Now showing 1 - 4 of 4
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    On the adequacy of the existing restrictions on the constitutive relations to ensure reasonable elastic response of compressible bodies
    We show that even when the constitutive relations for the elastic response of compressible bodies satisfy the empirical, Baker-Ericksen and ordered forces inequalities and ellipticity restrictions, they could result in physically unrealistic response. We pick a constitutive relation that satisfies the above inequalities and is also globally elliptic but its response to both uniaxial extension and inflation at constant length is physically unrealistic, based on the available experimental observations. However, the Coleman-Noll, pressure-compression, tension-extension and invertibility of force-stretch conditions and that proposed in Carroll and McCarthy (1995) are violated by this constitutive relation. © 2011 Elsevier Ltd. All rights reserved.
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    A three dimensional constitutive model for plain cement concrete
    (10-04-2019)
    Gokulnath, C.
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    Varaprasad, Dara
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    The validity of some of the assumptions made during systematic development of constitutive relation – homogeneity, isotropy, and non-dissipative response – is examined experimentally by testing plain concrete cylinders in the circumferential displacement controlled uniaxial compression tests. The tested cylinders indicate that the surface strains are not uniform and that the principal direction of the strain varies with the magnitude of the applied load. Hence, these cylinders are either deforming from a stressed state or anisotropic or both. The percentage dissipation computed as the area between the loading and unloading curves normalized using the area under the unloading curve is less than 10 percent up to 90 percent of the peak load. Therefore the mechanical response of concrete can be considered as non-dissipative. Assuming that the magnitude of the residual stresses present in the concrete panels would be small compared to the stresses arising due to the applied load, these residual stresses are ignored. Consequently, using the implicit constitutive theory framework for isotropic and compressible materials undergoing a non-dissipative process from a stress-free reference configuration, a three-dimensional constitutive relation for plain concrete is proposed. The material parameters in the proposed model are estimated from the uniaxial compression test and equal biaxial compression test. These parameters are expressed using initial Young's modulus, initial Poisson's ratio, maximum uniaxial compressive stress, the axial and transverse strain corresponding to the maximum uniaxial compressive stress, maximum equal biaxial compressive stress and the equal biaxial strain corresponding to maximum equal biaxial compressive stress. The ability of the proposed model to capture the response of various grade and type of concrete in ten biaxial experiments reported in the literature is examined. It is found that despite the limiting assumptions, the compression-compression, compression-tension and tension-tension stress strain response of the concrete in these ten experiments are adequately captured by the proposed model with mean R 2 value of 0.94.
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    Publication
    Modeling the non-dissipative response of vulcanized unfilled rubber
    (01-03-2020)
    Gokulnath, C.
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    Here the possibility of developing a better three dimensional model for rubber when Hencky strain is written as an explicit function of the Cauchy stress is examined. Based on the experimental evidence, vulcanized unfilled rubber is assumed to be isotropic, incompressible, and deforming from a stress-free reference configuration. Vulcanized unfilled rubber undergoes strain-induced crystallization when uniaxial stretch exceeds 2. Therefore, in this study, a non-dissipative model is sought for rubber only till the von Mises stress is below a critical value. Using the biaxial response reported in Kawabata et al. (1981), the material functions are arrived adopting Rivlin and Saunders methodology. The material constants in the determined material functions are found using biaxial tests for four other experimental studies on rubber reported in the literature. The ability of the arrived constitutive model to describe the uniaxial and equal biaxial response of the same rubber is evaluated. The proposed model is benchmarked with established models in the classical framework. Among the models studied the proposed model performed as well as the other models for Kawabata et al. data set and marginally better than the other models for the remaining four experimental data sets. However, while the proposed model performance does not critically depend on the experiments used to deduce the material parameters, for the other models the material parameters need to be found from fixed biaxial experiments for better performance.
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    Publication
    A new set of biaxial and uniaxial experiments on vulcanized rubber and attempts at modeling it using classical hyperelastic models
    (01-01-2016)
    Hariharaputhiran, H.
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    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.