A general weighted space-time averaging procedure is developed and utilized to obtain the average balance equations for granular materials. The method is applicable to both solid-like (quasi-static) and fluid-like (granular flow) modes of granular material behavior. The average balance equations take the same mathematical form while all average quantities involved in these equations retain the same clear physical meaning whether or not the continuum hypothesis is satisfied. If it is, the average variables are continuous and smooth functions of space and time and are independent of the averaging length and time scales. Otherwise, the average variables may be discontinuous and scale-dependent, but the same average balance equations hold within the framework of calculus of generalized functions.
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