The Constitutive Model And Finite Deformation Analysis Of Lipid Bilayer Membranes

The lipid bilayer membranes are an important part of cell membranes, vesicles and so on. It is closely linked with various biological function of cells. Therefore, it has great significance for the study of lipid bilayer membranes’mechanical properties. Nowadays, the main research methods include molecular dynamics, Monte Carlo method, the finite element method based on classical continuum and son on. In this article, we mainly use the quasi-continuum method. We have built a mechanical model of lipid bilayer membranes, present a continuous constitutive model based on higher order Cauchy-Born rule, and compute mechanical properties of lipid bilayer membranes.The mesh-free method has a great advantage with the Simulation of the large deformation, so we use the mesh-free method to establish the numerical framework of the finite deformation of lipid bilayer membranes and simulate the deformation of lipid bilayer membranes in this paper. From the simulation result, we found that the continuous constitutive model based on higher order Cauchy Born rule can be used to describe of the finite deformation of lipid bilayer membranes. In the tensile deformation, when the tensile displacement reaches a certain value, the shear band is found in the lipid bilayer membranes. In the shear deformation, when the shear displacement reaches a certain value, the slip band is found in the lipid bilayer membranes. We can effectively explain the deformation behavior by the representative cell of12molecules we have selected when we establish the continuum constitutive model.Therefore, from the simulation and analytical result, we can see that the constitutive of the lipid bilayer membrane we present is reasonable, and the mesh-free method to construct the computational framework of the large deformation is very effective. We can use them to accurately describe the deformation of lipid bilayer membranes.