Technical note: Coordinate representations of important differential operations in continuum mechanics

Abstract

This note is the last part in the trilogy Tensors in Continuum Mechanics. The first part was focused on the representations of m-linear functions on tensor spaces, especially on their duals and transpositions. The second part was dedicated to the memory of Prof. T. Salmi, and it was focused on the curvilinear coordinate systems in continuum mechanics (in Finnish). Because the relationship between stress and their strain conjugates has been discussed in several papers, the focus in the present third part is on a more specific area of continuum mechanics: representations of important differential operations (the gradient, divergence, rotor, and Laplace) in curvilinear coordinate systems.