ABSTRACT
This chapter combines the concepts of continuum mechanics in relating the nonlinear strain deformations to the body and external forces and applies the finite element method together with Kane's equation in dynamics to formulate a set of differential equations to describe the dynamics of deformable bodies undergoing large rotations and displacements. Plastic behavior of materials is characterized by a nonunique stress-strain relationship. The definition of plasticity may be the presence of irrecoverable strains on load removal. Composite materials are widely used in aerospace and automotive engineering. The effects of high temperature are very common in certain engineering applications and one can anticipate that with the advent of technology robots will be working continuously over large periods of time in these environmental conditions. The chapter also shows how Kane's equation combined with finite element and continuum mechanics could lead to equations of motion that rely greatly on the concepts of partial velocities and partial angular velocities.
