An analytical model for predicting the elastic constants for isotropic random sphere arrays is described. The model is based on the Hertz contact theory and accounts for the restructuring (neck growth) associated with initial stage sintering. The stress-strain relation is incremental since the stiffness depends on the loads at sphere contacts. As part of the model development, relationships are given for the elastic constants of an isotropic aggregate consisting of orthotropic parts. Predicted elastic constants are presented as functions of the neck size and hydrostatic compression, and comparisons are made with experimental data for cohesionless sphere arrays and fully restructured arrays approaching a porous body.
An Elastic Stress-Strain Relation for Sphere Arrays Undergoing Initial Stage Sintering
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George, T. L., Kennedy, T. C., and Peddicord, K. L. (March 1, 1985). "An Elastic Stress-Strain Relation for Sphere Arrays Undergoing Initial Stage Sintering." ASME. J. Appl. Mech. March 1985; 52(1): 98–104. https://doi.org/10.1115/1.3169034
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