Nanoscale dynamic mechanical analysis of a viscoelastic matrix inclusion within an elastic substrate

Advanced composite materials incorporate viscoelastic matrix inclusions in designated locations within elastic substrates, which grant them specialized energy dissipation capabilities of dynamic loadings. Identifying the local nanomechanical properties of the matrix-substrate complex within the composite is critical to its design and adaptation toward a specific target function. Here, we conduct FE simulations of nanoscale dynamic mechanical analysis (DMA) testing on hemispherical matrix inclusions within elastic substrates and analyze the variations in its indentation storage loss moduli measures for different matrix-substrate configurations. Then, we describe the mechanical system by simple spring models, identify the dominating parameters at different contact states of the nanoscale DMA testing, and obtain highly accurate analytical formulae that link the indentation measures of the matrix-substrate complex to the individual mechanical properties of the matrix and substrate parts. Our analysis can be directly integrated into benchmark nanomechanical testing methodologies of composite materials and promotes the local dynamic-mechanical characterization of complex materials systems, including nanomaterials, micro-architected structures, and bio-inspired designs.