Hygrothermoelastic Interactions In Hollow Spherical Composite Shells With Memory-Dependent Effects And Nonlocal Elasticity

This study presents a comprehensive analysis of the transient hygrothermoelastic response of a two-layer hollow spherical composite structure subjected to arbitrary time-dependent thermal and moisture loadings. Each layer is assumed to be homogeneous and isotropic with temperature-independent material properties, while imperfect thermal contact at the interface is modeled through finite interfacial conductance. Volume, surface, and interfacial source terms are incorporated as integrable functions of time, together with spatially uniform initial excitations. Initial excitations (temperature and moisture) are assumed to be spatially uniform. Surfaces are traction-free, with prescribed time-dependent thermal and moisture inputs at the outer radius. To capture delayed thermal and moisture transport phenomena, the governing equations are formulated within a single-phase-lag framework using memory-dependent fractional-order derivatives. The resulting coupled system is expressed in a dimensionless form to enhance generality and enable systematic parametric investigation. By applying the Laplace transform technique, semi-analytical solutions are obtained through eigenfunction expansions and numerical inversion of the transformed expressions, while boundary and interfacial continuity conditions are rigorously enforced. Closed-form expressions for temperature, moisture concentration, radial displacement, and stress components are derived for both layers of the composite sphere. The numerical results reveal that memory effects significantly retard diffusion processes and alter stress evolution, while hygrothermal coupling and interfacial imperfection markedly influence displacement and stress distributions, particularly near the interface. The proposed framework extends classical hygrothermoelastic models by integrating fractional calculus, memory-dependent behavior, Nonlocal elasticity is incorporated following Eringen’s framework, where stress depends on strain contributions from the surrounding domain and interfacial effects, providing valuable insights for the design and optimization of layered composite structures and smart materials operating under complex hygrothermal environments.