A lattice spring model of heterogeneous materials with plasticity

A three-dimensional lattice spring model of a heterogeneous material is pre sented. For small deformations, the model is shown to recover the governing equations for an isotropic elastic medium. The model gives reasonable agre ement with theoretical predictions for the elastic fields generated by a sp herical inclusion, although for small particle sizes the discretization of the underlying lattice causes some departures from the predicted values. Pl asticity is introduced by decreasing the elastic moduli locally whilst main taining stress continuity. Results are presented for a spherical inclusion in a plastic matrix and are found to be in good agreement with the predicti ons of Wilner.