A Ubiquitiformal One-Dimensional Steady-State Conduction Model for a Cellular Material Rod

Li, Guanying; Ou, Zhuo-Cheng; Xie, Ruiqing; Duan, Zhuo-Ping; Huang, Fenglei

doi:10.1007/s10765-015-2010-4

Cited by 12 publications

(11 citation statements)

References 12 publications

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“…From the above description, it appears that the ubiquitiform rather than the fractal should be used to describe the mesoscale structure of composite materials as well as the internal mesoscale morphology of PBXs. At the briefest glance, the ubiquitiformal characterization of the mesoscale structure of a PBX will be similar to that of the quasi-brittle materials described above [15,16,17]. However, it should be noticed that there exists a crucial difference in the mesoscale structure between the general quasi-brittle materials and the PBXs.…”

Section: Introductionmentioning

confidence: 70%

“…So far, the concept of ubiquitiform has been used successfully to describe some physical properties of composite materials. For example, Li et al [15] proposed a ubiquitiformal, one-dimensional, steady-state conduction model for a cellular material rod, by which, the explicit analytical expressions for both the temperature distribution and the equivalent thermal conductivity are obtained. Ou et al [16] presented both the conception and the explicit expression of the so-called ubiquitiformal fracture energy for quasi-brittle materials, and found that there is no size effect for the ubiquitiformal fracture energy, which implies that the ubiquitiformal fracture energy will be one of the reasonable fracture parameters.…”

Section: Introductionmentioning

confidence: 99%

“…Just as presented by Baer [18], a PBX is that a bimodal mixture of High melting explosive (HMX) crystals forms a skeletal matrix (the coarse particles) with a closely-packed configuration, with the fine crystallites of HMX (the fine particles) filled in the interstices between the large grains. Such a nesting mesoscale structure usually forms a “double peak” volume distribution of the explosive particles [18], which is difficult to be described by using an SU model, as is done for the quasi-brittle materials [15,16,17]. In the opinion of the present authors, such a nesting configuration may be described better by using a nesting ubiquitiform (NU) structure, one ubiquitiform nested in another, and the domains occupied by the two particle groups which are characterized, respectively, by two different SU models or sub-ubiquitiforms with different ubiquitiform complexities.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Ubiquitiformal Characterization of the Mesostructures of Polymer-Bonded Explosives

Duan

et al. 2019

Materials

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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.

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Section: Introductionmentioning

confidence: 70%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Ubiquitiformal Characterization of the Mesostructures of Polymer-Bonded Explosives

Duan

et al. 2019

Materials

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“…Essentially, the internal structure of complex materials has a certain regularity that can be described, that is, a certain form of regular or statistical self‐similarity. In addition, the macroscopic properties of materials can be determined by statistical parameters that have representative significance [51, 52]. It is worth noting that the nested ubiquitiform model of explosives was proposed by Ju et al.…”

Section: Introductionmentioning

confidence: 99%

Ubiquitiform Hotspot Ignition Model of PBX for Shock Initiation

Chun

Duan

et al. 2021

Propellants Explo Pyrotec

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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.

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“…In particular, a ubiquitiform has the same Hausdorff dimension as that of the initial element, which is always integral in practice, and a physical object in nature is a ubiquitiform. Recently, ubiquitiform has been applied successfully in the softening constitutive model of concrete (Ou et al, 2019), heat transfer in a bimaterial bar (Li et al, 2016), crack extension in concrete , and fracture energy of concrete .…”

Section: Introductionmentioning

confidence: 99%

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

Yang¹,

Duan³

et al. 2019

Journal of Theoretical and Applied Mechanics

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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.

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A Ubiquitiformal One-Dimensional Steady-State Conduction Model for a Cellular Material Rod

Cited by 12 publications

References 12 publications

The Ubiquitiformal Characterization of the Mesostructures of Polymer-Bonded Explosives

The Ubiquitiformal Characterization of the Mesostructures of Polymer-Bonded Explosives

Ubiquitiform Hotspot Ignition Model of PBX for Shock Initiation

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

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