Stroh–Hamiltonian Framework for Modeling Incompressible Poroelastic Materials

Kinza Arshad and Vincenzo Tibullo ()
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Kinza Arshad: Department of Mathematics, University of Salerno, 84084 Fisciano, Italy
Vincenzo Tibullo: Department of Mathematics, University of Salerno, 84084 Fisciano, Italy

Mathematics, 2025, vol. 13, issue 9, 1-13

Abstract: The Stroh sextic formalism, developed by Stroh, offers a compelling framework for representing the equilibrium equations in anisotropic elasticity. This approach has proven particularly effective for studying multilayered structures and time-harmonic problems, owing to its ability to seamlessly integrate physical constraints into the analysis. By recognizing that the Stroh formalism aligns with the canonical Hamiltonian structure, this work extends its application to Biot’s poroelasticity, focusing on scenarios where the solid material is incompressible and there is no fluid pressure gradient. The study introduces a novel Hamiltonian-based approach to analyze such systems, offering deeper insights into the interplay between solid incompressibility and fluid–solid coupling. A key novelty lies in the derivation of canonical equations under these constraints, enabling clearer interpretations of reversible poroelastic behavior. However, the framework assumes perfectly drained conditions and neglects dissipative effects, which limits its applicability to fully realistic scenarios involving energy loss or complex fluid dynamics. Despite this limitation, the work provides a foundational step toward understanding constrained poroelastic systems and paves the way for future extensions to more general cases, including dissipative and nonlinear regimes.

Keywords: Stroh formalism; Biot’s poroelasticity; Hamiltonian formalism; solid incompressibility (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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