While ventricular electromechanics is extensively studied in both physiological and pathological conditions, four-chamber heart models have only been addressed recently; most of these works however neglect atrial contraction. Indeed, as atria are characterized by a complex anatomy and a physiology that is strongly influenced by the ventricular function, developing computational models able to capture the physiological atrial function and atrioventricular interaction is very challenging. In this paper, we propose a biophysically detailed electromechanical model of the whole human heart that considers both atrial and ventricular contraction. Our model includes: (i) an anatomically accurate whole-heart geometry; (ii) a comprehensive myocardial fiber architecture; (iii) a biophysically detailed microscale model for the active force generation; (iv) a 0D closed-loop model of the circulatory system, fully-coupled with the mechanical model of the heart; (v) the fundamental interactions among the different core models, such as the mechano-electric feedback or the fibers-stretch and fibers-stretch-rate feedbacks; (vi) specific constitutive laws and model parameters for each cardiac region. Concerning the numerical discretization, we propose an efficient segregated-intergrid-staggered scheme that includes a computationally efficient strategy to handle the non-conductive regions. We also propose extending recent stabilization techniques - regarding the circulation and the fibers-stretch-rate feedback - to the whole heart, demonstrating their cruciality for obtaining a stable formulation in a four-chamber scenario. We are able to reproduce the healthy cardiac function for all the heart chambers, in terms of pressure-volume loops, time evolution of pressures, volumes and fluxes, and three-dimensional cardiac deformation, with volumetric indexes within reference ranges for cardiovascular magnetic resonance. We also show the importance of considering atrial contraction, fibers-stretch-rate feedback and the proposed stabilization techniques, by comparing the results obtained with and without these features in the model. In particular, we show that the fibers-stretch-rate feedback, often neglected due to the numerical challenges that it entails, plays a fundamental role in the regulation of the blood flux ejected by ventricles. The proposed model represents the state-of-the-art electromechanical model of the iHEART ERC project - an Integrated Heart Model for the Simulation of the Cardiac Function - and is a fundamental step toward the building of physics-based digital twins of the human heart.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).