Authors: Benjamin C Marchi Ellen M Arruda
Publish Date: 2015/10/16
Volume: 54, Issue: 11-12, Pages: 887-902
Abstract
The inverse Langevin function is an integral component to network models of rubber elasticity with networks assembled using nonGaussian descriptions of chain statistics The noninvertibility of the inverse Langevin often requires the implementation of approximations A variety of approximant forms have been proposed including series rational and trigonometric divided domain functions In this work we develop an errorminimizing framework for determining inverse Langevin approximants This method can be generalized to approximants of arbitrary form and the approximants produced through the proposed framework represent the errorminimized forms of the particular base function We applied the errorminimizing approach to Padé approximants reducing the average and maximum relative errors admitted by the forms of the approximants The errorminimization technique was extended to improve standard Padé approximants by way of understanding the error admitted by the specific approximant and using errorcorrecting functions to minimize the residual relative error Tailored approximants can also be constructed by appreciating the evaluation domain of the application implementing the inverse Langevin function Using a nonGaussian eightchain network model of rubber elasticity we show how specifying locations of zero error and reducing the minimization domain can shrink the associated error of the approximant and eliminate numerical discontinuities in stress calculations at small deformations
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