A theoretical model for the stress distribution in granular matter .1. Basic equations

This paper constructs the simplest model of granular matter such that the equations for the force distribution in the material can be derived and solved for simple geometries. This will be done by writing down an integral equation for the force field (which reflects the ability of athermal, friction dominated granular matter to shed the load it bears unevenly amongst their neighbours). This equation is then transformed into a differential one in order to obtain an equation for the force distribution within the system (which we will see is capable of describing mesoscopic systems). In subsequent publications we will consider the application of this theory to vertical and horizontal pipes and to the problem of the sandpile.