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Going beyond the classical Gaussian approximation of Einstein's fluctuation theory, Ruppeiner gave it a Riemannian geometric structure with an entropic metric. This yielded a fundamental quantity, the Riemannian curvature, which was used to extract information on the nature of interactions between molecules in fluids, ideal gases, and other open systems. In this article, we examine the implications of this curvature in a nonequilibrium thermodynamic system where relaxation is sufficiently slow so as not to invalidate the local equilibrium hypothesis. The nonequilibrium system comprises a rubbery polymer undergoing strain induced crystallization. The curvature is found to impart information on a spurious isochoric energy arising from the conformational stretching of already crystallized segments. This unphysical component perhaps arises as the crystallized manifold is considered Euclidean with the stretch measures defined via the Euclidean metric. The thermodynamic state associated with curvature is the key to determine the isochoric stretch and hence the spurious energy. We determine this stretch and propose a form for the spurious free energy that must be removed from the total energy in order for the correct stresses to be recovered. © 2022 American Physical Society.

Department of Civil & Infrastructure Engineering

World University root node

Physical Review E

Geometric thermodynamics of strain-induced crystallization in polymers

Hydrogels exhibit a wide range of responses to various stimuli, which makes them useful in myriad applications including the biomedical industry. To capture certain features of this varied response, several constitutive models have been proposed. However, few attempts have been made at the predictive modelling of temperature and moisture driven transition between fast and slowly relaxing states in physical hydrogels. We in this article focus on the changes that occur in the mechanical response due to such phase transitions. We propose a unified and thermodynamically consistent poro-visco-elastic framework for modelling the transition and the associated mechanical behaviour. Towards that, the effective temperature framework that has been previously exploited for such transitions by the authors and other researchers is used. The constitutive model is numerically solved for the uniaxial tensile response of equilibrated hydrogels and also validated against experimental data from the literature. It is also used for certain transient problems involving solvent diffusion with or without mechanical constrains. The aim of this exercise is to assess the predictive fidelity of the model against some standard poro-elastic problems and examine the influence of inter-molecular interactions on the saturation. The numerical studies are concluded with a set of simulations to showcase certain other capabilities of our approach such as modelling of visco-hyperelastic phase transitions. We also investigate through these simulations a few other coupling effects caused by changes in moisture, temperature, loading rates and prior ageing. © 2021 Elsevier Ltd

International Journal of Mechanical Sciences

A poroviscoelasticity model based on effective temperature for water and temperature driven phase transition in hydrogels

Regularized continuum damage models such as those based on an order parameter (phase field) have been extensively used to characterize brittle damage of compressible elastomers. However, the prescription of the surface integral and the degradation function for stiffness lacks a physical basis. In this article, we propose a continuum damage model that draws upon the postulate that a damaged material could be mathematically described as a Riemannian manifold. Working within this framework with a well-defined Riemannian metric designed to capture features of isotropic damage, we prescribe a scheme to prevent damage evolution under pure compression. The result is a substantively reduced stiffness degradation due to damage before the peak response and a faster convergence rate with the length scale parameter in comparison with a second-order phase field formulation that involves a quadratic degradation function. We also validate this model using results of tensile experiments on double notched plates. © 2021 by ASME.

Journal of Applied Mechanics, Transactions ASME

A geometrically inspired model for brittle damage in compressible elastomers

Phase segregated copolymers such as elastomeric copolymers find myriad applications especially in impact resistant structures. When domains with varying relaxation characteristics are present, these polymers exhibit thermorheologically complex behaviour. The multiple relaxation processes are herein captured using the effective temperature based thermodynamics, used extensively in modelling thermo-mechanical response of metals and polymers. Specifically, we use two slowly evolving configurational subsystems and a fast evolving kinetic-vibration (K-V) subsystem. The two configurational subsystems represent the inter-molecular and intra-molecular meso-scale configurational transformations occurring within the two domains. The K-V subsystem represents the faster atomic vibrations. The configurational subsystems are weakly coupled with the K-V through heat exchange which accounts for structural relaxations of the individual domains towards the equilibrium microstructure. Based on this, we are able to capture strain rate dependence and strain induced softening of these materials under cyclic loads. In comparison with the existing formulations for such copolymers, ours is perhaps a more transparent approach, as it uses quantities such as volume fraction, glass transition temperatures of individual domains as material parameters. Indeed, our formulation could be readily adapted for non-elastomeric copolymers. It should also be potentially useful as a design tool for copolymers with increased glass transition range. © 2019 Elsevier Ltd

A constitutive model for block-copolymers based on effective temperature

Posed within a two-temperature thermodynamic framework, our aim is to propose a unified glass-rubber constitutive model for thermo-rheologically simple thermoplastic polymers. This modelling set-up usually applies to phenomena wherein sub-macroscopic processes involving different time scales occur and accordingly the thermodynamic system may be interpreted as comprising of two subsystems. The configurational subsystem contains the slower states, while the kinetic-vibrational subsystem comprises of the faster moving states. The two subsystems fail to equilibrate within experimental timescales in the glassy regime (low temperature or high strain rate) due to low structural relaxation rates. As transition to the rubbery regime commences at temperatures higher than glass transition or at sufficiently low loading rates, the two subsystems equilibrate within microscopic timescales. The model exploits physically inspired prescriptions for the free energies due to different underlying mechanisms - elastic stretching, localised shear transformations and intra-molecular straightening of chains. A simple temperature dependent formulation for structural relaxation in terms of heat transfer between the subsystems is used to capture transition between these mechanisms. The model is then validated against experimental results of uniaxial compression tests for various strain rates and temperatures establishing its ability to seamlessly transit between the glassy and rubbery regimes. Also demonstrated is the model's efficacy in capturing the key features of physical ageing and mechanical rejuvenation. © 2018 Elsevier Masson SAS

European Journal of Mechanics, A/Solids

A constitutive model for thermoplastics based on two temperatures

First, a semi-analytical model for determining inter-yarn static and kinetic coefficients of friction for plain woven fabric is derived. The model requires few parameters from the load-displacement curve obtained in a pull-out experiment. The derived model is then applied to determine friction coefficients of Kevlar and the obtained values are found to be very consistent with the range reported in the literature. Next the ballistic response of plain woven Kevlar fabric structure is numerically studied through a simple FE model, wherein yarns are modeled by 1D truss element. The simplified model is validated against some equivalent experimental and numerical results reported in the literature. Effect of inter-yarn friction coefficient on failure mechanism and energy distribution characteristic of fabric structure are investigated. Based on the several numerical simulations, it is observed that higher inter-yarn friction may not always give better ballistic performance. Inter-yarn friction improves the ballistic performance up to a limiting value. Beyond this threshold value, increasing friction may adversely affect the energy dissipation and failure mechanism. © 2014 Elsevier Ltd.