Mechanics of surfaces: Continuum-based modeling and analysis for biomembranes and 2D fiber materials

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The objective of the proposed research is to establish a research program in the area of the mechanics of surfaces focused on developing continuum models and numerical techniques for the design and analysis of advanced 2D materials. In particular, the proposed research program will address the following two major branches of problems that have drawn a considerable attention due to their important applications in the fields of biomechanics and nanomechanics. 1. Mechanics of biomembranes subjected to thickness distension and non-uniform lipid distribution Lipid membranes have various useful medical and industrial applications including drug transport and delivery, and biomembrane-based sensors (e.g. water toxicity sensors). For such applications, it is important to simulate and predict their mechanical responses on vesicle formation, fusion and distension involved motions. Lipid bilayers are composed of transversely oriented lipid molecules containing hydrophilic head groups and hydrophobic tails. These molecules arrange themselves into a two layered sheet with opposing orientations that effectively shield the tail groups from the surrounding aqueous solution. In fact, the bilayer structure is characteristic of all biological membranes (biomembranes). The arrangement occurs over length scales on the order of molecular dimensions. Therefore, a lipid bilayer can be regarded as a closed membrane with distinct microscopic orientations of lipid molecules initially aligned with the surface normal. In this project, we will develop a complete continuum model and numerical method in the description of biomembrane morphology under the presence of thickness distension and non-uniform lipid distribution. More precisely, we will analytically model and examine a lipid bilayer by computing the energy variations of the membrane with respect to mean and Gaussian curvatures, lipid distension and its gradient on the membrane surface.  2. Strain-gradient integrated modeling for 2D fiber composites The research intends to develop general 2D continuum models that can accommodate fiber’s resistance to extension, bending and twist. This will allow more accurate descriptions for stress and displacement fields of 2D fiber composites subjected to various external loadings. In particular, through the proposed research program, we aim to build a strong theoretical and practical foundation in design and analysis of biocomposites reinforced with cellulose nanocrystals (CNC) which has drawn a considerable attention in recent years. By calculating strain-gradient fields of fibers, we will integrate fiber’s motions into the deformation fields of the film structure. We begin with the case of unidirectional fiber composites and subsequently extend the results to the more general scenarios where the film structure is supported by multi-directional fibers and initially non-straight fibers.