Breadth-first search algorithm on the finite element simulation of the electrical resistivity of the carbon black elastomeric pressurized sensor

Abstract

Resistivity and piezoresistive sensitivity of Carbon Black (CB) elastomeric nanocomposites are studied using a finite element method with a conductive network model. CB spheres are placed into Representative Volume Elements (RVEs) in random positions to perform simulations and obtain the strained state and new position of particles. Numerical results are implemented into a breadth-first search algorithm tailored to find percolation pathways from one end of the RVE to another based on the shortest distance between CBs in the strained regime. Percolation pathways are used by the conductive network model to determine the critical distance for resistivity. Resistivity diminishes as the critical distance increases attributed to a greater number of electrons penetrating the barriers. Critical distance at which tunneling can occur expands with an increase in barrier potential. Smaller CBs that can more efficiently occupy the gaps lead to a reduction in the critical distance range necessary for percolation to happen.