Geodesic
Some sigmoid and reverse-sigmoid response patterns emerging from high-power loading of solids
Theoretical and applied mechanics, Tome 45 (2018) no. 1, p. 95

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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.
DOI : 10.2298/TAM171203007M
Classification : 74R05, 37N15, 74E35, 65D10
Keywords: dynamic behavior of solids, sigmoid curve, high strain rate loading, curve fitting, nonlinear phenomenological modeling 
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, p. 95 . doi: 10.2298/TAM171203007M
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