Examinando por Materia "ONDAS ELASTICAS"

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    Elastic Wave Diffraction in Scale-Dependent Media : A Study within the Consistent Couple-Stress Theory
    (Universidad EAFIT, 2026-04-30) Martinod, Thomas; Guarín-Zapata, Nicolás
    Cauchy continuum mechanics is insufficient to capture size-dependent effects in materials with microstructure. The Consistent Couple-Stress Theory (C-CST) introduces a characteristic length scale $\ell$ that enables the modeling of such phenomena. In this thesis, we study the diffraction of elastic waves by an infinite cylinder embedded in an isotropic medium within the C-CST framework. The total displacement field is constructed as the superposition of an incident wave $\mathbf{u}^{(i)}$ and a scattered wave $\mathbf{u}^{(s)}$, where the latter satisfies the C-CST elastodynamic equation. The problem is solved by introducing elastodynamic potentials, decoupling the governing equations, and applying separation of variables. Three boundary conditions are considered: rigid inclusion, cavity (traction-free surface), and elastic cylinder. For each configuration, analytical series solutions are derived for both anti-plane and in-plane problems, including explicit expressions for the displacement fields, and the separation constants (when possible). The results are further examined through plots of the displacement fields, interfacial stresses, and the dynamic stress concentration factor, always analyzing their dependence on the dimensionless parameters $ka$ and $\ell/a$. The results show that size effects become more pronounced at higher frequencies, where wave-microstructure interactions lead to a redistribution of energy and a reduction of the classical shadowing in the far field.