Systematic Fitting and Comparison of Hyperelastic Continuum Models for Elastomers

authored by: Alexander Ricker, Peter Wriggers
Abstract: Hyperelasticity is a common modeling approach to reproduce the nonlinear mechanical behavior of rubber materials at finite deformations. It is not only employed for stand-alone, purely elastic models but also within more sophisticated frameworks like viscoelasticity or Mullins-type softening. The choice of an appropriate strain energy function and identification of its parameters is of particular importance for reliable simulations of rubber products. The present manuscript provides an overview of suitable hyperelastic models to reproduce the isochoric as well as volumetric behavior of nine widely used rubber compounds. This necessitates firstly a discussion on the careful preparation of the experimental data. More specific, procedures are proposed to properly treat the preload in tensile and compression tests as well as to proof the consistency of experimental data from multiple experiments. Moreover, feasible formulations of the cost function for the parameter identification in terms of the stress measure, error type as well as order of the residual norm are studied and their effect on the fitting results is illustrated. After these preliminaries, invariant-based strain energy functions with decoupled dependencies on all three principal invariants are employed to identify promising models for each compound. Especially, appropriate parameter constraints are discussed and the role of the second invariant is analyzed. Thus, this contribution may serve as a guideline for the process of experimental characterization, data processing, model selection and parameter identification for existing as well as new materials.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): German Institute of Rubber Technology (DIK e.V.)
Type: Review article
Journal: Archives of Computational Methods in Engineering
Volume: 30
Pages: 2257-2288
No. of pages: 32
ISSN: 1134-3060
Publication date: 04.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computer Science Applications, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s11831-022-09865-x (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{80894e0c0d734ca994bd6fb7585d935c,
title = "Systematic Fitting and Comparison of Hyperelastic Continuum Models for Elastomers",
abstract = "Hyperelasticity is a common modeling approach to reproduce the nonlinear mechanical behavior of rubber materials at finite deformations. It is not only employed for stand-alone, purely elastic models but also within more sophisticated frameworks like viscoelasticity or Mullins-type softening. The choice of an appropriate strain energy function and identification of its parameters is of particular importance for reliable simulations of rubber products. The present manuscript provides an overview of suitable hyperelastic models to reproduce the isochoric as well as volumetric behavior of nine widely used rubber compounds. This necessitates firstly a discussion on the careful preparation of the experimental data. More specific, procedures are proposed to properly treat the preload in tensile and compression tests as well as to proof the consistency of experimental data from multiple experiments. Moreover, feasible formulations of the cost function for the parameter identification in terms of the stress measure, error type as well as order of the residual norm are studied and their effect on the fitting results is illustrated. After these preliminaries, invariant-based strain energy functions with decoupled dependencies on all three principal invariants are employed to identify promising models for each compound. Especially, appropriate parameter constraints are discussed and the role of the second invariant is analyzed. Thus, this contribution may serve as a guideline for the process of experimental characterization, data processing, model selection and parameter identification for existing as well as new materials.",
author = "Alexander Ricker and Peter Wriggers",
note = "Funding Information: The authors would like to thank Jan Plagge, Deutsches Institut f{\"u}r Kautschuktechnologie e.V., Hannover for the fruitful discussion on the data preparation section. Moreover, the constructive and helpful feedback on the manuscript by Meike Gierig, Leibniz University Hannover, is highly appreciated.",
year = "2023",
month = apr,
doi = "10.1007/s11831-022-09865-x",
language = "English",
volume = "30",
pages = "2257--2288",
journal = "Archives of Computational Methods in Engineering",
issn = "1134-3060",
publisher = "Springer Netherlands",
number = "3",
}