Dynamics of an Electric Field Vulnerable Morpho-Elastic Biological Membranes

Abstract

This work presents the dynamic modeling and analysis of an electric field vulnerable morpho-elastic biological membranes. Such smart membranes combine electrical properties with active functionalities, creating flexible and responsive surfaces. A continuum physics-based electro-morpho-elastic model is developed to predict the dynamic response of the smart membrane and interrogate the impact of isotropic and anisotropic growth along with fiber orientations at different prestretches. The governing equation of motion for the membrane dynamics is derived by applying Newton’s second law. The findings of the model solutions offer an understanding of how the DC and AC dynamic actuation modes modify the nonlinear behavior of membranes. The free and forced vibrations are illustrated using the Poincaré map, phase diagrams, and time-history response. Notably, the steady oscillation around the stable equilibrium stretch, whose magnitude decreases with the enrichment in membrane anisotropy and fiber orientation, decreases with anisotropic growth. Additionally, the system energy rises with the anisotropy parameter and shifts from isotropic to anisotropic growth, decreasing with greater fiber orientation.