Material nonlinearity is implemented in finite element programs using mathematical models of material behaviour. These are typically defined by a set of parameters whose values are determined from experimental data. These constitutive models are phenomenological; that is they describe nonlinear material behaviour, but do not explicitly model the physical mechanisms that lead to plasticity. In this paper, the authors discuss how three different modelling strategies may improve realism; (i) Stochastic Monte Carlo Simulation, (ii) Image-based Modelling and (iii) Cellular Automata coupled with Finite Elements. Each of these techniques are linked to the underlying micromechanics in a different way. Case studies are presented for a range of materials (namely graphite, bone and polycrystalline iron) to give an overview of how each of these techniques might be used. This paper will be of interest to engineers who might not have previously considered (a) stochastic modelling being relevant to their work or (b) using X-ray tomography data and image-based modelling as an alternative method for calibrating a constitutive model. Furthermore, the three techniques could be used together by firms wanting to custom design novel materials for extreme engineering applications.