Objective Time Derivative Defined as Covariant Derivative

摘要

Choice of an objective time derivative is still an open problem, even in elasticity. A geometrically based approach, defining the time derivative as a covariant derivative in an appropriate nonlinear space - the infinite dimensional Riemannian manifold of deformation tensor fields - will be employed, and, via coordinate approach, the covariant derivative and its corresponding time derivative of an arbitrary tensor field will be explicitly expressed.