We investigate numerically the micro and macro mechanical behaviour of non-cohesive granular materials, especially in the static limit. To achieve this goal we performed numerical simulations generating two-dimensional "sand piles" from several thousands of convex polygonal particles with varying shapes, sizes and corner numbers, using a discrete element approach based on soft particles. We emphasize that the displacement (strain) fields inside sand piles have not been measured in experiments on sand piles. Averaging is made reproducible by introducing a representative volume element (RVE), the size of which we determine by careful measurements. Stress tensors are studied for both symmetric and asymmetric sand piles in two-dimensional systems, where the particles are dropped from a point source. Furthermore, we determine the fabric tensor inside the sand piles. A surprising finding is the behaviour of the contact density in this kind of heap, which increases where the pressure is at a minimum. The fabric is linearly proportional to the product of the volume fraction and the mean coordination number for a pile consisting of monodisperse mixture of particles. We observe that the macroscopic stress, strain and fabric tensors are not collinear in the sand piles. (C) 2010 Elsevier B.V. All rights reserved.