Auto-sensing materials research is critical for enabling smart structural health monitoring of civil engineering structures through digital twins~[1]. To achieve this, the relationship between the electrical field and strain field must be mapped for both low strain levels and material rupture. Carbon nanotube-based (CNT) composites are being developed to provide auto-sensing capabilities due to the piezoresistive effect that arises from the interactions between the nanofillers. In this study, we propose a mathematical framework for simulating the deformation and fracture of CNT-based composites in an electro-mechanical setting [2]. To obtain the constitutive properties needed for the finite element model, we use a trained machine learning model. Next, we numerically solve an electro-deformation-fracture problem using a phase-field fracture formulation [3, 4], which estimates crack propagation in arbitrary geometries based on Griffith's fracture theory. Finally, the phase-field variables are coupled with the electrical conductivity of the composite, which degrades due to the loss of mechanical stiffness. The case studies demonstrate the model's ability to capture the interplay between fracture and electromechanical material behaviour in CNT-based composites.