Discrete element method to predict the mechanical properties of pigmented coatings Dan Varney, Martti Toivakka, Doug Bousfield Ó American Coatings Association 2019 Abstract The mechanical properties of pigmented coating layers are important in a variety of applica- tions. However, the large number of parameters that influence these properties as well as the numerous types of deformations challenge the prediction of the performance of these systems. A discrete element method (DEM) is proposed to predict the mechanical properties of paper coating layers that have a range of starch and latex content. The model is developed in both 2D and 3D and is adapted to tensile and flexural deformations. The model predictions are compared to experimental results in the literature. The predictions are generally good for the moduli and the strain at failure of the systems, but underpredict the maximum stress. This result may be caused by the complex particle size distribution of the experimental systems or by the impact of the brittleness of the starch when making the freestanding films. Keywords Discrete element method, Mechanical properties, Pigmented coating, Cracking Introduction The mechanical properties of coatings are important in a number of applications. In paint applications, scuff or rub resistance is important. 1 In the production of lithium ion batteries, the coating layers must resist deformation without cracking. 2,3 For coated papers, the resistance to ‘‘picking’’ during the printing opera- tion is critical as well as the ability for the sample to be converted or folded without cracking of the coating layer. 4,5 The influence of binder content, binder type, and particle shape on paper coating cracking during the fold has been studied by a number of groups. 6–8 If the coating layer is a homogenous material, such as a specific polymer, the mechanical properties of that layer can be estimated from the bulk properties of that material. However, when the coating layer is a com- posite of pigments and binder, the mechanical proper- ties are difficult to predict. Finite element methods can be used to predict the deformation of coated paper by treating the coating layer as a continuum. 9–11 The compressive and tensile stresses during bending can be predicted. However, the elastic modulus and the Poisson ratio are inputs of the model; these would need to be measured for each coating formulation because they would depend on the latex type, starch loading, and the paper fiber properties. In addition, the basic mechanisms of crack formation and failure are not well understood if the coating layer is considered a uniform material. Some continuum-type models have been explored by modeling groups of particles connected by poly- meric bridges. 12 When the number of particles in- creases and the distance between particles is small, numerical analysis of this nature is costly. While some insight into mechanical properties of porous compos- ites has been obtained with a mesh-free continuum mechanics simulation, 13 an understanding of microme- Presented at the 19th International Coating Science and Tech- nology Symposium, September 16–19, 2018, in Long Beach, CA, USA D. Varney OMYA Inc., Proctor, VT 05765, USA D. Varney, D. Bousfield (&) Paper Surface Science Program, Department of Chemical and Biomedical Engineering, University of Maine, Orono, ME 04469, USA e-mail: bousfld@maine.edu M. Toivakka Laboratory of Paper Coating and Converting, A ˚ bo Akademi University, Turku, Finland J. Coat. Technol. Res. https://doi.org/10.1007/s11998-019-00255-w