Affiliation:
1. Institut za multidisciplinarna istraživanja, Beograd
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
National Library of Serbia
Subject
Applied Mathematics,Mechanical Engineering,Computational Mechanics
Cited by
4 articles.
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