Using a custom built experimental setup, biaxial and uniaxial extension tests are performed on the same specimen. In biaxial tests, the stretch ratio along y direction is held constant and the stretch ratio in the perpendicular x direction is increased gradually from 1 to 1.4. Stored energy function is obtained from seven different biaxial tests performed by varying the stretch ratio along the y direction at which it is held fixed. Stored energy functions are proposed for the tested rubber sheets by allowing the stored energy to be a function of the principal invariants of right Cauchy-Green deformation tensor or the invariants of the Hencky strain or the principal stretch ratios. To evaluate the performance of the developed stored energy functions, they are compared with 10 existing constitutive relations available in literature in terms of their ability to capture their biaxial response and predicting capability for the uniaxial experiments on the rubber specimens studied. This study reveals that the stored energy function developed in this study as a function of the principal invariants of the right Cauchy-Green deformation tensor predicts the uniaxial behavior the best and capture the biaxial response second best among the models studied for the tested material. However, even this model on an average has 25 percent error in the predicted stresses. © 2015 Elsevier Ltd. All rights reserved.

Umakanthan Saravanan

Department Of Civil Engineering

H. Hariharaputhiran

Deformation

ELASTICITY

TENSORS

BIAXIAL EXTENSION

INCOMPRESSIBLE

Isotropic

UNIAXIAL EXTENSION

VULCANIZED RUBBER

RUBBER

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Mechanics of Materials

In this study, we investigate the monotonic deformational response of Polyvinylidene fluoride (PVDF). Monotonic uniaxial and biaxial experiments are conducted and deformations are monitored using non-contact speckle monitoring method. The mechanical response of PVDF is observed to exhibit finite strains which are also anisotropic in nature. A hyper-elastic finite deformation transversely isotropic model is used to model the biaxial response of PVDF. Experimental data was shown to fit well with the proposed model. The model parameters obtained from biaxial tests were used to capture uniaxial response in two orthogonal directions and the ability of the model to predict any arbitrary mechanical response is assessed. © 2017, The Society for Experimental Mechanics, Inc.

Experimental Techniques

Characterization of the Monotonic Uniaxial and Biaxial Mechanical Response of Polyvinylidene Fluoride (PVDF) Films

A methodology for obtaining implicit constitutive representations involving the Cauchy stress and the Hencky strain for isotropic materials undergoing a non-dissipative process is developed. Using this methodology, a general constitutive representation for a subclass of implicit models relating the Cauchy stress and the Hencky strain is obtained for an isotropic material with no internal constraints. It is shown that even for this subclass, unlike classical Green elasticity, one has to specify three potentials to relate the Cauchy stress and the Hencky strain. Then, a procedure to obtain implicit constitutive representations for isotropic materials with internal constraints is presented. As an illustration, it is shown that for incompressible materials the Cauchy stress and the Hencky strain could be related through a single potential. Finally, constitutive approximations are obtained when the displacement gradient is small. © 2017, Springer International Publishing AG.

Zeitschrift fur Angewandte Mathematik und Physik

Representations for implicit constitutive relations describing non-dissipative response of isotropic materials

Many bodies of biological and engineering interest have a fibrous and layered structure. Hence, it is believed that these bodies are inhomogeneous and made up of anisotropic material. Classical mechanical experiments used to find the required material symmetry in the constitutive relation cannot distinguish inhomogeneous bodies made of isotropic material and homogeneous bodies made of anisotropic material. Therefore, it is of interest to find an alternative hypothesis so that inhomogeneity and anisotropy can be determined independent of the other. This study finds that the principal (or eigen) direction of the left Cauchy-Green deformation tensor, B does not vary with the magnitude of the applied uniaxial load at a given location whenever the body - homogeneous or inhomogeneous - is made of isotropic and hyperelastic material and the deformations are measured from a stress free reference configuration. In general, the principal direction of the left Cauchy-Green deformation tensor varies with the magnitude of the uniaxial load when the body is made up of anisotropic material. Thus, it is concluded that if the variation in the principal direction of B with the magnitude of the applied uniaxial load is experimentally investigated then one could ascertain whether the body is made up of isotropic or anisotropic material. © 2015 Elsevier Ltd.

Fulltext

International Journal of Solids and Structures

Identifying hyperelastic and isotropic materials by examining the variation of principal direction of left Cauchy-Green deformation tensor in uniaxial loading

Practically all experimental measurements related to the response of nonlinear bodies that are made within a purely mechanical context are concerned with inhomogeneous deformations, though, in many experiments, much effort is taken to engender homogeneous deformation fields. However, in experiments that are carried out in vivo, one cannot control the nature of the deformation. The quantity of interest is the deformation gradient and/or its invariants. The deformation gradient is estimated by tracking positions of a finite number of markers placed in the body. Any experimental data-reduction procedure based on tracking a finite number of markers will, for a general inhomogeneous deformation, introduce an error in the determination of the deformation gradient, even in the idealized case, when the positions of the markers are measured with no error. In our study, we are interested in a quantitative description of the difference between the true gradient and its estimate obtained by tracking the markers, that is, in the quantitative description of the induced error due to the data reduction. We derive a rigorous upper bound on the error, and we discuss what factors influence the error bound and the actual error itself. Finally, we illustrate the results by studying a practically interesting model problem. We show that different choices of the tracked markers can lead to substantially different estimates of the deformation gradient and its invariants. It is alarming that even qualitative features of the material under consideration, such as the incompressibility of the body, can be evaluated differently with different choices of the tracked markers. We also demonstrate that the derived error estimate can be used as a tool for choosing the appropriate marker set that leads to the deformation gradient estimate with the least guaranteed error. Copyright © 2013 by ASME.

Journal of Biomechanical Engineering

Fidelity of the estimation of the deformation gradient from data deduced from the motion of markers placed on a body that is subject to an inhomogeneous deformation field

Experimental Mechanics

Experimental Thermomechanical Analysis of Elastomers Under Uni- and Biaxial Tensile Stress State

European Journal of Mechanics - A/Solids

A hyperelastic constitutive model for rubber-like materials

International Journal of Non-Linear Mechanics

Problems in determining the elastic strain energy function for rubber

A new set of biaxial and uniaxial experiments on vulcanized rubber and attempts at modeling it using classical hyperelastic models

Journal	Data powered by TypesetMechanics of Materials
Publisher	Data powered by TypesetElsevier
ISSN	01676636
Open Access	No