Modeling plasticity of amorphous composites: Scalar is not enough

We use a continuous mesoscopic model to address the yielding properties of plastic composites, formed by a host material and inclusions with different elastic and/or plastic properties. We investigate the flow properties of the composed material under a uniform externally applied deviatoric stress. We show that due to the heterogeneities induced by the inclusions, a scalar modeling in terms of a single deviatoric strain of the same symmetry than the externally applied deformation gives inaccurate results. A realistic modeling must include all possible shear deformations. Implementing this model in a two-dimensional system we show that the effect of harder inclusions is very weak up to relatively high concentrations. For softer inclusions instead, the effect is much stronger, even a small concentration of inclusions affecting the form of the flow curve and the critical stress. We also present the details of a full three dimensional simulation scheme, and obtain the corresponding results, both for harder and softer inclusions.