Unsheared Pairs and Triads

Dr. Michael Hayes
Professor, Department of Mathematical Physics
University College Dublin
Belfield, Dublin 4, Ireland
Member of the Royal Irish Academy

Sponsored by a grant provided by Professor Emeriti C. Wayne Martin

Date: Tuesday, September 5, 2000
Time: 3:30 p.m.
Place: W128 Nebraska Hall


The concept of unsheared pairs of material line elements at a material point X is introduced. It is seen that at a particle there is an infinity of unsheared pairs in any plane. In general, corresponding to every material line element in a plane there is a companion element such that the pair is unsheared. However, there are two elements, neither of which has a companion forming with it an unsheared pair. These “limiting directions” are such that elements along them undergo the greatest shear in the plane. It is seen how unsheared pairs are obtained. Their properties are presented.

Then the concept of unsheared triads at X is introduced. It is seen that there is an infinity of such triads. It is shown how they are constructed and how these unsheared triads are linked to a new decomposition of the deformation gradient.