ABSTRACT
In the specific case of elastic material models, work done by stresses during loading is stored as elastic strain energy, which is fully recovered upon unloading, so that the work done over a complete loading and unloading cycle is zero. A material is said to exhibit elastic behavior if there are no permanent deformations or residual stresses in any loading and unloading cycle. Linear elasticity is based on the assumption of infinitesimal displacements and strains, which leads to unique definitions of stresses and strains, also recognized as engineering stresses and strains. The Cayley–Hamilton theorem states, that any symmetric second-order matrix satisfies its own characteristic equation. The primary characteristic of natural rubbers and many rubberlike materials is that they are incompressible or nearly incompressible, as well as being capable of sustaining large elastic deformations. This chapter considers an interesting and instructive problem that has attracted the attention of many researchers called as "balloon problem".
