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Ubiquitiformal fracture energy

Ou Z.-C., Yang M., Li G.-Y., Duan Z.-P., Huang F-L.

Journal of Theoretical and Applied Mechanics

2017

Vol. 55 nr 3

1101--1108

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.

Ubiquitiform in applied mechanics

Ou Z.-C., Li G.-Y., Duan Z.-P., Huang F-L.

Journal of Theoretical and Applied Mechanics

2014

Vol. 52 nr 1

37--46

We demonstrate that a physical object in nature should not be described as a fractal, despite an ideal mathematical object, rather a ubiquitiform (a terminology coined here for a finite order self-similar or self-affine structure). It is shown mathematically that a ubiquitiform must be of integral dimension, and that the Hausdorff dimension of the initial element of a fractal changes abruptly at the point at infinity, which results in divergence of the integral dimensional measure of the fractal and makes the fractal approximation to a ubiquitiform unreasonable. Therefore, instead of the existing fractal theory in applied mechanics, a new type of ubiquitiformal one is needed.