Advanced Thermomechanical Modeling of Soft Matter Systems

Abstract

This thesis deals with advanced thermomechanical modeling of complex soft matter systems, including polymers, gels, and biological tissues. It addresses a few fundamental limitations of classical theories, such as the paradox of infinite heat propagation speed and insufficient microstructural insights from the classical fluctuation theory, by employing geometric and non-Fourier approaches.

The thesis is structured around three core contributions. The first explores strain-induced crystallization (SIC) in polymers using Ruppeiner’s geometric thermodynamics. This approach reveals a "spurious isochoric energy" originating from the conformational stretching of already crystallized segments, an unphysical component attributed to considering the crystallized manifold as Euclidean. By analyzing scalar curvature and critical thermodynamic states, the work proposes a modified free energy formulation that eliminates this spurious energy, leading to accurate stress recovery and a more physically consistent constitutive theory for SIC.

The second part applies geometric thermodynamics to analyze the volumetric phase transition in polyacrylamide gels. Utilizing a Landau-Ginzburg type free energy functional in conjunction with Flory-Huggins theory, the scalar curvature is employed to gain insights into the evolving microstructure. Divergence in curvature at critical points is directly linked to the divergence of correlation length, indicating a heterogeneous microstructure during phase transition and supporting experimental observations of phase segregation. The study also confirms the universality class of the gel's phase transition, aligning it with van der Waals fluids and black hole systems. A proposed modification to the free energy addresses unphysical nonconvexity, negating the need for Maxwell construction.

The final contribution presents a robust two-dimensional finite element framework for small-strain coupled thermoelasticity, incorporating both classical Fourier and Dual-Phase-Lag (DPL) heat conduction models. This framework is rigorously validated against experimental data for processed bologna meat, conclusively demonstrating the DPL model's superior predictive capability in capturing finite speed of thermal signal propagation and wave-like heat transfer phenomena. The DPL model accurately predicts delayed onset, sharper transitions, and localized stress amplification in response to rapid thermal fronts and wave superposition effects, offering a more realistic representation of thermoelastic stress and strain fields compared to the Fourier model.

Overall, this thesis advances the understanding and modeling of soft matter systems under diverse thermal and mechanical conditions. It underscores the critical role of advanced, non-classical thermodynamic and heat conduction theories in accurately predicting material behavior and extracting crucial microstructural information, offering valuable insights for applications in bioengineering, materials science, and food processing. Future work is outlined to extend these methodologies to more complex geometries, large deformations, anisotropic and temperature-dependent material properties, and to explore inverse problems for parameter identification.