"Development of the stress trajectories element method (STEM)" supported by the EPSRC, UK
This project is aimed at the development of theory and numerical techniques for stress analysis in solids caused by applied forces or contacts with other solids. The key innovation of this proposal is the investigation of consistency between constitutive equations and stress trajectories. These cannot be given simultaneously and either of them could be used with equations of equilibrium to form a closed system of partial differential equations. We address three essentially different cases when stress trajectories are known (i) everywhere inside the domain; (ii) at discrete points inside the domain; (iii) on the boundary. In all these cases the stress trajectory concept is used as a unified approach; therefore the method proposed in this application is referred to as the stress trajectories element method, STEM.
The research programme includes thorough analysis of all situations (i)-(iii) and development of a variant of the STEM is the expected outcome of this project. The STEM method is novel and innovative; it has not been applied for different rheologies. The following applications of the STEM have been studied: stress field identification in stable blocks of lithosphere; and analysis of stresses near excavations in rocks of different rheology.