Authors

Title

Application of Clifford algebra Cl3(C) to continuum and engineering mechanics

In

Acta Mechanica

Volume

223

Pages

2493–2507

Publisher

Springer

Year

2012

Indexed by

Abstract

Abstract Multivectorial algebra is of both academic and technological interest. Its application, however, is
not always easy. A distinction must be made between polar and axial vectors and between scalars and pseudoscalars.
Eight element types are often considered even if they are not always identified as multivectors. In
some cases, for simplicity’s sake, only vectorial algebra or quaternion algebra is explicitly used for physical
and mechanical applications. It would, however, be more convenient to use more complex algebra directly in
order to have a wider range of mechanical applications. The aim of this paper is to examine one particular
type of Clifford algebra that could solve this problem. The present study focusses on showing how these
quantities can be used to model mechanical and engineering problems. First, continuum mechanics in a Cauchy
medium is investigated for elastic transformations. Second, a specific type of shot-peening application is
studied. Applications are then used to illustrate the scope and efficiency of this type of modeling based on
geometric algebra.

Affiliations

Offprint