Some applications of elastic notch theory to problems of geodynamics
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This paper is concerned with the behavior of surface features of the earth which are, or have been, acted on by a stress field. The theory used in this paper is that of classical elasticity. Mathematical models are made which represent perfectly elastic two-dimensional regions which have a notch (or protrusion as a reversed notch can be considered to be). The regions are assumed to be semi-infinite and the notch on the free surface. The loads, or boundary conditions, are then prescribed. The problem of determining the distribution of stress is then considered. Solutions to this problem are presented for the cases of a circular notch, a generalized circular notch and a type of notch whose mathematical representation is given parametrically. Using these solutions and applying a criterion for failure, it is possible to predict what the general trend of the faulting should be in an actual body which the model may represent. Possible applications to geological structures are indicated.
KeywordsBoundary Condition Mathematical Model Free Surface Stress Field General Trend
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