  We present a novel computational framework to simulate the electromechanical
response of self-sensing carbon nanotube (CNT)-based composites experiencing
fracture. The computational framework combines electrical-deformation-fracture
finite element modelling with a mixed micromechanics formulation. The latter is
used to estimate the constitutive properties of CNT-based composites, including
the elastic tensor, fracture energy, electrical conductivity, and linear
piezoresistive coefficients. These properties are inputted into a coupled
electro-structural finite element model, which simulates the evolution of
cracks based upon phase-field fracture. The coupled physical problem is solved
in a monolithic manner, exploiting the robustness and efficiency of a
quasi-Newton algorithm. 2D and 3D boundary value problems are simulated to
illustrate the potential of the modelling framework in assessing the influence
of defects on the electromechanical response of meso- and macro-scale smart
structures. Case studies aim at shedding light into the interplay between
fracture and the electromechanical material response and include parametric
analyses, validation against experiments and the simulation of complex cracking
conditions (multiple defects, crack merging). 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.
