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.

This paper presents the tractive performance of different grouser shapes in extremely soft seabed soil using finite element analysis (FEA). Consequently, the deformation characteristics and pattern of shear failure in the seabed soil can be predicted, eliminating expensive full-scale experiments. A three-dimensional FEA with the incorporation of geometric nonlinearity of shear rheometry is performed using coupled Eulerian–Lagrangian (CEL) technique in ABAQUS Explicit. The Mohr–Coulomb criterion is used to define the constitutive behaviour of the seabed soil sample used. To validate the model, the CEL simulation results are corroborated with experimental observations. The study reveals that the Mohr–Coulomb model with the governing parameters is able to capture the maximum rotational moment obtained from the experimental results with a maximum error of 3.5%. The Mohr–Coulomb model is therefore used to determine the maximum traction developed from two distinct grouser profiles to evaluate their tractive efficiency. It is observed that a triangular grouser offers better traction than an involute grouser.

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.

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.

A thermodynamic framework has been developed for a class of amorphous polymers used in fused deposition modeling (FDM), in order to predict the residual stresses and the accompanying distortion of the geometry of the printed part (warping). When a polymeric melt is cooled, the inhomogeneous distribution of temperature causes spatially varying volumetric shrinkage resulting in the generation of residual stresses. Shrinkage is incorporated into the framework by introducing an isotropic volumetric expansion/contraction in the kinematics of the body. We show that the parameter for shrinkage also appears in the systematically derived rate-type constitutive relation for the stress. The solidification of the melt around the glass transition temperature is emulated by drastically increasing the viscosity of the melt. In order to illustrate the usefulness and efficacy of the constitutive relation that has been developed, we consider four ribbons of polymeric melt stacked on top of each other such as those extruded using a flat nozzle: each layer laid instantaneously and allowed to cool for one second before another layer is laid on it. Each layer cools, shrinks and warps until a new layer is laid, at which time the heat from the newly laid layer flows into the previous laid layer and heats up the bottom layers. The residual stresses of the existing and newly laid layers readjust to satisfy equilibrium. Such mechanical and thermal interactions amongst layers result in a complex distribution of residual stresses. The plane strain approximation predicts nearly equibiaxial tensile stress conditions in the core region of the solidified part, implying that a preexisting crack in that region is likely to propagate and cause failure of the part during service. The free-end of the interface between the first and the second layer is subjected to the largest magnitude of combined shear and tension in the plane with a propensity for delamination.

We develop a 3D nonlinear viscoelastic model for filled elastomeric solids that exhibit good predictive capabilities across multiple deformation modes and strain rates using at most 11 parameters. Through the analysis-driven construction of the rate of dissipation within the rate-type thermodynamic framework of Rajagopal and Srinivasa (2000), we reduce the number of parameters and also introduce the mode-of-deformation-rate dependent viscosity (ηm(K3)) into the constitutive relations. The special form of ηm(K3) accounts for higher values of viscosity in tension as compared to that of other modes of deformation. The broad spectrum of relaxation times exhibited by the elastomers are characterized by categorizing it into short, medium, and long relaxations, each assumed to be associated with one of the three natural configurations. The strong mode-dependent response exhibited by HNBR50, where the compression–relaxation is faster than tension–relaxation, is predicted accurately only when all the natural configurations are active. In contrast, the response of NR is predicted by using just two natural configurations because the polymer molecules are restricted to two extremes of the relaxation spectrum as a consequence of the high affinity between carbon black and the polymer molecules. The entire model is implemented in Abaqus/Standard through the user subroutine UMAT that interacts with an external solver, DDASPK, which solves for the internal variables. We show that the analytical form for the consistent Jacobian can be derived, and establish the efficacy of the implementation by simulating non-homogeneous shear on a hockey puck geometry made of HNBR50 with a concave lateral surface. The simulation shows good agreement with experimental data.

This paper presents the implementation of a nonlinear viscoelastic multi-configurational rate type material model within the general framework of the commercial finite element package Abaqus (Implicit). A user-defined subroutine, UMAT for continuum elements, is employed to implement a model similar to the one developed and extensively validated experimentally by Devendiran et al. One of the major challenges of using an implicit finite element (FE) solver is the description of material Jacobian, which may be difficult to obtain in the form of an analytical equation for multi-configurational models. Hence, numerical approximations are used to implement the consistent material Jacobian used in the global Newton iterations. We have used a Jacobian that is formulated by perturbing the deformation gradient, by extending an idea developed by Miehe and widely implemented in hyperelasticity. In order to determine the multiple intermediate configurations that keep evolving with time, this study also examines the computational efficiency of a fully second order integrator in comparison to traditional first order BDF integrator. A highly efficient TR-BDF2 integrator, originally developed for simulating transients of silicon VLSI devices, is utilised to determine the “current relaxed configuration”, which to the author’s knowledge is the first implementation in literature for rate type viscoelastic constitutive equations. Coupling the numerically approximated Jacobian and TR-BDF2 integrator, the UMAT is generic and can easily be modified for various combinations of stored energy potential functions and rate of dissipation equations. The UMAT is validated against material point solution of the constitutive model in MATLAB; and is found to be exact within a tight tolerance. The implemented UMAT is used to determine the rolling resistance of a Grosch wheel which demonstrates the practical application of such a material model focussed towards the workflows for tyre analysis.

We study the initiation of damage in a polymeric body in which there is a line defect due to the formation of a "weld line" that occurs when two polymer streams join together and then solidify. We show that damage initiates in the region of weakness, namely the "weld line" based on a criterion for damage that was developed earlier. We also show that if there are other stress concentrators also additionally present, such as a hole, then there is a competition between the stresses induced due to the weakness and the stress as a consequence of the stress concentrator (in this instance a hole). This study adds more credence to the criterion for the initiation of damage that is based completely on knowledge of information at the current configuration of the body, that is, the criterion for damage is not based on the value of quantities that also need information based on a reference configuration such as the stress or strain.