Krishna Kannan

Comprehensive molecular dynamics simulations are conducted to identify material modifications which can improve strength and reduce hysteresis losses at the nanointerfaces formed between silica, silane coupling agent (SCA) and styrene-butadiene rubber (SBR), all of which are important ingredients of green tyres. Improving strength and reducing hysteresis losses at such interfaces are expected to reduce rolling resistance (RR), consequently lowering greenhouse emissions. Various modifications considered in this work include a variety of SBR blends, several SCA and surface occupancies of SCA on the silica surface. To tackle a large number of combinations possible and identify modifications which may improve the nature of the interfaces, a hierarchical computational framework is developed. The reduced sample space of such material modifications may be more amenable to comprehensive and computationally or experimentally expensive studies. It was found that some amino-based SCA in combination with certain blends of SBR can improve the interfaces strength and lower hysteresis losses, when compared to the commonly used bis[3-(triethoxysilyl)propyl]tetrasulfide (TESPT), which is a sulphur-based SCA.

Polyamide 66/hectorite nanocomposites exhibit superior mechanical properties compared with pure polymers and are promising for structural applications. X-ray diffraction results revealed reduced degree of exfoliation with increase in organoclay content. Flexural fatigue characteristics of polyamide 66/hectorite nanocomposites containing different quantities of clay content were investigated, under deflection control mode, using a custom built flexural fatigue test rig. Addition of organoclay improved the moduli of the material. An enhanced resistance to cyclic softening was noticed at high temperatures with the incorporation of organoclay. Nanocomposite samples exhibited a significant improvement in fatigue life compared with pure polymers; however, the degree of enhancement is governed by the nanostructure of organoclay in polymer matrix. The fatigue life of nanocomposite samples is strongly affected by specimen temperature and induced stress. Macroscopic fracture surfaces changed from flat featureless structure to a highly perturbed structure with increase in organoclay content. © 2010 Society of Plastics Engineers.

The objective of the present work is to predict the degree of curing for a rectangular slab of rubber, which was subjected to non-uniform thermal history. As the thermal conductivity of rubber is very low, the temperature gradient across a slab is quite large, which leads to non-uniform vulcanization, and hence non-uniform mechanical properties-an inhomogeneous material. Since curing is an exothermic reaction, heat transfer and chemical reactions are solved in a coupled manner. The effect of heat generation on curing is also discussed. © 2009 Elsevier B.V. All rights reserved.

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.

A rigorous, comprehensive, and thermodynamically consistent theory has been developed for the fused deposition modelling (FDM) of semi-crystalline polymers. It is sufficiently general in that it can accommodate multiple phase transition mechanisms (crystallization, glass transition, and melting) during the heating and cooling cycles of the process encountered during FDM. The theory predicts the residual stresses and the resulting warpage in the polymer part due to the temperature-dependent, spatially varying specific volumes of each phase, precipitated by the inhomogeneous distribution of temperature. The theory treats the semi-crystalline polymer as a constrained mixture of multiple phases, where glass is assumed to be a new phase of the polymer. The statistically based Avrami kinetics for crystallization, modified for non-isothermal processes, is recovered as a particular case of our non-equilibrium thermodynamic analysis. Moreover, the theory predicts the temperature corresponding to the local free energy minima as the ideal glass transition temperature analogous to that of Franz and Parisi's mean field theory with a statistical basis.

This paper presents the development of a constitutive model for describing the nonlinear viscoelastic behavior of deep-seabed sediments. To quantify the nonlinear response, shear rheological tests are carried out on deep-sea sediments substitute at different shear rates. These substitute samples are prepared by mixing bentonite with water based on the in-situ vane shear strength of deep-sea sediments. A compressible viscoelastic fluid model is formulated based on the thermodynamic framework developed by Rajagopal and Srinivasa (2000) to describe the experimental response of bentonite–water mixture. Experimental responses indicate that the effects of slip are significant in the shear rheometry of bentonite–water mixture. Hence a slip model is proposed, which relates the shear stress to slip velocity at the wall and the imposed shear rate values. The slip boundary conditions coupled with the viscoelastic model is validated using experimental data and is observed to be in good agreement. Further, the influence of shear rate on interfacial slip has been numerically analyzed and slip effects are found to be significant in defining rheological behavior with increasing shear rates.

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.

Fatigue and damage are the least understood phenomena in the mechanics of solids. Recently, Alagappan et al. (“On a possible methodology for identifying the initiation of damage of a class of polymeric materials”, Proc R Soc Lond A Math Phys Eng Sci 2016; 472(2192): 20160231) hypothesized a criterion for the initiation of damage for a certain class of compressible polymeric solids, namely that damage will be initiated at the location where the derivative of the norm of the stress with respect to the stretch starts to decrease. This hypothesis led to results that were in keeping with the experimental work of Gent and Lindley(“Internal rupture of bonded rubber cylinders in tension. Proc. R. Soc. Lond. A 1959; 249, 195–205 :10.1098) and agrees qualitatively with the results of Penn (“Volume changes accompanying the extension of rubber”, Trans Soc Rheol 1970; 14(4): 509–517) on compressible polymeric solids. Alagappan et al. considered a body wherein there is a localized region in which the density is less than the rest of the solid. In this study, we show that the criterion articulated by Alagappan et al. is still applicable when bodies have multiple localized regions of lower density, thereby lending credence to the notion that the criterion might be reasonable for a large class of bodies with multiple inhomogeneities. As in the previous study, it is found that damage is not initiated at the location where the stresses are the largest but instead at the location where the densities tend to the lowest value. These locations of lower densities coincide with locations in which the deformation gradient is very large, suggesting large changes in the local volume, which is usually the precursor to phenomena such as the bursting of aneurysms.

There are many alloys used in orthopaedic applications that are nonlinear in the elastic regime even when the strains are ‘small’ (see Hao et al., 2005; Saito et al., 2003; Sakaguch et al., 2004). By using conventional theories of elasticity, either Cauchy or Green elasticity, it is impossible to systematically arrive at constitutive equations, which would be applicable in the elastic domain of such metals as such materials exhibit non-linear response for small strains1 where the classical linearized response is supposed to hold in the sense that the norm of the squares of the displacement gradient are much smaller than the displacement gradient. We delineate a new framework for developing constitutive equations for a new class of elastic materials, termed as implicit elastic materials, which can be used to describe the response of such alloys. In addition to a fully implicit constitutive relation, we discuss a non-linear constitutive relation between the linearized strain and the stress that can be properly justified to describe the response of such alloys. By using the example of a rectangular plate with a hole subject to uniform loading, a classical problem, we illustrate the differences in the stress and strain fields when compared to that predicted by the classical linearized relation.

We propose an innovative procedure by exploiting the physical meaning of natural strain or Lode invariants with the following salient contributions: 1) Uniaxial data for human brain tissue is used to stipulate the mathematical structure of the potential in terms of the Lode invariant that quantifies the magnitude of distortion along with the modulus term being an unknown function of the Lode angle that quantifies the mode or type of distortion. 2) By a priori analysis using the Baker-Ericksen inequalities, the mathematical form of the modulus function is determined in a novel manner. 3) The derived modulus function is corrected by adding a constant, which in turn is determined using analysis involving sufficient conditions of the stronger Hill inequality. 4) In addition, we also prove that any potential that satisfies Hill inequality also satisfies true-stress-true-strain monotonicity condition in plane stress. Compared to Mihai-Ogden model, besides excellent quantitative agreement with data for human brain tissue (see Mihai et al., 2017), the constructed model also emulates the observed non-linear behavior of shear stress with respect to the amount of shear as opposed to the nearly linear response predicted by the antecedent model. Additionally, when only tension-compression data is available for determining material parameters, the predicted combined tension and shear response associated with the proposed constitutive relation shows monotone decreasing Poynting stress (compressive), while the former predicts an unexpected non-monotone response for certain levels of tension.