A rigorous universal model for the dynamic strength of materials across loading rates

The dynamic strength for a broad range of materials with different microstructures exhibits surprisingly similar behavior. Two distinct regimes are observed with a sharp transition between them. At low loading rates, the strength has a weak linear dependence on the log loading rate until a critical rate above which a dramatic increase is observed. We explain this behavior by considering material failure as a bond-breaking process driven by external loading and thermal fluctuation within a Langevin dynamics framework. The analysis leads to nondimensional measures for which the dynamic response collapses onto a universal curve, independent of material properties, describing both loading rate regimes and the transition between them. A simple approximate model is derived that provides an excellent fit to experimental data for a broad range of materials, including concrete, ceramics, and metals.