# Loading-unloading contact law for micro-crystalline cellulose particles under large deformations

## TL;DR

This paper introduces a semi-empirical contact law for micro-crystalline cellulose particles that models large deformations, capturing elastic-plastic behavior and strain-hardening effects through experimental calibration.

## Contribution

It develops a generalized contact law for irregular particles incorporating shape, elastic, and plastic properties, validated against experimental force-displacement data.

## Key findings

- Good agreement between model predictions and experimental data.
- Plastic properties follow a log-normal distribution.
- The model captures strain-hardening behavior during compression.

## Abstract

A semi-empirical mechanistic contact law for micro-crystalline cellulose (Avicel PH-200) particles is proposed and characterized experimentally using force-displacement curves obtained from diametrical compression of single particles. The concepts of a shape factor and a master contact law are introduced first for elastic ellipsoidal particles, and subsequently generalized to plastic irregular particles. The proposed loading-unloading contact law is a function of three characteristic diameters (lengths of the principal axes of an approximated ellipsoid), a geometric parameter associated with the loading condition, three plastic and one elastic material properties. The force-displacement curves obtained using a micro-compression tester exhibit an apparent strain-hardening at distinctly different strain values, which is captured by the shape factor function and its geometric parameter. The three plastic material properties are log-normal distributions estimated from the loading experimental curves, while the elastic property is estimated from the unloading experimental curves. The study shows a very good agreement between predictions of the calibrated loading-unloading contact law and the experimental values.