Contribution of microscale stochastic truss models to investigate the macroscale elasticity constants of porous ceramics

Abstract

This paper deals with modelling the mechanical behaviour of silica-alumina open-cell porous ceramics obtained by viscous flow sintering. The modelling approach is based on the similarity of the material microstructure to a truss of sintering bridges connecting alumina particles. This makes it possible to use two-node elements, leading to a low computational cost. The method includes the building of a random packing of spheres (alumina particles) and the setup of connections between their centres (silica sintering bridges). An equivalent stiffness is then assigned to each bridge, based on the material parameters. The macroscale elasticity constants have been derived from the natural frequencies of such micrometric cylindrical volume elements made of thousands of particles. The reliability of the underlying assumptions is discussed and the dependence to the material parameters is emphasized. The method is suitable to handle more complex behaviours, which opens the door to fracture modelling.