12 - Effective Mechanical Response of Biological Membranes

Abstract

The effective elastic response of biological membranes viewed as repetitive beam networks is evaluated based on the asymptotic homogenization method. A systematic methodology is set up to predict the overall mechanical properties of biological membranes in the nonlinear regime, reflecting the impact of the geometrical and mechanical network micro-parameters on the overall response of the effective substitution continuum. A classification of biomembranes networks is made based on nodal connectivity, so we analyze in this connectivity networks, which are deemed to be representative of most biological encountered networks. The individual network filaments are modeled as undulated beams prone to entropic elasticity, and the persistence length is one important parameter entering the tensile modulus. An effective micropolar substitution continuum of the biological network is evaluated, with a kinematics including nodal displacements and rotations, reflecting the discrete network deformation modes. The ratio of the characteristic bending lengths of the effective micropolar continuum to the unit cell size is a non-dimensional parameter used to quantify the importance of micropolar effects. The peptidoglycan network may present re-entrant hexagonal configuration caused by thermal or pressure fluctuations, for which micropolar effects become important. The predictive nature of the employed homogenization technique allows identifying a strain energy density of a hyperelastic model.