Martensite Crystallography - the apparent controversy between the infinitesimal deformation approach and the phenomenological theory of martensitic transformations

The aim of this article is to demonstrate that the apparent controversy between the infinitesimal deformation (ID) approach and the phenomenological theory of martensitic transformations (PTMTs) in predicting the crystallographic characteristics of a martensitic transformation is entirely based on unjustified approximations associated with the way in which the ID calculations are performed. When applied correctly, the ID approach is shown to be absolutely identical to the PTMT. Nevertheless, there may be some advantages in using the ID approach. In particular, it is somewhat simpler than the PTMT; it is based on a physical concept that is easier to understand and, most important, it may provide a tool for investigating some of the features of martensitic transformations that have eluded explanation via the PTMT.

The displacement and strain field of three-dimensional rheologic model of earthquake preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains epsilon(xx) (r, t), epsilon(yy) (r, t) and epsilon(zz) (r, t) and the bulk strain theta (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (alpha, beta, gamma) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.