Session: 16-01-01: Poster Session: NSF-Funded Research (Grad & Undergrad)

Paper Number: 99597

99597 - Modeling Curvature-Resisting Surfaces of Soft Solid-Bilayer Hybrids 

Complex surface (or interface) stresses arise from bonded coatings, bilayer hybrids, or lower dimensional energetics. They play a significant role in the overall mechanical properties of soft materials. Gurtin and Murdoch proposed a theory to study the solid-surface coupled mechanical behavior by incorporating a zero-thickness elastic surface bonded to the bulk. Steigmann and Ogden extended their work by considering the surface to resist change in curvature. Recent studies have demonstrated that curvature-resisting surfaces can explain some anomalies observed in the mechanical behavior of nanostructures and soft solids with chemically-treated surfaces. Curvature-resisting surfaces are also crucial from the perspective of biological bilayers, where the membrane bending leads to the formation of complex shapes such as buds and tubules. The growing interest in understanding complex material surface effects demands a robust computational framework incorporating solid-surface coupled mechanical behavior. Most of the computational frameworks dealing with surface effects in solids ignore the Steigmann and Ogden's extension to consider surface flexural-resistance. The reason for this is that incorporating curvature-dependent surface energy in the current surface-elasticity enhanced Galerkin FE models is challenging. The surface in the Steigmann-Ogden model is assumed to be a zero-thickness shell embedded in the three-dimensional space, necessitating a precise calculation of surface curvature. Surface curvature depends on second-order derivatives in space and therefore requires a surface representation with at-least C^1-continuity in the entire domain. The surface enrichment using the Lagrange basis function results in C^0-continuity across element boundaries. The C^1 continuous surface representation provided by Hermite basis functions is only limited to two-dimensional formulations. In this work, we address this challenge by proposing a 3D computational framework of curvature-dependent surface energetics at finite strains using surface-enriched NURBS-based isogeometric analysis (IGA). NURBS basis functions are C^n (n>1) continuous, and therefore can be used to directly calculate the surface curvature tensor. We first perform model verification using an analytical solution for a radially compressed thick hollow sphere with a coated inner surface. Using several numerical examples, we then show that bending-resistance of material surfaces furnishes a physical length-scale, i.e., the elastobending length. Our results indicate that surface curvature-resistance has a stiffening effect on the overall behavior of solids. We also demonstrate how surface curvature resistance regularizes the deformations around the line load applied to a thin cylinder. Finally, we illustrate complex budding deformations of a liquid-shell like biological membrane, modeled as a zero-thickness surface attached to a thin hyperelastic bulk. The proposed methodology provides a robust computational foundation to help advance our understanding of the mechanics of soft solids-bilayer hybrids.

 

Presenting Author: Animesh Rastogi UT Austin

Presenting Author Biography: 2nd year MS-PhD student in the Department of Civil Engineering at UT Austin. Research interests are: Mechanics of soft materials, computational mechanics, non-linear finite element and isogeometric analysis. Currently working in the Computational Mechanics of Soft Materials Lab - https://sites.utexas.edu/berkin/

Authors:

Animesh Rastogi UT Austin
Berkin Dortdivanlioglu UT Austin