I will talk about the existence of minimizers of the 3D neo-Hookean energy in the critical case, i.e., Sobolev exponent $p=2$. In this case the coercivity of the neo-Hookean energy is not sufficient to ensure compactness in a suitable space, as shown by an example of Conti-De Lellis. However, the example suggests a specific relaxed energy.  This allows to transform the lack of compactness problem into a regularity problem. I will provide a description for this relaxed energy.