simulations of thin shells. The proposed framework is demonstrated to be second order accurate for simply-supported and clamped boundary conditions.We demonstrate the application of these techniques for the numerical simulation of red blood cell models. Mechanical models of human red blood cells are a necessary component for microstructural simulation of blood flow for artificial organ design. Two specific simulations are demonstrated for constant-volume deformation of a red blood cell: micropipette aspiration and point load application.