Mathematical wave equation modeling in smart materials and composite continuous systems
Article Sidebar
elastodynamics,
wave propagation,
composite materials,
metamaterials
Main Article Content
Abstract
Wave-propagation modeling in smart materials and continuous composite systems remains challenging due to multiphysics interactions, scale-dependent nonlocality, constitutive nonlinearities, and structural heterogeneity. This scoping review synthesizes recent advances in wave equations, elastodynamics, and solution techniques published during 2019–2026 for smart-material and composite-continuum applications. Using the Population–Concept–Context (PCC) framework and PRISMA-ScR guidelines, verified DOI-indexed studies were classified into five themes: piezoelectric and magneto-electro-elastic (MEE) structures, functionally graded materials (FGMs) and metamaterials, layered composites and nonlocal nanostructures, field-responsive smart composites, and guided-wave-based structural health monitoring (SHM). The findings indicate a shift from classical linear elastodynamics toward multiscale formulations incorporating microstructural length scales, surface elasticity, flexoelectricity, porosity, and nonlocal effects. FGMs and metastructures have evolved from passive stress-mitigation systems into active mechanisms for band-gap tuning, wave-mode conversion, and impedance matching. In SHM applications, guided waves and Lamb waves remain dominant, increasingly supported by mesh-free orthogonal polynomial methods and machine-learning-based feature extraction. Environmental variability and the standardization of validation protocols remain major implementation challenges.
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