The Mechanics of Lipid Bilayer and Fiber-reinforced Composite Sheet
Creators: Yao, Wenhao
Publisher: name: University of Alberta Library
Year: 2024

<p>The thesis delves into the mechanics of hyperelastic materials, specifically lipid bilayers and fiber-reinforced composites (FRC). The primary objective is to achieve an advanced understanding of cell physiology from the aspect of lipid membrane mechanics and provide qualitative analysis of the mechanical properties of fiber-reinforced composites by elucidating the continuum models of lipid membrane and fiber-reinforced composites, respectively. Due to the commonly observed abnormal morphology of cells in current literature, the study emphasizes investigating the non-uniform morphogenesis of lipid membranes subjected to interaction forces and lateral pressure to enhance our understanding of membrane-protein interactions and membrane inflammation. The highlight of the thesis has been given to developing the three-dimensional theory of FRC sheets within the context of lipid membrane theory, unveiling the concurrent three-dimensional deformation of FRC and the embedded meshwork. </p>

<p>To accomplish these objectives, first, we derive the Euler equations within the variational framework of the Canhanm-Helfrich model by accounting for the non-uniform (coordinate-dependent) strain energy distributions of lipid membranes. Then, the corresponding partial differential equations (PDEs) are obtained by projecting the equilibrium equations on the polar and Cartesian coordinate systems and numerical cases are applied to demonstrate the capability of describing lipid membrane morphology. In cases of membrane-protein interactions and membrane inflammation, the resulting homogeneous and inhomogeneous PDEs are solved numerically or/and analytically, where the obtained results reasonably describe the circumferentially and radially non-uniform membrane properties, providing quantitative proofs for understanding the cell membrane morphology in the pathological research of cell.</p>

<p>In the proceeding efforts of studying lipid membrane morphology, emphasis is placed on uncovering the effects of intra-surface viscous flow on membrane morphologies and surface dilatation, particularly in the scenarios involving membrane-protein interactions and cell membrane inflammation. Within the variational framework, we derive and solve equilibrium equations by accommodating the viscous stress into the equilibrium equations, where the viscous stress is considered to be induced by intra-surface viscous flow, and the viscous effects on membrane surface dilatation are unveiled. In particular, our findings from continuum models are theoretically evidenced by the results of molecular dynamics simulation, illustrating that the protein-membrane interaction forces can induce local bending effects on the membrane, leading to surface compressions near the substrate-interaction boundaries. Notably, the proposed continuum model offers quantitative descriptions of highly curved membrane morphologies and associated thickness reductions, especially when nuclear pore complexes (NPCs) interact with the nuclear envelope.</p>

<p>More importantly, a three-dimensional model for analyzing the concurrent three-dimensional performance of FRC sheets is proposed based on the theory of lipid membrane. This involves modeling the FRC by incorporating the Neo-Hookean strain energy model for the matrix material and computing the strain energy of fiber meshwork by accounting for the stretching, bending, and twisting of fibers. To elucidate the three-dimensional deformation of the FRC, we derive the Euler equations and admissible boundary conditions via the surface coordinate configurations and solve the model numerically in the Cartesian coordinate system. The numerical results reasonably indicate the microstructural kinematics of fiber (for instance, bending, twisting, and stretching of fibers within the matrix material) determines the overall deformation of FRC. In particular, the concurrent three-dimensional deformations of FRC provide a reasonable understanding of the damage patterns in the FRC used in the construction sector, the formation of hemispherical domes in bamboo poly (lactic) acid (PLA) composites, and out-of-plane deformations in woven fabrics. This work offers quantitative and qualitative contributions to the design and analysis of FRC in terms of the deformation profiles, stress-strain responses, strain distributions, and deformations of fiber meshwork.</p>