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Some sigmoid and reverse-sigmoid response patterns emerging from high-power loading of solids

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2018
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Authors
Mastilović, Sreten
Article (Published version)
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Abstract
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 systematica...lly 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:
sigmoid curve / nonlinear phenomenological modeling / high strain rate loading / dynamic behavior of solids / curve fitting
Source:
Theoretical and Applied Mechanics, 2018, 45, 1, 95-119
Publisher:
  • Srpsko društvo za mehaniku, Beograd

DOI: 10.2298/TAM171203007M

ISSN: 1450-5584

WoS: 000438527800007

Scopus: 2-s2.0-85049036904
[ Google Scholar ]
2
URI
http://rimsi.imsi.bg.ac.rs/handle/123456789/1117
Collections
  • Radovi istraživača / Researchers’ publications
Institution/Community
Institut za multidisciplinarna istraživanja
TY  - JOUR
AU  - Mastilović, Sreten
PY  - 2018
UR  - http://rimsi.imsi.bg.ac.rs/handle/123456789/1117
AB  - 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.
PB  - Srpsko društvo za mehaniku, Beograd
T2  - Theoretical and Applied Mechanics
T1  - Some sigmoid and reverse-sigmoid response patterns emerging from high-power loading of solids
EP  - 119
IS  - 1
SP  - 95
VL  - 45
DO  - 10.2298/TAM171203007M
ER  - 
@article{
author = "Mastilović, Sreten",
year = "2018",
abstract = "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.",
publisher = "Srpsko društvo za mehaniku, Beograd",
journal = "Theoretical and Applied Mechanics",
title = "Some sigmoid and reverse-sigmoid response patterns emerging from high-power loading of solids",
pages = "119-95",
number = "1",
volume = "45",
doi = "10.2298/TAM171203007M"
}
Mastilović, S.. (2018). Some sigmoid and reverse-sigmoid response patterns emerging from high-power loading of solids. in Theoretical and Applied Mechanics
Srpsko društvo za mehaniku, Beograd., 45(1), 95-119.
https://doi.org/10.2298/TAM171203007M
Mastilović S. Some sigmoid and reverse-sigmoid response patterns emerging from high-power loading of solids. in Theoretical and Applied Mechanics. 2018;45(1):95-119.
doi:10.2298/TAM171203007M .
Mastilović, Sreten, "Some sigmoid and reverse-sigmoid response patterns emerging from high-power loading of solids" in Theoretical and Applied Mechanics, 45, no. 1 (2018):95-119,
https://doi.org/10.2298/TAM171203007M . .

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