We investigate the dissipative mechanisms exhibited by creased material sheets when subjected to mechanical loading, which comes in the form of plasticity and relaxation phenomena within the creases. After demonstrating that plasticity mostly affects the rest angle of the creases, we devise a mapping between this quantity and the macroscopic state of the system that allows us to track its reference configuration along an arbitrary loading path, resulting in a powerful monitoring and design tool for crease-based metamaterials. Furthermore, we show that complex relaxation phenomena, in particular memory effects, can give rise to a non-monotonic response at the crease level, possibly relating to the similar behavior reported for crumpled sheets. We describe our observations through a classical double-logarithmic time evolution and obtain a constitutive behavior compatible with that of the underlying material. Thus the lever effect provided by the crease allows magnified access to the material's rheology.

9 pages, 10 figures