Ph.D. (Engg) :VAM-Based Elastic and Thermo-elastic Micromechanics Models for Homogenization and a VAM2 Multi-scale Model for Composite Beam-Like Structures.

In diverse domains of engineering and high-performance applications, the use of Fiber-Reinforced Polymer Matrix Composites (FRPMCs) and Metal Matrix Composites (MMCs) has experienced rapid and sustained growth. This trend is primarily attributable to their high specific stiffness, elevated strength-to-weight ratio, low Coefficients of Thermal Expansion (CTE), and inherently lightweight characteristics, coupled with the ability to tailor their properties to meet specific design requirements. The effective utilization of such advanced materials necessitates a comprehensive understanding of their structural response, both at the global and constituent levels. In particular, precise knowledge of homogenized material properties, CTEs, and spatially resolved local fields within the reinforcement and matrix phases is indispensable for predicting structural behavior, conducting performance assessments, and achieving optimal designs suited to demanding engineering applications. The growing demand for accelerated yet accurate design cycles further underscores the need for computationally efficient, yet physically rigorous, predictive models.

Conventional micro-mechanics and multi-scale modeling techniques are frequently constrained by restrictive kinematic assumptions, such as pre-specified displacement or stress fields, whose validity is not inherently guaranteed by the governing equations of three-dimensional elasticity, and often employ oversimplified treatments of interface continuity conditions. Numerical approaches, while flexible, typically rely on computationally intensive discretization and may not rigorously satisfy all interface continuity requirements. These limitations collectively compromise the generality, accuracy, and physical fidelity of predicted material and structural responses.

To address these shortcomings, this doctoral research develops a unified, analytically rigorous, and asymptotically consistent multi-scale modeling framework for the accurate prediction of homogenized elastic properties, CTEs, and fully three-dimensional local field distributions within the constituents of composite materials, with particular emphasis on beam-like structural configurations. The first segment of the thesis introduces an asymptotically correct micromechanics formulation that eliminates arbitrary field assumptions, deriving its governing equations directly from the stationary conditions of the total strain energy functional expressed in generalized strain measures. The Variational Asymptotic Method (VAM) is adopted as the mathematical foundation, while the Hashin–Rosen Composite Cylinder Model (CCM) serves as the physical idealization for the composite Representative Unit Cell (RUC). This approach enables the derivation of closed-form expressions for homogenized elastic properties, including elastic moduli, shear moduli, and Poisson’s ratios, while rigorously enforcing displacement continuity and transverse stress equilibrium at the reinforcement–matrix interface. The resulting expressions are explicit functions of constituent material properties, volume fractions, and geometric parameters.

The formulation is subsequently extended to the thermo-elastic regime, wherein the governing relations are derived from the stationary conditions of the Helmholtz free energy functional, expressed in generalized strain measures and CTEs. This extension yields closed-form expressions for the effective longitudinal and transverse coefficients of thermal expansion. The predicted elastic moduli and CTEs are extensively validated against existing micro-mechanical solutions, experimental results, and literature data for a wide range of composite systems.

Building upon this foundation, the research advances a VAM2-based multi-scale analytical methodology in which the generalized micromechanics formulation is seamlessly integrated with a macro-scale structural model, free from restrictive kinematic simplifications. The macro-scale solution prescribes traction boundary conditions to the micro-scale problem in a manner consistent with three-dimensional equilibrium, while the micro-scale formulation rigorously enforces interface elasticity constraints. This enables the derivation of closed-form expressions for fully three-dimensional local displacement, strain, and stress fields in both reinforcement and matrix phases, parameterized by one-dimensional strain measures, curvature terms, constituent properties, and spatial coordinates.

The proposed multi-scale framework achieves computational accuracy comparable to concurrent multi-scale approaches, while preserving the computational efficiency characteristic of hierarchical methods. Its predictive capability is validated through high-fidelity three-dimensional finite element simulations for arbitrary RUC locations on the beam cross-section, under simultaneously applied multi-load conditions.

Overall, this research establishes a generalizable, physically consistent, analytically tractable, and computationally efficient paradigm for predicting homogenized elastic properties, CTEs, and performing multi-scale structural analysis of composite materials. It represents a substantive advancement over prevailing micro-mechanical and multi-scale modeling strategies, combining theoretical rigor with practical utility for the design and analysis of advanced composite structures.

This MS Teams Meeting Link is just for those unable to join pīrēśvarā, Dr MVVS mūrti & me in-person@CVH Conference Hall, IISc: AE PhD Colloquium: VAM2 Multiscale Model for Composite Beams & VAM-based Thermoelastic MicroMechanic Homogenization | Meeting-Join | Microsoft Teams : https://teams.microsoft.com/meet/45114276357578?p=KPgojv0HqsJhQKrSzd

Speaker: śrī M. V. PEERESWARA RAO

Research Supervisors: Dineshkumar Harursampath & Dr MVVS Murthy, Division Head, Spacecraft Systems Engg. Group, URSC, ISRO