Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Auxetic foams were fabricated using thermo-mechanical process. Image analysis was performed to find Poisson’s ratio values. Compression tests were performed to generate stress–strain data. Experimental data is used to determine the parameters for a variant of Ogden model (proposed by Ciambella et al., 2015) for negative Poisson’s ratio (auxetic) material. Experimental data of two different auxetic foams (fabricated using 2.06 and 2.98 compression factors) are used. Constrained optimization was performed in MATLAB to determine the best values of the model parameters. This material model can be used in finite element simulations to study the behavior of auxetic foams in various cushioning applications.

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School of Mechanical Engineering

Vellore Campus

Centre for Biomaterials, Cellular and Molecular Theranostics

Materials Today: Proceedings

Mathematical modeling of auxetic foams

Based on a Gibbs potential formulation for implicit elastic bodies, we propose a new strain limiting constitutive relation using Lode invariants of stress, and numerically study a non-dimensionalized problem of a plate with radiused V-notch subjected to tensile traction. The stress predicted by the new relation agrees with the linearized elastic model beyond a certain distance from the notch-tip. As we approach the tip, the stress associated with the new constitutive relation increases rapidly, and it is nonlinear in the vicinity of the radiused-tip, unlike bounded stress predicted by the linearized elastic model. © 2020, © 2020 Taylor & Francis Group, LLC.

Mechanics of Advanced Materials and Structures

Stress growth in the vicinity of radiused V-notch subjected to in-plane loading for a strain limiting model based on Lode invariants of stress

In the previous part of this work (see Devendiran et al. (2018)), a new non-linear rate-type compressible viscoelastic model with independent volumetric and distortional limiters was proposed. In the present work, the developed constitutive equation is validated using experimental data generated in-house for two cyclic inhomogeneous deformations which are predominantly two-dimensional: non-uniform planar extension and barreling compression of carbon-black filled elastomeric sheets and circular cylinders, respectively, under different rates of cyclic deformations. In the finite element simulations of these two boundary value problems, the two-dimensional governing equations are formulated in Lagrangian basis and the resulting system of partial differential equations are solved using COMSOL®. A good agreement is observed between the numerical results and the corresponding experimental data, including the cyclic stress softening effect (Mullins effect). © 2019 Elsevier Ltd

International Journal of Non-Linear Mechanics

Validation of a thermodynamically consistent compressible rate-type viscoelastic model with independent limits on dilation, contraction, and distortion

Carbon black filled natural and synthetic rubbers used in automobile tires have to sustain a very large hydrostatic tensile stress between the two steel belts, especially near the belt edge. In addition, the rate effect of the volumetric and the distortional response of filled elastomers becomes significant for vehicles running at high speeds. In other words, by limiting the volumetric and distortional response and making it rate dependent, one can emulate the high stresses observed in tires. There are a number of constitutive equations of the rate and integral type for filled elastomers, but none of the available models employ a rate-dependent dilatational limit. In this paper, we propose a new non-linear rate-type compressible viscoelastic incorporating individual limits for dilatation, contraction, and distortion. The rate type thermodynamic framework of Rajagopal and Srinivasa (2000) is extended to include such limits. By establishing the physical meaning of various parameters used in the constitutive equation, we show that they are tightly correlated with the certain type of experiments and can be determined from the available data in the literature. Only a few parameters need to be determined by curve fitting. The proposed model is validated using in-house as well as the other experimental data available in the literature. In Part B of the paper, extensive validation of the proposed constitutive equation for cyclic barreling and cyclic inhomogeneous planar extension will be demonstrated. © 2018 Elsevier Ltd

Journal of the Mechanics and Physics of Solids

A thermodynamically consistent compressible rate-type viscoelastic model with independent limits on dilation, contraction, and distortion. Part A: Modeling

Models based on mixture theory allow for a systematic study of the response of mixtures by considering the responses of individual constituents and their interactions. Several classical models and their generalizations can be derived consistently from continuum theory of mixtures using special constitutive assumptions and approximations. In this paper some intriguing applications, where mixture theory approach is applied under different settings, are discussed. The need and scope for experimental design and measurement techniques for validation of mixture models is also discussed. A brief note on the boundary conditions and mathematical issues concerning the numerical simulations is made.

International Journal of Advances in Engineering Sciences and Applied Mathematics

Remarks on continuum theory of mixtures: editorial to special issue on mixture theory

Stress power-law fluids are a special sub-class of fluids defined through implicit constitutive relations, wherein the symmetric part of the velocity gradient depends on a power-law of the stress (see Eq. (2.2)), and were introduced recently to describe the non-Newtonian response of fluid bodies. Such fluids are counterparts to the classical power-law fluids wherein the stress is given in terms of a power-law for the symmetric part of the velocity gradient. Stress power-law fluids can describe phenomena that cannot be described by classical power-law fluids (see [1]). In this paper, first a new exact solution for a variant of Stokes' first problem for stress power-law fluids, when the exponent n=0 (Navier-Stokes fluid), is obtained. Such an exact solution for the stress is in terms of a convolution integral, for which we establish bounds. We then compute the convolution integral using Gauss-Kronrod quadrature by ensuring that its value always lies within the bounds. Using the validated quadrature, we can accurately evaluate the exact solution and we the exact solution it to validate the numerical scheme employed in solving the governing equations for stress-power law fluids with arbitrary exponent n. Finally, for stress power-law fluids wherein the exponent n<0 (stress-thickening fluids), we obtain an approximate solution for the stress that agrees well with the numerical solution. © 2015 Elsevier Ltd. All rights reserved.

Exact, approximate and numerical solutions for a variant of Stokes' first problem for a new class of non-linear fluids

We study the propagation of circumferential stress waves in an annular cylindrical region comprised of a new class of isotropic homogeneous elastic bodies. The class of elastic bodies under consideration does not belong to either the classical Cauchy elastic or Green elastic bodies. Unlike the case of classical elasticity theory that reduces to the classical linearized elasticity theory when the displacement gradients are sufficiently small, it is possible that in the new class the linearized strain is related non-linearly to the stress. This possibility leads to a non-linear system of equations that admits the propagation of circumferential shear stress waves in the body.

The Quarterly Journal of Mechanics and Applied Mathematics

Circumferential stress waves in a non-linear cylindrical annulus in a new class of elastic materials

A thermodynamic framework for chemically reacting systems is put to use in kinetic modeling of any chemical system with N species undergoing M reactions. A new approach of deriving kinetic models from a Gibbs potential, of multivariate polynomial function, is demonstrated with an example of single reaction system involving three species. Also, the usual first order kinetics is deduced as a special case in the example. The distinct advantages of the new approach lies in obtaining the evolution of concentrations of species, their individual chemical potentials and the specific Gibbs potential and is demonstrated for a single reaction system as an example. Oxidation in polymer composites is studied with a coupled reaction-diffusion model obtained using first order kinetics and is solved for a boundary value problem that predicts the concentration of species over space and time. Concentration of oxidized products is correlated with modulus of aged sample and degradation effects is calculated in case of simple torsion. Copyright © 2013 by ASME.

ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE)

A new approach in kinetic modeling using thermodynamic framework for chemically reacting systems and oxidative ageing in polymer composites

The analysis of the pre-tensioned twisted cables when subjected to axial loading pose a challenge and this is because the analysis has been done by various investigators and yielded different responses. Investigators proposed different hypotheses to report the predictions. There is no unique methodology or mathematical model to predict the response of a strand under a load, as accurately as desired. The theoretical predictions also differ by small margin from the experimental findings. There are several significant factors but they have not been considered together in most of the works. The test results show that all the theoretical predictions underestimate strand extension under fixed end conditions and free end conditions. The fixed end conditions and free end conditions are two degrees of fixity. The aim of the present work is to devise a finite element model that would narrow down the gap between the predicted and experimentally found responses. The emphasis was placed on the linear elastic global behaviour of a simple isotropic straight steel strand under small strain.