Rates, Convected Time Derivatives, Objective Tensors and Objective Rates
Karan S. Surana · 2021
Since the deformation of a volume of matter is continuously evolving, i.e., the state of the matter changes as time elapses, all measures describing the deformation are naturally functions of time in addition to coordinates. This chapter discusses the rate of deformation of length, area and volume, strain rate tensors, spin tensors and convected time derivatives of various orders of stress and strain tensors. It presents the derivations to establish objectivity and objective rates of various tensors commonly encountered in classical continuum mechanics. The chapter discusses Galilean as well as Euclidean or non-Galilean transformations. Objective tensors are independent of the observer.