Understanding how rotational motion develops after an impact remains a central problem in continuum mechanics, impact dynamics, and solid mechanics. Classical theories successfully describe stress propagation, elastic deformation, plasticity, contact mechanics, and wave transmission within struck bodies. Nevertheless, they generally describe the observed dynamics through stress and displacement fields without explicitly considering the transient evolution of the material density field as an independent internal variable.In the present work, a new continuum-mechanics framework is proposed in which density is introduced as an evolving thermodynamic state variable coupled to elastic deformation through a free-energy functional. The central hypothesis is that a localized impact generates a transient density perturbation that propagates throughout the body as a relaxation wave. During this process, density gradients, pressure gradients, and elastic stresses evolve simultaneously while continuously exchanging energy through thermodynamically admissible relaxation mechanisms. Rather than assuming that the density field instantaneously returns to equilibrium, the proposed model considers its progressive redistribution until the initial homogeneous state is recovered.The formulation combines the conservation laws of continuum mechanics with a variational free-energy approach and a dissipative gradient-flow evolution equation. The resulting model satisfies thermodynamic consistency, admits a Lyapunov free-energy functional, and naturally predicts monotonic energy dissipation toward equilibrium. Classical elasticity is recovered as a limiting case when density relaxation becomes negligible.To investigate the physical consequences of the proposed formulation, preliminary numerical simulations were performed using custom two-dimensional and three-dimensional computational models. The simulations indicate that off-centre impacts generate transient misalignment between density and pressure gradients, producing a measurable rotational source proxy that reaches a maximum for intermediate impact eccentricities. Although these simulations do not constitute experimental validation, they provide a proof of concept demonstrating that the proposed mathematical framework generates physically meaningful behavior consistent with several qualitative trends reported in the impact-mechanics literature.The theoretical predictions are further discussed through comparison with established results in elasticity, contact mechanics, finite-element analysis, stress-wave propagation, impact dynamics, and thermodynamics. Rather than replacing existing continuum theories, the proposed framework extends them by introducing density relaxation as an additional internal mechanism contributing to energy redistribution following mechanical impact.The proposed formulation establishes a unified theoretical basis for future numerical and experimental investigations of transient density evolution in impacted solids and suggests that density relaxation may represent a useful additional state variable in continuum descriptions of dynamic deformation and rotational response.