One of the challenges of the ICME initiative is to link modelling descriptions on different length and time scales. Over the past decade, the phase field crystal model has emerged as a concept that unifies continuum descriptions on diffusive timescales with atomic resolution, therefore offering a link between atomistic descriptions on the one hand and phase field and continuum mechanics on the other hand.
Here we demonstrate in particular how large elastic deformations are represented in this description. Two sources of non-linearity are found, one of them based on geometric non-linearity expressed through a finite strain tensor. It reflects the Eulerian structure of the continuum model and correctly describes the strain dependence of the stiffness. The predicted isotropic low temperature non-linear elastic effects are directly related to the Birch-Murnaghan equation of state. These predictions are in agreement with ab initio results for large strain bulk deformations of various bcc elements and graphene. Physical non-linearity arises if the strain dependence of the density wave amplitudes is taken into account and leads to elastic weakening. For anisotropic deformations the magnitudes of the amplitudes depend on their relative orientation to the applied strain.