Non-Fick diffusion–elasticity based on a new nonlocal dual-phase-lag diffusion model and its application in structural transient dynamic responses

Mechanical-diffusion coupling analysis at micro/nanotemporal and spatial scale has aroused great research interests with flourishing development of nanobattery system and fast rising of rapid charging technology, where the spatial nonlocal effects of mass transfer and elastic deformation as well as the influences of temporal nonlocal effects of mass transport (i.e., the phase laggings of diffusion flux vector and molar concentration gradient) will remarkably increase. In such cases, however, the accurate prediction of mechanical-diffusion responses is challenged: Firstly, the existing non-Fick diffusion–elasticity models are established by merely introducing mass diffusion model associated with the time rate of diffusion flux (i.e., phase laggings of diffusion flux); secondly, the spatial nonlocal effect of mass transfer is still not considered in the current on dual-phase-lag diffusion model. This work aims to develop a non-Fick diffusion–elasticity based on a new nonlocal dual-phase-lag diffusion model, which fully incorporates spatial and temporal nonlocal effects of mass transport. New constitutive and field equations are strictly derived via nonlocal continuum mechanics. To illustrate its application values, a one-dimensional isotropic homogeneous thin layer of finite thickness subjected to transient shock loadings of molar concentration is investigated. Dimensionless results are graphically presented to illustrate the effects of both nonlocal mass transfer and nonlocal elasticity on diffusive wave propagation and mechanical-diffusion responses.