Gradient of mechanical properties in polymer nanocomposites: From atomistic scale to the strain gradient effective continuum

It is well known that glassy polymer nanocomposites (PNC) exhibit heterogeneous mechanical properties, with a distinct polymer/nanoparticle (NP) interfacial region. The interphase rigidity in particular can significantly influence the overall response of PNCs. Continuum theories typically describe behavior such to depend only on deformation and, thus, they discard strong internal gradients within interphase, are necessary for enriched continuum models PNC’s. Here we formulate higher-gradient elasticity constitutive law polymer/NP region through systematic micro–meso–macro coupling, using data from atomistic molecular dynamics (MD) simulations. From physical standpoint, show order accurately consider it as strain gradient material, whereas bulk material may still behave Cauchy experiencing much lower effects, compared interphase. Using MD simulations, thickness PNCs examined by probing density profile distribution at equilibrium. By upscaling towards model, effective model emerges, whereby hyperstress tensor and conjugate gradient, together stress strain, computed each atom In further step, continuum-based homogenization scheme based unfolding method elaborated identification strain-gradient elastic moduli composite materials, according which obeys second-gradient linear law, an inner reinforcement outer surrounding matrix obeying first-gradient model.