Model-free data-driven computational mechanics (DDCM) is a new paradigm for simulations in solid mechanics. One of the its advantagesis the fact that it avoids regression-based, bias-prone constitutive modeling. However, many materials do display a simple linear response in the low-strain regime while also presenting complex behavior after a certain deformation threshold. Motivated by this fact, we present a novel refinement technique that turns regular elements (equipped with a linear-elastic constitutive law) into data-driven ones if they are expected to surpass the threshold known to trigger material non-linear response. We term this technique
data refinement'',d-refinement” for short. The methodology is ideal to run simulations that feature non-linear response in relatively small portions of the domain while the rest remains linear-elastic. The method is validated against a traditional incremental solver (i.e., Newton-Raphson method) and we show that the d-refinement framework can outperform it in terms of speed at no accuracy cost.