DISPERSION AND WAVE-PROPAGATION IN DISCRETE AND CONTINUOUS MODELS FORGRANULAR-MATERIALS

A generalised continuum model for granular media is derived jy direct homogenisation of the discrete equations of motion. In contrast to pre vious works on this topic, continuum concepts such as stress and momen t stress are introduced after homogenisation. First, a very simple one -dimensional model is considered and the continuum version For this mo del is derived by replacing the difference quotients of the discrete m odel by differential quotients. The dispersion relations of the discre te and the continuous model are derived and compared. Variational boun dary conditions for the continuous model are deduced from the stationa rity of the corresponding Lagrangian. The three-dimensional case is tr eated in an essentially similar fashion. The resulting continuum theor y is a combination of a Cosserat Continuum and a higher-order deformat ion gradient continuum. The salient features of the theory are illustr ated by means of the dispersion relations for planar wave propagation. Copyright (C) 1996 Elsevier Science Ltd.