Zhuo-Cheng Ou

Some explicit analytical expressions of the dynamic shear load-carrying capacity for brittle materials under a quadratic waveform loading are presented on the basis of the incubation time fracture criterion, by which the dynamic shear load-carrying capacity can be determined from the quasi-static material parameters, incubation time and stress wave loading conditions (loading amplitude, loading duration, and waveform). The numerical results are in good agreement with the previous experimental data. It is found that the incubation time fracture criterion can be adopted to describe the time-dependence of the dynamic shear failure of brittle materials and predict shear failure. Meanwhile, the so-called dynamic shear strength should be the dynamic shear load-carrying capacity, which is a computable result rather than a material parameter, and the strain rate enhancement effect on the shear failure strength cannot be considered as a material property but should be a structure response of brittle materials to stress wave loading conditions.

Considering the self-similar characteristic of irregular pore network of materials during the damage evolution process, a pore ubiquitiform model (PUM) is developed to characterize the multiscale pore or microcrack network of quasi-brittle materials, and then based on the PUM, the ubiquitiform damage model (UDM) is proposed to describe the damage evolution process of quasi-brittle materials under quasi-static uniaxial tensile loading. The values of porosity and pore specific surface area estimated from the PUM and the stress-deformation curves including the softening curve calculated from the UDM are in good agreement with previous experimental data, respectively. It can be found that, the PUM can be adopted to characterize the self-similar multiscale pore network and estimate the porosity and pore specific surface area, and the UDM can describe the damage evolution process of quasi-brittle materials under quasi-static uniaxial tensile loading. Meanwhile, the UDM can characterize the self-similar characteristic of pore network during the damage evolution process of quasi-brittle materials through the evolving ubiquitiform complexity.

In recent decades, the incubation time has become a critical parameter to study dynamic failures for materials, but its underlying physical meaning is still vague and the corresponding model remains lacking. In this study, we first established a theoretical framework to evaluate incubation time, wherein a double atomic chain model with atomic thermal vibrations is leveraged. We leveraged three external force loading conditions to analyze incubation time and its associated dynamic load-carrying capacity (DLC). It can be found that the theoretical results for three metal materials (iron, tungsten and aluminum) exhibit reasonable consistencies with the experimental data, thus the model can be used to conduct preliminary studies for incubation time and DLC. The model suggests that, under the ramp loading with a platform amplitude of static strength, the amplitude duration does not remain constant but can quickly reach a constant with increasing ramp or loading rate, which implies that treating incubation time as a constant parameter is reasonable and thus lays a solid foundation for the previous macroscopic models on basis of incubation time. Meanwhile, it also suggests that the rate enhancement effect of failure strength can be obtained from external load and the constant atomic bond parameters without involving microscopic changes in material properties. Therefore, we microscopically unravel the rate enhancement effect of failure strength. Our study indicates that this effect is indeed a structural response, which accords with the previous macroscopical model.

In this study, a ubiquitiform hotspot ignition model with cross‐scale characteristics is proposed to describe the ignition stage of PBX, which can account for heterogeneous effects. Firstly, a ubiquitiform model of hotspot intensity is obtained. The model can describe the hotspot information after PBX is impacted. In which, a hotspot distribution model based on the nested ubiquitiform model of explosives is used to characterize geometric properties of hotspot, including the size and location of hotspot; and the Weibull statistical distribution function is used to describe the distribution of hotspot intensity. Then, combining the ubiquitiform model of hotspot intensity with Arrhenius model, the ubiquitiform hotspot ignition model is developed to characterize the ignition stage of PBX. Finally, it is found that the equivalent reaction rate constants calculated by our ignition model are in good agreement with the previous experimental data.

In this study, similarity analysis and mesoscale simulations were performed to investigate hot spot temperatures in triangular voids inside polymer‐bonded explosives (PBXs). We found that there are two different void collapse modes, namely single and double hydrodynamic jet modes. The hot spot temperatures achieved in the double hydrodynamic jet mode are much higher than previous predictions, such as predictions based on circular voids, which agrees with recent experimental observations. Additionally, we verified that void configuration (position and shape) plays a significant role in increasing hot spot temperatures, implying that when establishing a mesoscale reaction rate model, it is insufficient to use void volume alone to characterize the impact sensitivity of PBXs. Finally, two semi‐empirical analytical expressions are proposed to represent the dependence of hot spot temperature on both the void configuration and shock intensity. The resulting theoretical predictions are in good agreement with the numerically simulated results. Such mesoscale analytical expressions can be used for establishing theoretical mesoscale hot spot ignition rate models in the future.

The crack extension path of concrete materials was simulated numerically based on the non-uniform numerical model of Weibull distribution, and the complexities of various ubiquitiform fracture surfaces were calculated to explore the relationship between complexity and fracture energy. To study the influence of specific crack extension law and fracture mode on the relationship between the complexity and fracture energy, numerical simulation of the crack extension was carried out based on the numerical model with random aggregate distribution, and the reason for the change of the relationship between complexity and fracture energy were discussed.

A nesting ubiquitiform (NU) approach was developed to characterize the mesostructural features of polymer-bonded explosives (PBXs), and then used to predicate some equivalent physical properties of PBXs, which can also be expected to be extended to other composites with complicated internal mesostructures. To verify the availability, two NU models for two kinds of PBX with different compositions are presented, which are PBX 9501 and LX-17, based on which, the equivalent thermal conductivities were calculated. Particularly, it is so encouraging that an analytical expression of the equivalent thermal conductivity was obtained only under a simply assumption of homogeneity. Moreover, it was found that the numerical results calculated by both the recursive algorithm and the analytical expression were in good agreement with the experimental data. In addition, it is also shown that such a physical property as the equivalent thermal conductivity is indeed independent of the meso-configuration of the location distribution of the explosive particles and the voids inside the PBX, which seems consistent with the common expectations and lays the foundations for the application of ubiquitiform to investigating some equivalent properties of composites.

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...

A stereological ubiquitiformal softening model for describing the softening behavior of con- crete 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...