scholarly journals Measuring magnetic moments of polydisperse ferrofluids utilizing the inverse Langevin function

2019 ◽  
Vol 100 (13) ◽  
Author(s):  
Ingo Rehberg ◽  
Reinhard Richter ◽  
Stefan Hartung ◽  
Niklas Lucht ◽  
Birgit Hankiewicz ◽  
...  
Keyword(s):  
Magnetic Moments ◽  
Langevin Function ◽  
Inverse Langevin Function

A generalized approach to generate optimized approximations of the inverse Langevin function

2018 ◽  
Vol 24 (7) ◽  
pp. 2047-2059 ◽  
Author(s):  
Vahid Morovati ◽  
Hamid Mohammadi ◽  
Roozbeh Dargazany
Keyword(s):  
Langevin Function ◽  
Inverse Langevin Function

Improvement of HIA model and the impact of the inverse Langevin function proposed by Marchi and Arruda

2020 ◽  
Vol 60 (1) ◽  
pp. 49-58
Author(s):  
Moustapha Mohamadou Bachirou ◽  
Bale Baidi Blaise ◽  
Kaoutoing Maxime Dawoua ◽  
Gambo Betchewe ◽  
Tibi Beda
Keyword(s):  
Langevin Function ◽  
Inverse Langevin Function ◽  
The Impact

A new based error approach to approximate the inverse langevin function

2014 ◽  
Vol 53 (8) ◽  
pp. 585-591 ◽  
Author(s):  
Alain Nkenfack Nguessong ◽  
Tibi Beda ◽  
François Peyraut
Keyword(s):  
Langevin Function ◽  
Inverse Langevin Function

scholarly journals On a new class of non-Gaussian molecular-based constitutive models with limiting chain extensibility for incompressible rubber-like materials

2021 ◽  
pp. 108128652110010
Author(s):  
Afshin Anssari-Benam
Keyword(s):  
Strain Hardening ◽  
Large Deformations ◽  
Structural Basis ◽  
Deformation Tensor ◽  
Model Parameters ◽  
New Class ◽  
Langevin Function ◽  
Inverse Langevin Function ◽  
Limiting Chain Extensibility ◽  
Non Gaussian

In constitutive modelling of rubber-like materials, the strain-hardening effect at large deformations has traditionally been captured successfully by non-Gaussian statistical molecular-based models involving the inverse Langevin function, as well as the phenomenological limiting chain extensibility models. A new model proposed by Anssari-Benam and Bucchi ( Int. J. Non Linear Mech. 2021; 128; 103626. DOI: 10.1016/j.ijnonlinmec.2020.103626), however, has both a direct molecular structural basis and the functional simplicity of the limiting chain extensibility models. Therefore, this model enjoys the benefits of both approaches: mathematical versatility, structural objectivity of the model parameters, and preserving the physical features of the network deformation such as the singularity point. In this paper we present a systematic approach to constructing the general class of this type of model. It will be shown that the response function of this class of models is defined as the [1/1] rational function of [Formula: see text], the first principal invariant of the Cauchy–Green deformation tensor. It will be further demonstrated that the model by Anssari-Benam and Bucchi is a special case within this class as a rounded [3/2] Padé approximant in [Formula: see text] (the chain stretch) of the inverse Langevin function. A similar approach for devising a general [Formula: see text] term as an adjunct to the [Formula: see text] part of the model will also be presented, for applications where the addition of an [Formula: see text] term to the strain energy function improves the fits or is otherwise required. It is concluded that compared with the Gent model, which is a [0/1] rational approximation in [Formula: see text] and has no direct connection to Padé approximations of any order in [Formula: see text], the presented new class of the molecular-based limiting chain extensibility models in general, and the proposed model by Anssari-Benam and Bucchi in specific, are more accurate representations for modelling the strain-hardening behaviour of rubber-like materials in large deformations.

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