Indentation modelling of heterogeneous materials

The computational modelling of the indentation response of heterogeneous materials is studied using the finite element method. The material system consists of hard particles embedded within a soft matrix. Two material models with exactly the same overall stress-strain characteristics are simulated: one specifically incorporating dispersed elastic particles in an elastic-plastic matrix and the other a simple elastic-plastic continuum having a homogenized constitutive response of the particle-containing material. The material model with particles explicitly included shows a harder response than that of the homogenized model, even when the particle size is much smaller than the indent size. This is primarily due to the local increase in particle concentration directly underneath the indentation, which cannot be easily accounted for in the homogenized model. As a consequence, treating a heterogeneous material as a simple continuum in a straightforward manner appears to be an invalid approach in indentation modelling.