The Mooney-Rivlin constitutive model is often used for the characterization of hyperelastic rubber-like materials. To obtain the material constants for a model, only a uniaxial-tension-data set is usually used. Though it is regularly used for its easiness of processing data in a simple and practical way, the method is considered to be insufficiently accurate. To analyse the shortcoming of the method, a detailed examination was done with the Mooney-Rivlin two-parameter model. This paper discusses the variations related to three basic load curves, i.e., uniaxial, equibiaxial and pure-shear curves. For a visual observation of the fitted-data dispersion, two data-fitting cases were considered. The first one was the data fitting only through uniaxial data while the second one was a combination of uniaxial and pure-shear experimental-data curve fitting. A detailed one-to-one comparison of the curves was done to achieve an accurate estimation of the variations. Keywords: uniaxial tension, equibiaxial loading, pure shear/planar shear loading, curve fitting, Mooney-Rivlin constitutive modelMooney-Rivlinov temeljni model se pogosto uporablja za karakterizacijo gumi podobnih hiperelasti~nih materialov. Za materialne konstante se obi~ajno uporablja set podatkov, dobljenih z enoosnim nateznim preizkusom.^eprav se ta na~in uporablja zaradi enostavnosti in prakti~nosti metode pa ga lahko smatramo kot manj natan~nega. Zato, da bi avtorji tega prispevka ugotovili neskladje, so izvedli natan~no analizo z Mooney-Rivlinovim dvoparametri~nim modelom. V~lanku avtorji obravnavajo variacije, ki se nana{ajo na tri osnovne krivulje obremenjevanja: enoosno, ekvivalentno dvoosno in~isti strig. Vizualno opazovanje raztrosa prilagojenih podatkov so izvedli na osnovi dveh na~inov prilagajanja podatkov. Prvo prilagajanje podatkov so izvedli na osnovi rezultatov enoosnega nateznega preizkusa. V drugem primeru so uporabili kombinacijo obeh: eksperimentalne rezultate enoosnega nateznega preizkusa in~istega striga. Izvedli so natan~no primerjavo krivulj in ocenili odstopanja. Klju~ne besede: enoosni nateg, ekvivalentna biaksialna obremenitev,~isti strig, ravninska stri`na obremenitev, prilagajanje krivulje, Mooney-Rivlinov konstitutivni (temeljni) model
The experimental study deals with the effect of modification of the surface layer by irradiation cross-linking on the mechanical properties of the Poly (methyl methacrylate) - PMMA tested using the instrumented microhardness test. The surface layer of PMMA specimen made by injection technology was modified by irradiation cross-linking using beta irradiation, which significantly influences mechanical properties of the surface layer. Compared to the heat and chemical-heat treatment of metal materials (e.g. hardening, nitridation, case hardening), cross-linking in polymers affects the surfaces in micro layers. These mechanical changes of the surface layer are observed in the instrumented microhardness test. Our research confirms the comparable properties of surface layer of irradiated PMMA with highly efficient polymers. The subject of this research is the influence of irradiation dosage on the changes of mechanical properties of PMMA.
The risk of error in using only uniaxial data for fitting constitutive model curves is emphasized by many hyperelastic material researchers over the years. Unfortunately, despite these indications, often the method is utilized in finding material constants for mathematical models. The reason behind this erroneous practice is the difficulty in obtaining biaxial data. Therefore, as a remedial measure, in this research work we suggest a method of forecasting biaxial data from uniaxial data with a reasonable accuracy. Initially, a set of data is collected through standard uniaxial test. A predefined generalized function is then used to generate a set of values which subsequently used as multiplication factors in order to get biaxial tension data. Eventually, with availability of two data sets, Mooney-Rivlin two parameter model was used for combined data fitting. Material constants were then obtained through least squares approach and thereby theoretical load curves namely uniaxial, equi-biaxial tension and pure shear were drawn. The results of this work suggest a definite improvement related to three curves when compared with only uniaxial test data fitted outcomes. For validation of secondary biaxial data, separate eqi-biaxial test was done and resulting curves were compared. Biaxial primary data curve and forecasted data driven curve show identical data distribution pattern though there is a shift and therefore provide a basis for further research in this direction.
Mooney-Rivlin is the most frequently used model from all models used for mechanical characterization of the hyperelestic materials. Simplicity, applicability in a large rage of strains are the key reasons for regular use of this model. However, depending on the number of parameters, the Mooney model can take several forms. While, nine parameter being the highest order noticed, two parameter model is the most commonly found form in the current research domain. Since two parameter model used repetitively, we investigated the effect of incremental change in two material constant values one at a time, on model curve. As Drucker Stability Criterion is governing the extreme values of material parameters, changes in the model curves are discussed related to it. Resultant effects on stress-strain curves due to change in parameter values were examined and physical effect on the characterization is interpreted accordingly.
The presented study focuses on measuring volume changes in elastomeric materials using digital image correlation (DIC), specifically the 2D DIC universal system and the 2D DIC video-extensometer directly implemented to the universal testing machine. Optical measurement methods were applied in twodimensional (2D) configurations during the mechanical testing of dumbbell-shaped test specimens under uniaxial tension. The measured data were used to determine the dependencies of the bulk modulus and Poisson's ratio on the strain. The dependencies obtained by both methods correspond to the model behavior of rubber-like materials. Compared to the 2D DIC implemented video-extensometer, the 2D DIC universal system provides a tool for measuring transverse and longitudinal strain, and a wide range of post-processing options, including change of the input parameters, settings, or calculation relations.
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