The review of the bond-based peridynamics modeling

2019 ◽  
Vol 04 (01) ◽  
pp. 1830001 ◽  
Author(s):  
Duanfeng Han ◽  
Yiheng Zhang ◽  
Qing Wang ◽  
Wei Lu ◽  
Bin Jia

Peridynamics theory is a nonlocal meshless method that replaces differential equations with spatial integral equations, and has shown good applicability and reliability in the analysis of discontinuities. Further, with characteristics of clear physical meaning and simple and reliable numerical calculation, the bond-based peridynamics method has been widely applied in the field. However, this method describes the interaction between material points simply using a single elastic “spring”, and thus leads to a fixed Poisson’s ratio, relatively low computational efficiency and other inherent problems. As such, the goal of this review paper is to provide a summary of the various methods of bond-based peridynamics modeling, particularly those that have overcome the limitations of the Poisson’s ratio, considered the shear deformation and modeling of two-dimensional thin plates for bending and three-dimensional anisotropic composites, as well as explored coupling with finite element methods. This review will determine the advantages and disadvantages of such methods and serve as a starting point for researchers in the development of peridynamics theory.

Materials ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 2193 ◽  
Author(s):  
Krzysztof K. Dudek ◽  
Daphne Attard ◽  
Ruben Gatt ◽  
James N. Grima-Cornish ◽  
Joseph N. Grima

In this work, through the use of a theoretical model, we analyse the potential of a specific three-dimensional mechanical metamaterial composed of arrowhead-like structural units to exhibit a negative Poisson’s ratio for an arbitrary loading direction. Said analysis allows us to assess its suitability for use in applications where materials must be able to respond in a desired manner to a stimulus applied in multiple directions. As a result of our studies, we show that the analysed system is capable of exhibiting auxetic behaviour for a broad range of loading directions, with isotropic behaviour being shown in some planes. In addition to that, we show that there are also certain loading directions in which the system manifests negative linear compressibility. This enhances its versatility and suitability for a number of applications where materials exhibiting auxetic behaviour or negative linear compressibility are normally implemented.


2020 ◽  
Vol 8 (44) ◽  
pp. 15771-15777
Author(s):  
Kashif Hussain ◽  
Umer Younis ◽  
Imran Muhammad ◽  
Yu Qie ◽  
Yaguang Guo ◽  
...  

Motivated by the recent synthesis of three-dimensional (3D) porous borocarbonitride (Angew. Chem., Int. Ed., 2019, 58, 6033–6037), we propose a porous 3D-BC2N structure composed of BC2N nanoribbons.


2019 ◽  
Vol 90 (5-6) ◽  
pp. 617-630
Author(s):  
Kun Luan ◽  
Andre West ◽  
Emiel DenHartog ◽  
Marian McCord

Negative Poisson’s ratio (NPR) material with unique geometry is rare in nature and has an auxetic response under strain in a specific direction. With this unique property, this type of material is significantly promising in many specific application fields. The curling structure commonly exists in knitted products due to the unbalanced force inside a knit loop. Thus, knitted fabric is an ideal candidate to mimic natural NPR materials, since it possesses such an inherent curly configuration and the flexibility to design and process. In this work, a weft-knitted Miura-ori fold (WMF) fabric was produced that creates a self-folding three-dimensional structure with NPR performance. Also, a finite element analysis model was developed to simulate the structural auxetic response to understand the deformation mechanism of hierarchical thread-based auxetic fabrics. The simulated strain–force curves of four WMF fabrics quantitatively agree with our experimental results. The auxetic morphologies, Poisson’s ratio and damping capacity were discussed, revealing the deformation mechanism of the WMF fabrics. This study thus provides a fundamental framework for mechanical-stimulating textiles. The developed NPR knitted fabrics have a high potential to be employed in areas of tissue engineering, such as artificial blood vessels and artificial folding mucosa.


Recent results of theoretical and practical importance prove that the two-dimensional (in-plane) effective (average) Young’s modulus for an isotropic elastic material containing voids is independent of the Poisson’s ratio of the matrix material. This result is true regardless of the shape and morphology of the voids so long as isotropy is maintained. The present work uses this proof to obtain explicit analytical forms for the effective Young’s modulus property, forms which simplify greatly because of this characteristic. In some cases, the optimal morphology for the voids can be identified, giving the shapes of the voids, at fixed volume, that maximize the effective Young’s modulus in the two-dimensional situation. Recognizing that two-dimensional isotropy is a subset of three-dimensional transversely isotropic media, it is shown in this more general case that three of the five properties are independent of Poisson’s ratio, leaving only two that depend upon it. For three-dimensionally isotropic composite media containing voids, it is shown that a somewhat comparable situation exists whereby the three-dimensional Young’s modulus is insensitive to variations in Poisson’s ratio, v m , over the range 0 ≤ v m ≤ ½, although the same is not true for negative values of v m . This further extends the practical usefulness of the two-dimensional result to three-dimensional conditions for realistic values of v m .


2016 ◽  
Vol 25 (5) ◽  
pp. 054005 ◽  
Author(s):  
Chan Soo Ha ◽  
Michael E Plesha ◽  
Roderic S Lakes

Author(s):  
ChunYan Wang ◽  
SongChun Zou ◽  
WanZhong Zhao

The crash box can absorb energy from the beam as much as possible, so as to reduce the collision damage to the front part of the car body and protect the safety of passengers. This work proposes a novel crash box filled with a three-dimensional negative Poisson’s ratio (NPR) inner core based on an inner hexagonal cellular structure. In order to optimize and improve the crash box’s energy absorption performance, the multi-objective optimization model of the NPR crash box is established, which combines the optimal Latin hypercube design method and response surface methodology. Then, the microstructure parameters are further optimized by the multi-objective particle swarm optimization algorithm to obtain an excellent energy absorption effect. The simulation results show that the proposed NPR crash box can generate smooth and controllable deformation to absorb the total energy, and it can further enhance the crashworthiness through the designed optimization algorithm.


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