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Research on one-dimensional ubiquitiformal constitutive relations for a bimaterial bar

Yang Min, Ou Zhuo-Cheng, Duan Zhuo-Ping, Huang Feng-Lei

Journal of Theoretical and Applied Mechanics

2019

Vol. 57 nr 2

291--301

A one-dimensional ubiquitiformal constitutive model for a bimaterial bar is proposed in this paper. An explicit analytical expression for the effective Young modulus is then obtained, which, unlike the fractal one, leads to a continuous displacement distribution along the bar. Moreover, numerical results for concretes are calculated and found to be in agreement with previous experimental data. In addition, some previous empirical and semi-empirical constitutive models are also examined, which shows that each of these models can correspond well to a ubiquitiformal one under a certain complexity.

A stereological ubiquitiformal softening model for concrete

Ou Zhuo-Cheng, Li Guan-Ying, Duan Zhuo-Ping, Huang Feng-Lei

Journal of Theoretical and Applied Mechanics

2019

Vol. 57 nr 1

27--35

A stereological ubiquitiformal softening model for describing the softening behavior of concrete under quasi-static uniaxial tensile loadings is presented in this paper. In the model, both the damage evaluation process of fracture cross-sections and their distribution along the specimens axis are taken into account. The numerical results of a certain kind of full grade concrete made of crushed coarse aggregate are found to be in good agreement with the experimental data. Moreover, an experiental relation between the lower bound to the scale invariance of concrete and its tensile strength is also obtained by data fitting of the experimental data, which provides an effective approach to determine the lower bound to scale invariance of concrete.

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.