caa a22 4500 477063934 CHVBK 20180405111407.0 cr unu---uuuuu 170330e19960301xx s 000 0 eng 10.1007/BF00192066 doi (NATIONALLICENCE)springer-10.1007/BF00192066 Nagahama H. Institute of Geology and Paleontology, Faculty of Science, Tohoku University, 980, Kawauchi, Sendai, Japan aut Non-riemannian and fractal geometries of fracturing in geomaterials [Elektronische Daten] [H. Nagahama] The mechanism of earthquakes is presented by use of the elastic dislocation theory. With consideration of the continuous dislocation field, the general problem of medium deformation requires analysis based on non-Riemannian geometry with the concept of the continuum with a discontinuity ("no-more continuum”). Here we derive the equilibrium equation (Navier equation) for the continuous dislocation field by introducing the relation between the concepts of the continuous dislocation theory and non-Riemannian geometry. This equation is a generalization of the Laplace equation, which can describe fractal processes like diffusion limited aggregation (DLA) and dielectric breakdown (1313). Moreover, the kinematic compatibility equations derived from Navier equation are the Laplace equations and the solution of Navier equation can be put in terms of functions which satisfy the biharmonic equation, suggesting a close formal connection with fractal processes. Therefore, the relationship between the non-Riemannian geometry and the fractal geometry of fracturing (damage) in geomaterials as earthquakes can be understood by using the Navier equation. Moreover, the continuous dislocation theory can be applied to the problem of the earthquake formation with active folding related with faulting (active flexural-slip folding related to the continuous dislocation field). Springer-Verlag, 1996 dislocation nationallicence non-Riemannian geometry nationallicence fractal geometry nationallicence active flexural-slip folding nationallicence Navier equation nationallicence Geologische Rundschau Springer-Verlag 85/1(1996-03-01), 96-102 0016-7835 85:1<96 1996 85 531 https://doi.org/10.1007/BF00192066 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00192066 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Nagahama H. Institute of Geology and Paleontology, Faculty of Science, Tohoku University, 980, Kawauchi, Sendai, Japan aut NATIONALLICENCE 773 0- Geologische Rundschau Springer-Verlag 85/1(1996-03-01), 96-102 0016-7835 85:1<96 1996 85 531 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer