Some sigmoid and reverse-sigmoid response patterns emerging from high-power loading of solids
2018
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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 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.
Ključne reči:
sigmoid curve / nonlinear phenomenological modeling / high strain rate loading / dynamic behavior of solids / curve fittingIzvor:
Theoretical and Applied Mechanics, 2018, 45, 1, 95-119Izdavač:
- Srpsko društvo za mehaniku, Beograd
DOI: 10.2298/TAM171203007M
ISSN: 1450-5584
WoS: 000438527800007
Scopus: 2-s2.0-85049036904
Institucija/grupa
Institut za multidisciplinarna istraživanjaTY - 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 . .