<p>In this paper, we investigate the long-time behavior of a swelling porous elasticity system incorporating a single nonstandard nonlinear Kelvin–Voigt damping mechanism. This type of damping, which acts through a nonlinear viscoelastic law, significantly influences the dissipative structure of the system. By carefully analyzing the behavior of the damping term near the origin, we derive an explicit and general decay rate formula for the energy functional. Our results reveal that the nonlinear damping is sufficiently strong to stabilize the system asymptotically, even in the absence of additional damping sources. To the best of our knowledge, this is the first work that considers this specific form of damping in the context of swelling porous media. The findings of this study constitute a novel contribution to the field and improve upon several existing results in the literature.</p>