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

Yang, Min; Ou, Zhuo-Cheng; Duan, Zhuo-Ping; Huang, Fenglei

doi:10.15632/jtam-pl/104510

Cited by 4 publications

(2 citation statements)

References 15 publications

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“…The ubiquitiform, defined as a self-similar or self-affine structure with finite levels generated by a finite number of iterations under specific rules, has since been applied to various fields [28]. These include characterizing the equivalent elastic modulus of bimaterial bars [29], modeling one-dimensional steady-state conduction in cellular material rods [30], studying concrete softening behavior [31,32], researching material fracture energy parameters [33], crack propagation in quasi-brittle materials [34], and mesostructural characterization of polymer-bonded explosives [35]. Furthermore, the drawbacks of the fractal modeling approach have become increasingly apparent, particularly regarding fractal measurement.…”

Section: Introductionmentioning

confidence: 99%

A Novel Contact Stiffness Model for Grinding Joint Surface Based on the Generalized Ubiquitiformal Sierpinski Carpet Theory

An,

Liu,

Huang

et al. 2024

Fractal Fract

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A novel analytical model based on the generalized ubiquitiformal Sierpinski carpet is proposed which can more accurately obtain the normal contact stiffness of the grinding joint surface. Firstly, the profile and the distribution of asperities on the grinding surface are characterized. Then, based on the generalized ubiquitiformal Sierpinski carpet, the contact characterization of the grinding joint surface is realized. Secondly, a contact mechanics analysis of the asperities on the grinding surface is carried out. The analytical expressions for contact stiffness in various deformation stages are derived, culminating in the establishment of a comprehensive analytical model for the grinding joint surface. Subsequently, a comparative analysis is conducted between the outcomes of the presented model, the KE model, and experimental data. The findings reveal that, under identical contact pressure conditions, the results obtained from the presented model exhibit a closer alignment with experimental observations compared to the KE model. With an increase in contact pressure, the relative error of the presented model shows a trend of first increasing and then decreasing, while the KE model has a trend of increasing. For the relative error values of the four surfaces under different contact pressures, the maximum relative error of the presented model is 5.44%, while the KE model is 22.99%. The presented model can lay a solid theoretical foundation for the optimization design of high-precision machine tools and provide a scientific theoretical basis for the performance analysis of machine tool systems.

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Section: Introductionmentioning

confidence: 99%

A Novel Contact Stiffness Model for Grinding Joint Surface Based on the Generalized Ubiquitiformal Sierpinski Carpet Theory

An,

Liu,

Huang

et al. 2024

Fractal Fract

View full text Add to dashboard Cite

show abstract

“…The ubiquitiform was defined as a self-similar or self-affine structure with finite levels, which can usually be generated by a finite number of iterations under some given generation rule. Subsequently, the ubiquitiform theory has been applied to the equivalent elastic modulus characterization for a bimaterial bar [38], the one-dimensional steady-state conduction model for a cellular material rod [39], the softening behavior for concrete [40,41], and the research of parameters for material fracture energy characterization [42], the crack propagation in quasi-brittle materials [43], and the mesostructural characterization of polymer-bonded explosives [44]. Relevant scholars have introduced the concept of ubiquitiform theory into the analysis of contact characteristics of rough joint surfaces.…”

Section: Introductionmentioning

confidence: 99%

A Novel Modeling Method of Micro-Topography for Grinding Surface Based on Ubiquitiform Theory

Liu

Huang

et al. 2022

Fractal Fract

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In order to simulate the grinding surface more accurately, a novel modeling method is proposed based on the ubiquitiform theory. Combined with the power spectral density (PSD) analysis of the measured surface, the anisotropic characteristics of the grinding surface are verified. Based on the isotropic fractal Weierstrass–Mandbrot (W-M) function, the expression of the anisotropic fractal surface is derived. Then, the lower bound of scale invariance δmin is introduced into the anisotropic fractal, and an anisotropic W-M function with ubiquitiformal properties is constructed. After that, the influence law of the δmin on the roughness parameters is discussed, and the δmin for modeling the grinding surface is determined to be 10−8 m. When δmin = 10−8 m, the maximum relative errors of Sa, Sq, Ssk, and Sku of the four surfaces are 5.98%, 6.06%, 5.77%, and 4.53%, respectively. In addition, the relative errors of roughness parameters under the fractal method and the ubiquitiformal method are compared. The comparison results show that the relative errors of Sa, Sq, Ssk, and Sku under the ubiquitiformal modeling method are 5.36%, 6.06%, 5.84%, and 4.53%, while the maximum relative errors under the fractal modeling method are 23.21%, 7.03%, 83.10%, and 7.25%. The comparison results verified the accuracy of the modeling method in this paper.

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Experimental investigation on brittleness characteristics of rock based on the ubiquitiformal complexity: strain rate effect and size effect

Yang

Wang

et al. 2023

Bull Eng Geol Environ

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

Cited by 4 publications

References 15 publications

A Novel Contact Stiffness Model for Grinding Joint Surface Based on the Generalized Ubiquitiformal Sierpinski Carpet Theory

A Novel Contact Stiffness Model for Grinding Joint Surface Based on the Generalized Ubiquitiformal Sierpinski Carpet Theory

A Novel Modeling Method of Micro-Topography for Grinding Surface Based on Ubiquitiform Theory

Experimental investigation on brittleness characteristics of rock based on the ubiquitiformal complexity: strain rate effect and size effect

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