Mapping Internal Damage Fields Induced by Stress Softening in Dissipative Nanocomposite Elastomers

Abstract

The pronounced stress-softening effect (SSE)─a consequence of strain-induced invisible internal damage─is a defining feature of nanocomposite elastomers. However, SSE under real-world, heterogeneous deformation remains poorly understood due to a historical focus on simple uniaxial testing. Here, we propose a methodology to quantify and map this elusive internal damage entirely within an experimental framework, operating completely independently of any specific constitutive model. By calibrating an invariant-based damage function (IDF) for a nanocomposite elastomer from cyclic loading–unloading tests across various uniform deformation modes, we convert strain fields measured by digital image correlation (DIC) into full-field internal damage maps. This DIC-IDF approach is applied to two representative two-dimensional heterogeneous deformation scenarios in thin-film geometries: (i) notch opening, and (ii) stretching with a circular defect. The former reveals teardrop-shaped damage zones that drive stress redistribution and enhance crack-growth resistance. The latter highlights a shift of the maximum SSE zone from the lateral edge to the diagonal region as the applied stretching increases. We also verify that local principal-stretch axes exhibit no substantial net rotation during these heterogeneous deformations, particularly within active damage zones, validating the scalar IDF─where the induced damage anisotropy is not explicitly incorporated─as a reasonable first-order approximation. This DIC-IDF approach provides a powerful tool for decoding SSE and elucidating the fracture and toughening mechanisms of dissipative nanocomposite elastomers.