Abstract
A unit model consisting of two particles in contact and under compression, leading to the development of an internal state variable (ISV) constitutive model incorporating the particle-to-particle contact during large deformations, is studied. Following Matthews' approximation that a general form of the Hertz elastic contact solution holds for nonlinear materials, an analytical solution based on the ISV constitutive model and valid for the small contact stage is first derived for the unit problem. To account for large contact areas, the analytical solution is modified based on numerical results obtained from a detailed finite element analysis of the compression of two identical spherical aluminum particles in contact. A set of unified relations is derived from this analysis that accounts for the strain rate effects and accurately represents the particle-to-particle contact behavior for both small and large contact areas. The performance of the proposed model is validated through comparisons with detailed numerical results obtained for a wide range of strain rates.
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