This is an introductory lecture that presupposes virtually no previousexperience with topics in finite elasticity. The kinematics of finite deformationis characterized by the polar decomposition theorem, and Euler's laws of balanceand the local field equations of continuum mechanics are described. The generalconstitutive equation of hyperelasticity theory is deduced from a mechanicalenergy principle, and the implications of frame invariance and material symmetryare presented. This leads to constitutive equations for compressible and incom-pressible, isotropic hyperelastic materials. Two major problems of finite elas-ticity theory are described. Some results concerning Ericksen's problem oncontrollable deformations possible in every isotropic hyperelastic material, andTruesdeirs problem concerning analytical restrictions imposed on constitutiveequations to assure meaningful physical behavior are outlined. Some examplesof nonuniqueness, including that of a neo-Hookean cube subject to uniform loadsover its faces, are illustrated. Elastic stability criteria and their connectionwith uniqueness in the theory of small deformations superimposed on largedeformations are introduced. Several examples of applications are sketchedthroughout the work
www.ima.umn.edu
