Determination of stress fields in the elastic lithosphere by methods based on stress orientations

Stress field in the Antarctic tectonic plate: elastic and plastic models

“…Therefore a 2D model reflecting driving forces applied at the AP boundary can be considered separately, while the complete 3D stress tensor can be obtained by superimposing the stresses caused by the rock weight and ice sheet load on the continental part of the plate. Gravitational potential energy differences which produce lateral body forces and have been recognised as an important source for intraplate stresses in AP, see Kreemer and Holt [15], in the elastic problem affect neither principal stress orientations nor deviatoric stresses if potential of body forces is approximated by harmonic function, as explained in Mukhamediev et al [16]. Lateral body forces caused by harmonic potential only influence the magnitudes of principal stresses by adding to them the same amount which can be different from point to point.…”

Introduction of STEM for stress analysis in statically determined bodies

“…Its solution is non-unique: although stress trajectories can be found uniquely, stress magnitudes are determined with some degree of arbitrariness. This approach has been suggested in [11][12][13] and tested for plane elasticity.…”

FEM type method for reconstruction of plane stress tensors from limited data on principal directions

“…This structure of the data makes it impossible to directly transfer the methods used in photoelasticity to the problem of stress identification in the lithosphere. Therefore special approaches have recently been developed in [4][5][6]. These approaches make use of mathematical theory of plane elasticity [7], where the mean stress and deviatoric stress functions are described by means of two holomorphic functions, complex potentials.…”

“…In this paper an example from photoelasticity for a beam under three point bending test is presented to verify the effectiveness of the proposed approach. It is further applied for geophysical data to study stresses in the Australian continent [4,5]. In these papers single plane domains have been considered.…”