A STATISTICAL MICROMECHANICS FRAMEWORK FOR PIEZORESISTIVITY IN VISCOELASTIC FOAMS: UNIFYING STRUCTURAL EVOLUTION FROM CRACK TO CONTACT REGIMES

Abstract

We introduce a comprehensive computational framework to simulate the complex electro-mechanical response of flexible, porous piezoresistive sensors. Existing simulation approaches face a critical bottleneck: they either rely on homogenized material properties that ignore the determinative porous micro-architecture, or they employ simplified, idealized geometries that fail to capture the stochastic nature of real foams. Most critically, prior models have overwhelmingly neglected the intrinsic viscoelasticity of the polymer matrix, a fundamental property governing the material's time-dependent mechanical response. Our framework overcomes these limitations by integrating three key elements within a Finite Element (FE) environment: (1) A stochastic 2D Representative Volume Element (RVE) based on a novel, computationally-stable abstracted pore geometry; (2) A Generalized Maxwell model to capture the experimentally-verified viscoelastic stress relaxation of the polyurethane (PU) substrate; and (3) A "segmented quasi-static" (SQS) solution strategy, developed to circumvent the documented limitations of commercial FE software in handling fully-coupled dynamic, conductive-contact simulations. The model is built by generating an ensemble of over 200 RVEs, each with randomly-distributed internal pore geometries, to represent the foam's statistical heterogeneity. By performing an ensemble average of the simulation results, our model successfully generates a macroscopic resistance-strain curve that is in high agreement with experimental observations. Crucially, this work provides a unified, structure-based origin for the two distinct sensing regimes widely reported in the literature: the initial, high-sensitivity "crack effect" (GF > 25) is shown to be a statistical emergent property of the initial contact events of the most vulnerable pores in the stochastic distribution, while the stable, high-strain "contact effect" corresponds to the progressive, large-scale pore collapse and contact area growth across the ensemble. This framework bridges the gap between stochastic microstructure and predictable macroscopic performance, opening a pathway for the inverse design of foam-based sensors.