Mathematical Modeling of Hyperelastic Materials Undergoing Swelling

(1) Boundary Value Problems in Non Linear Elasticity WHEN Solid Mechanics is Coupled with other effects; (2) Mathematical Modeling of Hyperelastic Materials Undergoing Swelling

In standard nonlinear continuum mechanics it is the case that the continuity equation, the principles of linear and angular momentum, and the energy equation hold for any material regardless of its constitution. However, unless the body can be regarded as rigid, these equations are in general insufficient to determine the motion produced by given boundary conditions and body forces. They need to be supplemented by a further set of equations, known as constitutive equations, which characterize the material composition of the body. Such a set of constitutive equations usually serves to define an ideal material, and much of the work on modern continuum mechanics has been concerned with the formulation of constitutive equations to model as closely as possible the behavior of real materials. Recently a new constitutive framework for treating finite deformations when conventional elastic behavior is modified by the action of an additional balance requirement was proposed by Pence and Tsai. Other well-known examples of such frameworks are Gurtin’s theory of configurational forces and the Ericksen model of liquid crystals. Pence and Tsai have been motivated by the fact that in the event of substructural reconfiguration the notion of simple deformation X → y must be broadened so as to incorporate a more detailed kinematic description. In my thesis I have studied the solution of pure azimuthal shear problem in this new framework and compared the result with the solution of pure azimuthal shear problem in standard nonlinear elasticity. I have observed that such a treatment offer interesting possibilities for the development of singular surfaces that can be interpreted as locations of concentrated microstructural rearrangement.