caa a22 4500 605466807 CHVBK 20210128100308.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00397-015-0880-9 doi (NATIONALLICENCE)springer-10.1007/s00397-015-0880-9 An error-minimizing approach to inverse Langevin approximations [Elektronische Daten] [Benjamin Marchi, Ellen Arruda] The inverse Langevin function is an integral component to network models of rubber elasticity with networks assembled using non-Gaussian descriptions of chain statistics. The non-invertibility 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 error-minimizing 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 error-minimized forms of the particular base function. We applied the error-minimizing approach to Padé approximants, reducing the average and maximum relative errors admitted by the forms of the approximants. The error-minimization technique was extended to improve standard Padé approximants by way of understanding the error admitted by the specific approximant and using error-correcting 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 non-Gaussian, eight-chain 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. Springer-Verlag Berlin Heidelberg, 2015 Inverse Langevin function nationallicence Rubber elasticity nationallicence Statistical mechanics nationallicence Non-Gaussian chain statistics nationallicence Padé approximation nationallicence Marchi Benjamin Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA aut Arruda Ellen Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA aut Rheologica Acta Springer Berlin Heidelberg 54/11-12(2015-12-01), 887-902 0035-4511 54:11-12<887 2015 54 397 https://doi.org/10.1007/s00397-015-0880-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00397-015-0880-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Marchi Benjamin Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA aut NATIONALLICENCE 700 1- Arruda Ellen Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA aut NATIONALLICENCE 773 0- Rheologica Acta Springer Berlin Heidelberg 54/11-12(2015-12-01), 887-902 0035-4511 54:11-12<887 2015 54 397