Abstract
Stress strain relationships of a granular system are derived based on the premise that the mean field of displacement is the best fit of actual particle displacements. Based on the best fit hypothesis, two fundamental relationships are derived: (1) the average strain as a function of contact displacements, and (2) the mean field of contact force as a function of stress. These two relationships lead to a stress-strain law without the kinematic constraint of uniform strain. For an assembly with isotropic packing structure, closed-form stress-strain relationships are explicitly derived in which the modulus can be determined from the inter-particle stiffness. The difference between the derived stress-strain relationship and that derived from Voigt hypothesis is discussed. The effect of fabric variation is illustrated in the theory. Discrete element analyses are also performed and the results are used to compare with the estimated moduli from the proposed theory. In the comparison, the solution bounds for granular assembly system are illustrated.
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