Mechanics of Continuum Media: Modeling Elastic Behavior of Membranes

This lecture covers the modeling of continuum media, focusing on the elastic behavior of membranes. Topics include building axisymmetric membrane models, parametrization, rubber constitutive behavior, non-linear elastic behavior, energy formulation, discrete models, numerical solutions, homogeneous solutions, equilibrium equations, internal stress interpretation, and deriving equilibrium equations. Emphasis is placed on the universal procedure for constructing models, the benefits of the energy approach for numerical simulations and stability analysis, material instabilities, and geometric instabilities. The lecture concludes with a discussion on spherical balloons.