Frequency domain homogenization for the viscoelastic properties of spatially correlated quasi-periodic lattices

Mukhopadhyay, T.; Adhikari, Sondipon; Batou, Anas

doi:10.1016/j.ijmecsci.2017.09.004

Cited by 58 publications

(28 citation statements)

References 80 publications

(64 reference statements)

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“…Therefore, the main contributing of this work lies in development of the analytical formulae for shear modulus of monoplanar and multiplanar hexagonal nanostructures and nano-heterostructures. In this context, it can be noted that the mechanics of honeycomb-like structural form is investigated extensively in micro and macro scales based on principles of structural mechanics [49][50][51][52][53][54][55].…”

Section: Shear Modulus Of Hexagonal Nanostructures and Heterostructuresmentioning

confidence: 99%

Probing the shear modulus of two-dimensional multiplanar nanostructures and heterostructures

et al. 2018

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Generalized high-fidelity closed-form formulae have been developed to predict the shear modulus of hexagonal graphene-like monolayer nanostructures and nano-heterostructures based on a physically insightful analytical approach. Hexagonal nano-structural forms (top view) are common for nanomaterials with monoplanar (such as graphene and hBN) and multiplanar (such as stanene and MoS) configurations. However, a single-layer nanomaterial may not possess a particular property adequately, or multiple desired properties simultaneously. Recently, a new trend has emerged to develop nano-heterostructures by assembling multiple monolayers of different nanostructures to achieve various tunable desired properties simultaneously. Shear modulus assumes an important role in characterizing the applicability of different two-dimensional nanomaterials and heterostructures in various nanoelectromechanical systems such as determining the resonance frequency of vibration modes involving torsion, wrinkling and rippling behavior of two-dimensional materials. We have developed mechanics-based closed-form formulae for the shear modulus of monolayer nanostructures and multi-layer nano-heterostructures. New results of shear modulus are presented for different classes of nanostructures (graphene, hBN, stanene and MoS) and nano-heterostructures (graphene-hBN, graphene-MoS, graphene-stanene and stanene-MoS), which are categorized on the basis of fundamental structural configurations. The numerical values of shear modulus are compared with the results from the scientific literature (as available) and separate molecular dynamics simulations, wherein a good agreement is noticed. The proposed analytical expressions will enable the scientific community to efficiently evaluate shear modulus of a wide range of nanostructures and nanoheterostructures.

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Section: Shear Modulus Of Hexagonal Nanostructures and Heterostructuresmentioning

confidence: 99%

Probing the shear modulus of two-dimensional multiplanar nanostructures and heterostructures

et al. 2018

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“…Wang et al [22] proposed the re-entrant star-shaped honeycomb, and studied the deformation modes under different impact velocities, and found that the structure exhibits excellent impact resistance with the same cell wall thickness compared with classical re-entrant honeycomb and star-shaped honeycomb. Mukhopadhyay et al [23,24] developed an analytical framework to predict the equivalent in-plane elastic moduli of irregular auxetic honeycombs and the effect of viscoelasticity on irregular hexagonal lattices.…”

Section: Introductionmentioning

confidence: 99%

In-plane crashworthiness of re-entrant hierarchical honeycombs with negative Poisson’s ratio

Tan

et al. 2019

Composite Structures

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Both auxetic structures and hierarchical honeycombs are marked with lightweight and excellent mechanical properties. Here, we combine the characteristics of auxetic structures and hierarchical honeycombs, and propose two re-entrant hierarchical honeycombs constructed by replacing the cell walls of re-entrant honeycombs with regular hexagon substructure (RHH) and equilateral triangle substructure (RHT). The honeycombs are subjected to in-plane impact in order to investigate the crashworthiness by using the commercial software LS-DYNA. The plateau stress of RHH and RHT in x and y directions are derived by a two-scale method. The results from numerical simulation indicate that the specific energy absorption of RHT and RHH is improved by up to 292% and 105%. RHT and RHH improve the mean crushing force value by 298%, 108% respectively compared with the classic re-entrant honeycomb (RH) under quasi-static loading at stress plateau region. The RHT and RHH still have the characteristic of negative Poisson's ratio. Additionally, the parametric studies are further carried out to investigate the effects of impact velocities and relative densities on crashworthiness. All the findings of this study indicate that the proposed two hierarchical honeycombs exhibit an improved crushing performance, and RHT provides the highest energy absorption capacity among all specimens.

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“…In case of mono‐planar structural configurations the atoms are placed in a single plane to form the lattice‐like forms (such as graphene and hBN), while the atoms are placed in multiple planes in multi‐planar 2D materials (such as stanene and MoS 2 ). The unit cell [ 49–52 ] of a 2D material lattice could either be formed using multiple atoms (such as hBN and MoS 2 ) or one single atom (such as graphene and stanene), based on which the 2D materials could further be classified to have heterogeneous and homogeneous atomic distribution, respectively. Depending on the mono or multi‐planar configuration and homogeneity or heterogeneity in the atomic distribution, the nanostructures of 2D materials can be classified into four different groups as shown in Figure 1A–D.…”

Section: Resultsmentioning

confidence: 99%

Probing the Effective Young's Modulus of ‘Magic Angle’ Inspired Multi‐Functional Twisted Nano‐Heterostructures

Mukhopadhyay

Mahata

Naskar

et al. 2020

Advcd Theory and Sims

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Two-dimensional (2D) materials are crucially important nanomaterials because of their exciting multi-functional properties. However, a single layer of 2D materials may not have a certain property adequately, or multiple application-specific properties simultaneously to the desired and optimal level. For mitigating this lacuna, a new trend has emerged recently to develop nano-scale engineered heterostructures by stacking multiple layers of different 2D materials, wherein each of the layers could also be twisted. The vast advantage of combining single layers of different 2D materials with different twisting angles has dramatically expanded this research field well beyond the scope of considering a 2D material mono-layer, leading to a set of multifunctional physical properties corresponding to each possible combination of number of layers, different 2D materials therein, stacking sequence and the twisting angle of each layer. Effective mechanical properties such as Young's moduli are generally of utmost importance for analyzing the viability of such engineered nano-heterostructures in various nanoelectromechanical applications. Efficient closed-form generic formulae are proposed for the effective Young's moduli of twisted multi-layer heterostructures. Based on this physics-based analytical approach, a wide range of insightful new results are presented for twisted heterostructures, covering mono-planar and multi-planar configurations with homogeneous and heterogeneous atomic distributions.

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Frequency domain homogenization for the viscoelastic properties of spatially correlated quasi-periodic lattices

Abstract: Frequency domain homogenization for the viscoelastic properties of spatially correlated quasi-periodic lattices,

Cited by 58 publications

References 80 publications

Probing the shear modulus of two-dimensional multiplanar nanostructures and heterostructures

Probing the shear modulus of two-dimensional multiplanar nanostructures and heterostructures

In-plane crashworthiness of re-entrant hierarchical honeycombs with negative Poisson’s ratio

Probing the Effective Young's Modulus of ‘Magic Angle’ Inspired Multi‐Functional Twisted Nano‐Heterostructures

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