Abstract
This paper defines a synthetic slip plane as the linear combination of a pair of twinned and untwinned e-planes in a single calcite crystal. This auxiliary slip plane can be used together with the twinned e-plane either to further constrain the extents of the compression and tension axes in graphic dynamic analysis or to better estimate the reduced stress in numerical dynamic analysis. In this paper we proposed the novel method that solves for the reduced stress by maximizing the sum of the shear stress along the slip line on each twinned e-plane or synthetic slip plane under the constraint of the 1-valued second stress invariant. This new method yields an analytical solution of stress. It is applied to a series of artificial examples without any measurement error generated under the prescribed stresses. The estimated stresses are generally accurate and robust, which illustrates the feasibility of this new method.
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