A sequential mobile packing algorithm for micromechanical assessment of heterogeneous materials

Abstract

A new non-uniform sequential mobile packing (NSMP) algorithm featuring an efficient collision detection scheme was developed to rapidly generate representative volume elements (RVEs) for advanced heterogeneous and/or composite material systems with either spherical or cylindrical inclusions and a broad range of microstructural characteristics (i.e., various inclusion orientations and sizes, and agglomerations). Statistical assessment of inclusion spatial dispersion using nearest neighbor-based and pair correlation functions revealed that the NSMP algorithm generated RVEs with realistic microstructures for all cases considered. Subsequent statistical finite element micromechanical modeling was conducted to compute the effective properties for each generated microstructure. A case study for a 3D-printed nanocomposite material revealed that a combination of aligned and misoriented rod inclusions was the most representative microstructure. Contour plots of normalized effective stiffness for the 3D-printed composites and normalized average hydrostatic stress in the matrix phase enabled comparison of RVEs with different microstructures. The material system with aligned rod inclusions benefited from simultaneous high effective stiffness and effective load transfer to the inclusions (at higher inclusion volume fractions), which is indicated by low average hydrostatic stress in the matrix. The microstructures comprising spherical inclusions exhibited moderate stiffness, while those with clustered misoriented rod inclusions had the lowest effective stiffness and load transfer to the inclusions. The NSMP algorithm can be used for further microstructural optimizations and assessments of renifornced or porous heterogeneous and/or composite materials using machine learning, while the generated contours can be used as general design guidelines.