This paper discusses Chrono's Continuous Representation Model (called herein Chrono::CRM), a general-purpose, scalable, and efficient simulation solution for terramechanics problems. Built on Chrono's Smoothed Particle Hydrodynamics (SPH) framework, Chrono::CRM moves beyond semi-empirical terramechanics approaches, e.g., Bekker-Wong/Janosi-Hanamoto, to provide a physics-based model able to address complex tasks such as digging, grading, as well as interaction with deformable wheels and complex grouser/lug patterns. The terramechanics model is versatile in that it allows the terrain to interact with both rigid and flexible implements simulated via the Chrono dynamics engine. We validate Chrono::CRM against experimental data from three physical tests, including one involving NASA's MGRU3 rover. In addition, the simulator is benchmarked against a high-fidelity Discrete Element Method (DEM) simulation of a digging scenario involving the Regolith Advanced Surface Systems Operations Robot (RASSOR). Being GPU-accelerated, Chrono::CRM achieves computational efficiency comparable to that of semi-empirical simulation approaches for terramechanics problems. Through an ``active domains'' implementation, Chrono::CRM can handle terrain stretches up to 10 km long with 100 million SPH particles at near interactive rates, making high-fidelity off-road simulations at large scales feasible. As a component of the Chrono package, the CRM model is open source and released under a BSD-3 license. All models and simulations used in this contribution are available in a public GitHub repository for reproducibility studies and further research.