Abstract

An asymptotic analysis is conducted on a two-dimensional heterogeneous Canham–Helfrich flexoelectric biomembrane with constitutive laws rooted in thermodynamic principles. In the linearized Canham–Helfrich theory, the biomembrane’s elasticity is characterized by a fourth-order energy density. For a Canham–Helfrich lipid bilayer membrane with protein inclusions, periodic homogenization yields four distinct effective coefficients. Numerical simulations illustrate the dependence of these homogenized coefficients on the volume fraction and externally applied electric field. This theoretical & computational approach provides a framework that enhances biomembrane behavior understanding under complex loading and complex microstructures, with promising applications in advanced materials modeling and simulation.

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