Geodesic
Some sigmoid and reverse-sigmoid response patterns emerging from high-power loading of solids
Theoretical and applied mechanics, Tome 45 (2018) no. 1.

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The objective of the present review is twofold. First, it aims at highlighting some sigmoid and reverse-sigmoid response patterns observed recently in the course of simulations of the high-strain-rate loading of (mostly, quasibrittle) solids. Second, it aims at reviewing various properties of two models used frequently as curve fitting tools for nonlinear and saturable phenomena. These two models-inspired by the Hill and the Weibull cumulative distribution functions-are bounded by two horizontal asymptotes with a smooth transition between the baseline and the final saturation state, characterized by a non-negative (a non-positive) derivative at each point for the sigmoid (the reverse-sigmoid) shape. Although they were used primarily for data fitting because of their flexibility and effectiveness, these nonlinear models possess other properties useful for the analysis of the irreversible, nonlinear and far-from-equilibrium phenomena. The main features of these two models are systematically examined in this review. In spite of the fact that satisfactory curve-fitting of data could not be considered a proof of causality it could underline a pattern of behavior and, perhaps, provide an investigation guidance.
Keywords: dynamic behavior of solids, sigmoid curve, high strain rate loading, curve fitting, nonlinear phenomenological modeling 
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     author = {Sreten Mastilovi\'c},
     title = {Some sigmoid and reverse-sigmoid response patterns emerging from high-power loading of solids},
     journal = {Theoretical and applied mechanics},
     pages = {95 - 119},
     publisher = {mathdoc},
     volume = {45},
     number = {1},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/TAM_2018_45_1_a7/}
}
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Sreten Mastilović. Some sigmoid and reverse-sigmoid response patterns emerging from high-power loading of solids. Theoretical and applied mechanics, Tome 45 (2018) no. 1. http://geodesic.mathdoc.fr/item/TAM_2018_45_1_a7/