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Hybrid Monte Carlo–MLP prediction of tunneling percolation and conductivity in conductive polymer composites under compressive strain
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DOI：10.1016/j.commatsci.2026.114736.png)
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Abstract
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Conductive polymer composites (CPCs) are promising materials for compression-responsive sensing applications. However, their deformation-induced nonlinear electrical response complicates efficient material design. This study proposes a hybrid computational framework that integrates three-dimensional Monte Carlo particle-network simulations with a multilayer perceptron (MLP) surrogate model to rapidly predict spanning-cluster evolution (quantified by the spanning cluster fraction, SCF) and to evaluate tunneling-governed network conductivity under compressive strain. A representative volume element (RVE) is populated with randomly dispersed, non-overlapping spherical fillers using a hard-core constraint, and compressive kinematics are modeled with Poisson's ratio to capture transverse expansion. Electrical connectivity is determined by a soft-shell tunneling criterion, and tunneling resistance is evaluated using the Simmons tunneling model to compute network-level conductivity. Conductive network formation is quantified by the spanning cluster fraction (SCF) in a finite RVE, defined as the fraction of particles belonging to the cluster that bridges the two opposite electrode faces. The spanning cluster is identified efficiently using a depth-first search (DFS) algorithm. A simulation database was generated from 100 independent runs per condition and was used to train the MLP surrogate by varying five design parameters: filler volume fraction ( Vf ), particle volume ( Vp ), Poisson's ratio ( ν ), compressive strain ( ε ), and tunneling cutoff distance ( δ ). Permutation-importance analysis further quantified the relative influence of key design variables on percolation evolution, indicating that Vf dominates network formation (76.0%), while ε and δ primarily regulate sensing sensitivity, with an optimal sensing window near the percolation threshold ( Vf≈20−28% ). The trained MLP achieved strong predictive performance for SCF, with a test-set coefficient of determination ( R2 ) of 0.9744 and a mean 5-fold cross-validated R2 of 0.9927, providing an interpretable and computationally efficient tool for CPC design-space screening under compressive loading. A literature-based comparison with reported compression-responsive CPC conductivity trends was additionally included to assess the qualitative consistency of the simulated network evolution.
Keywords:
Conductive polymer composites
Tunneling percolation
Monte Carlo simulation
Multilayer perceptron
Compressive strain
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