A comparative study on hyperelastic constitutive models on rubber: State of the art after 2006

2019-01-01
Dal, Hüsnü
Acikgoz, K.
Denli, F. A.
The micromechanically based network models are known to be superior over the purely phenomenological models in the analysis of unfilled rubber. However, various factors play a crucial role in the selection of the appropriate constitutive model for the analysis of technical rubbers. These are; ( i) the number of available experiments under various loading conditions, (ii) maximum stretch level expected in the critical loading scenarios of the rubber component, and (iii) percentage of fillers and additives that might distort the mechanical response from that of an ideal rubber. Moreover, the number of material parameters to be identified should be as low as possible and the parameters should be physically interpretable. 12 years have passed since the celebrated work of Marckmann and Verron [Rubb. Chem. Tech. 79.5, 835-858, 2006] where they have compared 20 hyperelastic constitutive models for rubber. Since then, the rubber community witnessed emergence of many more hyperelastic models. Although the recent reviews have been very useful for the assessment of the strengths and weaknesses of various constitutive models, especially on the modeling of uncrosslinked ideal rubber, it is still a challenging endeavor for engineers to decide the best constitutive model for the specific rubber compound at hand. This paper presents a novel parameter identification toolbox based on various multi-objective optimization strategies for the selection of the best constitutive models from a given set of uniaxial tension, pure shear and equibiaxial tension experiments. The toolbox aims at providing an objective model selection procedure along with the material parameters for the rubber compound at hand. To this end, we utilize the multi-objective optimization using a successive genetic algorithm and gradient based search through the FMINCON utility in MATLAB. The novelty of our approach is (i) simultaneous fitting - the use of variable weight factors for uniaxial, equibiaxial, and pure shear data which accommodates for the (in) capability of the specific constitutive model to the specific deformation modes ( ii) the sorting of the models based on an objective normalized quality of fit metric and (iii) simultaneous fittings are conducted for the models that are inherently incapable of catching large deformations, starting from zero stretch, and with 5% stretch increments until the model breaks where its quality of fit value goes above a predetermined set value. This allows identification of their validity region, i.e., the region they can work within an acceptable quality of fit margin. Accordingly, over 40 hyperelastic models are sorted with respect to the experimental data of Treloar and Kawabata.

Suggestions

The nonextensive generalization of Boltzmann-Gibbs statistics and its application
Bağcı, Gökhan Barış; Sever, Ramazan; Department of Physics (2005)
This thesis analyzes the nonextensive generalization of Boltzmann-Gibbs statistics and study its applications to some physical models such as isotropic rigid and non-rigid rotators. The thesis will also try to show what kind of internal energy constraint must be chosen for entropy optimization in a mathematically consistent manner.
A Comparative Study on Isolator Modeling Approaches
Çabuk, Eser; Akyüz, Uğurhan; Sütcü, Fatih; Nobuo, Murota (2023-01-01)
Due to the complexity in the development of highly nonlinear models, engineers tend to use more practical ones such as smoothed or sharp bilinear models. It has been shown that differences in hysteresis characteristics may lead to variance in performance parameters, resulting in possible overdesign or underdesign. In this study, to assess the effect of the modelling approach on seismic performance, high damping rubber bearing was designed and evaluated in terms of structural performance for a selected hospi...
An Assessment of BIM-CAREM Against the Selected BIM Capability Assessment Models
YILMAZ, GÖKÇEN; Akçamete Güngör, Aslı; DEMİRÖRS, ONUR (2018-10-04)
Although various BIM capability and maturity models have been developed to meet different BIM capability/maturity assessment purposes, there has not been a model which is broadly used and commonly accepeted in the literature. A Reference Model for BIM Capability Assessment (BIM-CAREM) was developed based on the meta-model of ISO/IEC 33000 to be used for assessing BIM capability levels of AEC/FM processes. This paper aims to compare the components of BIM-CAREM with the assessment questions of the identified ...
A micro-macro approach to rubber-like materials?Part I: the non-affine micro-sphere model of rubber elasticity
Miehe, C; Göktepe, Serdar; Lulei, F. (Elsevier BV, 2004-11)
The contribution presents a new micro-mechanically based network model for the description of the elastic response of rubbery polymers at large strains and considers details of its numerical implementation. The approach models a rubber-like material based on a micro-structure that can be symbolized by a micro-sphere where the surface represents a continuous distribution of chain orientations in space. Core of the model is a new two-dimensional constitutive setting of the micro-mechanical response of a singl...
First-order marginalised transition random effects models with probit link function
Asar, Ozgur; İlk Dağ, Özlem (2016-04-03)
Marginalised models, also known as marginally specified models, have recently become a popular tool for analysis of discrete longitudinal data. Despite being a novel statistical methodology, these models introduce complex constraint equations and model fitting algorithms. On the other hand, there is a lack of publicly available software to fit these models. In this paper, we propose a three-level marginalised model for analysis of multivariate longitudinal binary outcome. The implicit function theorem is in...
Citation Formats
H. Dal, K. Acikgoz, and F. A. Denli, “A comparative study on hyperelastic constitutive models on rubber: State of the art after 2006,” 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/49282.