Efficient and robust numerical determination of stress trajectories in 2D and 3D domains

Abstract

This work presents an efficient and robust computational procedure for the determination of stress trajectories in 2D and 3D domains. This is preceded by a brief review of the historical context of stress trajectories, since their existence was implied by Lamé in 1841, together with other stress visualisation techniques used before the advent of computers. Application examples, obtained from analytical solutions or from finite element stress fields, for 2D, 3D and plate bending elastic problems, illustrate some characteristics of stress trajectories and the choices made in the proposed technique. This procedure, being general in nature, can be used in the visualisation of any real symmetric second order tensor field.