  This study presents the formulation, the numerical solution, and the
validation of a theoretical framework based on the concept of variable-order
mechanics and capable of modeling dynamic fracture in brittle and quasi-brittle
solids. More specifically, the reformulation of the elastodynamic problem via
variable and fractional order operators enables a unique and extremely powerful
approach to model nucleation and propagation of cracks in solids under dynamic
loading. The resulting dynamic fracture formulation is fully evolutionary hence
enabling the analysis of complex crack patterns without requiring any a prior
assumptions on the damage location and the growth path, as well as the use of
any algorithm to track the evolving crack surface. The evolutionary nature of
the variable-order formalism also prevents the need for additional partial
differential equations to predict the damage field, hence suggesting a
conspicuous reduction in the computational cost. Remarkably, the variable order
formulation is naturally capable of capturing extremely detailed features
characteristic of dynamic crack propagation such as crack surface roughening,
single and multiple branching. The accuracy and robustness of the proposed
variable-order formulation is validated by comparing the results of direct
numerical simulations with experimental data of typical benchmark problems
available in the literature.
