Two distinct two-dimensional theories for the modeling of thin elastic bodies are developed. These are demonstrated through numerical simulation of various types of membrane deformation. The work includes a continuum thermomechanics-based theory for wrinkled thin films. The theory takes into account single-layer sheets as well as composite membranes made of multiple lamina. The resulting model is applied to the study of entropic elastic elastomers as well as Mylar/aluminum composite films. The latter has direct application in the area of solar sails. Several equilibrium deformations are illustrated numerically by applying the theory of dynamic relaxation to a finite difference discretization based on Green’s theorem. In addition, a shell theory based on the peridynamic theory of Silling is developed. Peridynamics is a reformulation of classical continuum theory particularly suited to the modeling of damage and fracture. This theory is extended to include viscoelasticity and viscoplasticity. Several dynamic simulations are presented using a mesh-free explicit code.
Taylor, M. J. (2008). Numerical simulation of thermo -elasticity, inelasticity and rupture in membrane theory (Ph.D.). University of California, Berkeley, United States -- California.