Photoelastic Tomography with Linear and Non-linear Algorithms

Tomography is a powerful method for the investigation of the internal structure of 3D objects from human bodies to atomic reactors. Classical tomography has been elaborated for the determination of scalar fields, i.e. fields, each point of which is characterized by a scalar. Due to that, algorithms of classical tomography can not be directly applied by investigating stress fields since stress is a tensor. In this paper it is shown that photoelastic tomography can be based on the equations of integrated photoelasticity. In the linear approximation the problem of stress field tomography is decomposed into a number of problems of scalar field tomography for single components of the stress tensor. In the non-linear case the axisymmetric stress field can be determined using a genetic algorithm. The paper is illustrated by several examples.