Title: Notes on rate equations in nonlinear continuum mechanics,
Abstract: The paper gives an introduction to rate equations in nonlinear continuum
mechanics which should obey specific transformation rules. Emphasis is placed
on the geometrical nature of the operations involved in order to clarify the
different concepts. The paper is particularly concerned with common classes of
constitutive equations based on corotational stress rates and their proper
implementation in time for solving initial boundary value problems. Hypoelastic
simple shear is considered as an example application for the derived theory and
algorithms.