Nowadays, computational modelling and simulation have become effective tools in medical sciences due to their significant potential to help physicians in detecting the origins of a disease, determining the kind of therapy, or training for a surgical procedure. Its importance is underlined by the fact that cardiovascular diseases are currently the leading cause of the death worldwide. Despite remarkable advancements in recent decades, cardiac modelling and simulation remain the focus of extensive study. It is a challenging task to develop an effective computational cardiac model that includes all relevant components. The overall aim of the present work is to create a robust and accurate computational model of rat heart electromechanics, which is calibrated with experimental data. First, we focus on creating a novel material model for passive cardiac mechanics. It is calibrated with experimental data based on mechanical testing of healthy rat cardiac tissue and of tissue 14 days after an induced myocardial infarction. The simulation results using the derived parameters show a close agreement with the experimental data. Second, utilising the proposed model and the determined parameters, it is studied how a weakened heart, suffering from a restrictive cardiomyopathy, could be supported from the outside by applying an external support pressure on the epicardial surface. Based on the simulation model, the optimal support pressure needed for the restoration of the healthy left-ventricular ejection fraction and end-diastolic volume is computed for different stages of ventricular fibrosis. Third, apart from the improvements on the material modelling level, the work focuses on a novel numerical method for the simulation of cardiac mechanics, in particular multiple smoothed finite element methods are extended for the modelling and simulation of active cardiac contraction. We conclude that these methods are very suitable for the simulation of the cardiac cycle. This is due to their ability to significantly reduce the volumetric locking problem, being present when large deformations occur, nearly incompressible material is utilised and the computational domain is discretised with tetrahedrons.