A microstructure-informed hyperelastic model for CNT-based polymer nanocomposites under large deformations

Modeling the mechanical response of carbon nanotube (CNT)-reinforced polymer nanocomposites (PNCs) under large deformations remains an open and complex challenge. Microstructural phenomena such as the formation of CNT agglomerates and the progressive detachment of CNTs from the polymer matrix significantly influence the macroscopic mechanical behavior, particularly in the nonlinear regime. These effects are further complicated by variability introduced during fabrication, which can significantly affect both internal morphology and mechanical performance. Despite progress in the field, a comprehensive hyperelastic model capable of capturing these phenomena and linking them to continuum-level response is still lacking. This work presents a physically motivated hyperelastic model informed by scanning electron microscopy (SEM) observations. The growth of agglomerates and the local increase in CNT concentration are incorporated using functions derived from underlying statistical distributions. The reinforcement contributions of CNTs in agglomerated and non-agglomerated regions are described by strain energy functions reflecting microstructural observations. Interfacial detachment is captured within the framework of continuous softening hyperelasticity, introducing critical strain invariants to define the onset of debonding. All model parameters retain a clear physical interpretation and can be directly estimated from SEM imaging, making the model fully predictive without requiring mechanical test data. To demonstrate practical applicability, the model is implemented in a finite element framework and validated against experimental simple tension and bending tests. Additionally, a simplified version of the model is proposed for cases where microstructural data are unavailable, following a more classical phenomenological approach in nonlinear mechanics. This formulation requires only stress–strain data for calibration and is shown to accurately reproduce experimental results from three independent datasets, confirming the effectiveness and versatility of the proposed approach.