Ubiquitiformal fracture energy

The ubiquitiformal fracture energy is proposed in the paper and its explicit expression is
obtained. Moreover, the numerical results for concrete are found to be in good agreement
with those for the critical strain energy release rate. The discrepancy between the numerical
results of the traditional fracture energy and the critical strain energy release rate can be
explained reasonably, which implies that the ubiquitiformal fracture energy should be taken
as an available fracture parameter of materials. Finally, it is numerically found for some
concrete that there is not size effect for the ubiquitiformal fracture energy.