Equivalent inclusion method based simulation of the sedimentation of many particles toward functionally graded material manufacturing
Huiming Yin (Columbia University)
Prager Medal Symposium in honor of George Weng: Micromechanics, Composites and Multifunctional Materials
Tue 4:20 - 5:40
MacMillan 117
A novel numerical approach based on Eshelby's equivalent inclusion method is presented to simulate the Stokes flow of many particles moving in a viscous fluid at a small Reynolds number. For each particle, an eigenstrain rate, which is given by a polynomial function, is introduced to represent the mismatch between the particle and the rest fluid. Based on Eshelby�s equivalent condition, the eigenstrain rate of each particle can be solved and the sedimentation process of a many-particle system can be simulated. Because the Stokes� flow is obtained by the integral of eigenstrain in all particles, which can be analytically derived for spherical particles, therefore, no mesh is needed for each particle. This approach creates a possibility to simulate a large-scale particle system. Using a mix of aluminum and high-density polyethylene spherical powders in sedimentation, one can simulate the microstructural evolution during the sedimentation process, which will lead to a manufacturing method for functionally graded materials.