The stress response of a semi-infinite micropolar granular material subject to a concentrated force normal to the boundary

We consider the problem of a two dimensional semi-infinite granular material subject to a concentrated or point force normal to the boundary. This boundary value problem was originally solved for a classical elastic material by Flamant in 1892 and, hence, is also known as the ‘‘Flamant problem’’ (Johnson [8]). In this paper, the granular material is considered as an elastic micropolar or Cosserat continuum and is represented by a particular form of the general constitutive law derived in Walsh and Tordesillas [29]. The stress distribution predicted by the model is in good agreement with experimental data for small strains. In particular, two important features that are captured by the proposed model are: (i) the presence of tensile stress response regions, and (ii) the dependence of the stresses on the microstructural properties, i.e. the particles’ normal, tangential and rotational stiffness constants. The proposed analysis utilizes two new stress functions, similar to Airy’s stress functions in classical elastic theory.