Projects

Dual Phase Lag Model

This study investigates the thermo-mechanical response of a two-dimensional solid under small strain conditions, incorporating heat conduction effects modeled using both the classical Fourier law and the non-Fourier Dual Phase Lag (DPL) theory. A finite element formulation is developed to solve the coupled thermoelastic equations, where mechanical deformation is influenced by temperature gradients and vice versa. The governing equations are discretized using bilinear quadrilateral (Q4) elements in space and an implicit Newmark-beta scheme for temporal integration. 

Comparative insights are provided on displacement, stress, strain, and temperature evolution under both models. The results highlight significant deviations between DPL and Fourier predictions, particularly in the transient regime, emphasizing the importance of phase lag effects in dynamic thermoelastic phenomenoa and accurately capturing the thermal response in microscale or fast-transient applications. These findings contribute toward improved modeling of heat-induced deformation in fast processes and microstructured materials.

Geometric thermodynamics of strain-induced crystallization in polymers

The work involved the use of geometric thermodynamics to the study of strain induced crystallization in polymers. It involved the use of modified fluctuation theory to reveal microscale information in a thermodynamic system describing strain induced crystallization (SIC) in a rubber specimen. SIC is a non-equilibrium phenomenon in which regions of a rubber sample undergoes crystallization when stretched.

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.

Geometric thermodynamics of collapse of gels

Stimulus-induced volumetric phase transition in gels may be potentially exploited for various bio-engineering and mechanical engineering applications. Since the discovery of the phenomenon in the 1970s, extensive experimental research has helped in understanding the phase transition and related critical phenomena. Yet, little insight is available on the evolving microstructure. In this article, we aim at unravelling certain geometric aspects of the micromechanics underlying discontinuous phase transition in polyacrylamide gels. Towards this, we use geometric thermodynamics and a Landau-Ginzburg type free energy functional involving a squared gradient, in conjunction with Flory-Huggins theory. We specifically exploit Ruppeiner’s approach of Riemannian geometry-enriched thermodynamic fluctuation theory that has been previously employed to investigate phase transitions in van der Waals fluids and black holes. The framework equips us with a scalar curvature that relates to the microstructural interactions of a gel during phase transition and at critical points. This curvature also provides an insight into the universality class of phase transition and the nature of polymer-polymer interactions. 

Geometric thermodynamics of helix-coil transition in DNA