<p>Accurate dynamics analysis of crewed rover vehicles (CRV) on loose and rough terrain is crucial for rover performance evaluation and optimization design. However, current wheel-terrain interaction analyses either rely on numerical simulations with high computational demands or employ simplified mechanical models based on quasi-static rigid wheel assumptions, which struggle to achieve real-time computations while considering wheel elasticity. Therefore, this study develops a mechanical model of elastic wheel-terrain interaction that accounts for the wheel's physical structure. The elastic wheel model incorporates calculations for tread bending force, sidewall deformation force, and collision contact force between the tread and the inner frame. To advance the field, an extended terramechanics for deformable wheels is proposed, enabling the calculation of coupled dynamic forces and analysis of the lug effect on the wheel surface. A wheel prototype was built, and soil bin experiments were conducted to validate the proposed model, demonstrating its accuracy and reliability. Furthermore, to extend the model's applicability, a quarter rover vertical dynamics model and a 14-DOF rover dynamics model were developed. These models allow for a detailed comparison between the rigid wheel and the proposed model in analyzing the dynamic behaviors of the rover driving in rough terrain. The proposed wheel-terrain interaction model facilitates real-time physical simulation and control strategy validation for extraterrestrial crewed mobility systems, offering significant engineering implications for the design and operation of such vehicles.</p>