Extending Hertzian Contact Area Theory to Plastic Deformation of Glassy Polymer Particles

Quantifying the mechanical response of polymer particles under compression is fundamentally hindered by a deceptively simple problem: the contact area between the particle and compression plate can rarely be directly measured during deformation. Since Hertz formulated his contact theory in 1881, widely used Hertzian and adhesive contact models have remained largely confined to the elastic regime, leaving the plastic deformation behavior of polymer particles fundamentally out of reach. Here, we extend the original Hertzian contact area relation from elastic deformation to plastic deformation by combining it with the Boyce–Parks–Argon constitutive model. The contact area predicted by the model agree well with those obtained directly from all-atom molecular dynamics simulations of poly(methyl methacrylate) and poly(methyl acrylate) particles. When the framework is applied to experimental compression data of polystyrene and acrylic particles, it identifies clear yield points and shows that crosslinking density and particle-size effects can be understood within the established framework of bulk polymer mechanics. The framework provides a route to the intrinsic mechanical properties of polymer particles beyond the yield point without direct measurement of the contact area, supporting the rational design of particles with tailored mechanical properties.