This paper presents the first model capable of predicting the electromechanical and fracture behaviour of self-sensing carbon nanotube (CNT)-based composites. The model captures the nano-scale mechanisms and constitutive behaviour of CNTs using a mixed micromechanics formulation. This is combined with a coupled electrical-deformation-fracture finite element model. The resulting multi-scale and multi-physics computational model is then used to simulate deformation and fracture in piezo-resistive CNT-based composites. The presented numerical results showcase the efficiency and robustness of the computational framework,as well as its ability to model a large variety of structural configurations and damage patterns. The deformation-electrical-fracture finite element code developed is made freely available to download.