Bina, C. R., Complex propagation of strain energy in icosahedral networks, Eos, Transactions of the American Geophysical Union, 86, Fall Meeting Supplement, NG33A-0170, 2005.
We have modeled the propagation of strain energy in both a vertex-based icosahedral network (12 nodes of degree 5, maximum geodesic of 3, icosahedral graph) and a face-based icosahedral network (20 nodes of degree 3, maximum geodesic of 5, dodecahedral graph), in which initial perturbation from a pre-strained state results in successive episodes of release of strain energy governed by threshold failure. The method may be extended to larger networks through icosahedral discretization of the sphere by higher-order triangulations. Relative to a reference case, we have begun to explore the effects of varying a number of network parameters. These include: the initial distribution of strain energies, the size of the initial perturbation, the nature (quantized vs. total) of threshold-governed energy release, the magnitude of syn-propagational damping, the extent of post-propagational relaxation, and the directionality (weighted mixtures of omnidirectional with either constant unidirectional or variable unidirectional) of post-failure propagation.For most cases explored thus far, simple patterns of nodal failure and energy release emerge, with networks exhibiting constant, decaying, or quasi-periodic behavior. More complex network behavior, exhibiting more complicated power spectra and less uniform levels of nodal activity, emerge only when various forms of directionality (i.e., radiation patterns) are introduced. Results from such modeling may eventually prove useful in studies of deformational microstructures or of triggered seismicity.
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