Modeling and Analysis of the Buckling Phenomena in the Homogeneous and Heterogeneous Biomembranes

Buckling;Membrane;Mechanical Engineering

Madani Tonekaboni, Seyed Ali

University of Waterloo

关键词: Buckling;    Membrane;    Mechanical Engineering;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/7686/1/MadaniTonekaboni_SeyedAli.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

In this project, nonlinear behavior of biomembrane are modeled as heterogeneous elasticbiological systems. In addition to the static behavior of the membranes, their dynamicbehavior are modeled to be able to investigate time-dependency of the variables of thesystems. Some of the available models are used and some new ones are developed to studystatic and dynamic analysis of monolayer and bilayer membranes as well as circular axisymmetric biomembranes. The presented models are developed based on the Euler-Bernoulliconstitutive law and employed to investigate buckling phenomena in the membranes as oneof the most important physical phenomena in biological environment.Static and dynamic behavior of Buckling phenomenon in biological membranes are modeled.The static model results in nonlinear ordinary di erential equation for one-dimensionalapproximation. In order to extend the model for circular membranes, the criteria of constantlength in one-dimensional membranes is changed to constant surface. Moreover,tension-compression and bending springs are added to the model and employed to studybuckling of biomembranes. Similar to the procedure of obtaining the equations of staticlarge deformation of the membrane, the equations of motion of the membrane is obtainedusing free body diagram of an in finitesimal element of the membrane and employing Euler-Bernoulli constitutive law. Hence, nonlinear integro partial di erential equations are obtainedt model the dynamic behavior of the membrane. All of the equations, includingstatic and dynamic ones, are changed to the dimensionless forms so that the results can beconsidered general and can be employed to analyze diff erent systems with diff erent properties.The nondimensional equations of each part of the project are solved using di erent iterativeand time-dependent schemes. The schemes are used to obtain the discretized formsof the equations. The discretized equations of all nodes of the domain, with due attentionto the considered boundary conditions, are gathered in a matrix and the matrix solved toobtain the solution of the variables at each node and time stage.The solutions obtained for diff erent problems investigated in this project are employed to illustrate variations of diff erent dependent variables of the models with respect to the independentvariables and parameters of the problems. As the important step to analyze theproblems, diff erent results of the problems investigated in the project are verifi ed using theavailable information in literature. Membrane pro le are obtained for di erent parametervalues and external forces in the stationary condition. In addition, variation of maximumdeflection and slope are studied with respect to the variation of diff erent dimensionlessparameters of the system. As a verifi cation of the solution, the incompressibility of bilayermembrane is shown as well. Growth of di fferent variables is shown with respect to timeemploying the solution of dynamic modeling of the membrane. As one of the importantparts of this project, e ects of heterogeneity on dynamic behavior of the membrane underbuckling is investigated. The heterogeneous region is considered to have di fferent materialproperties and it position is changed to also study the geometrical e ffects.