Stress tensor determination from the study of e twins in calcite: A linear programming method

Abstract

Abstract A new method for the determination of the stress tensor from calcite e twin lamellae has been discovered. All e planes (twinned and untwinned) are taken into account to enable derivation of tensor characteristics. The basic assumption is that the resolved shear stress, a linear function of the unknown stress tensor components, is greater (respectively lower) than the critical resolved shear stress for the twinned (respectively untwinned) planes; the relevant inequality constraints can be solved using linear programming algorithms. The application to experimental (Carrara marble) and natural samples (a goniatite from Morocco) has come up against one major difficulty — polyphase deformation. Thus, before applying this method, it is necessary to operate some selection of the data. One procedure based upon linear programming is proposed. The results are consistent with those expected both for the experimental and natural cases. For the Carrara marble, an estimate of the critical resolved shear stress ( t c ) for twinning gave a value around 300–400 bar. The method can give, in principle, the stress tensor orientation and the relative magnitude of principal stresses simultaneously.