Numerical derivation of a normal contact law for compressible plastic particles

A new contact law is proposed to describe the behaviour of plastically compressible particles. The law was derived from contact simulations in which a general continuum constitutive model, the von Mises Double Cap (VMDC) model, was introduced to represent the particle material behaviour, allowing distinct dilatory, shearing and densification plastic flow regimes. Elastic and plastic properties were prescribed as functions of density. Parametric studies were conducted covering the parameter space of published experimental data for a range of pharmaceutical powders and granules. The analysis showed plastic zones corresponding to the three flow regimes developing within the particle, with size, shape, location and onset conditions being dependent on the strength ratios of the constitutive model. The contact law established combines an initial quasi-linear region followed by an exponential hardening region, arising from the initiation, growth and hardening of plastic zones, and the development of dense and stable loadbearing structures within the particle. The outcome of these studies is a new contact law, relationships for predicting contact law parameters from material parameters for both loading and unloading, and guidelines for the analytical treatment of plastic compressibility in particle contact. The contact law can be employed in discrete element and homogenisation models to predict macroscopic properties of porous granular materials, while the analytical framework and qualitative findings can be used in the design of granules.