According to a well-known model due to J. M Ball, the behaviour of nonlinearly elastic solids can be understood via properties of their energy minimisers. In this talk we will address the question of smoothness of minimisers. In particular, we will show that when the condition of 'positive twist' holds, then in the two-dimensional setting energy minimisers are Holder continuous. We also give a characterisation of positive twist in terms of star-shapedness, demonstrating that, in principle, it is straightforward to check whether a mapping has positive twist or not.