An atomistic-based Föppl–von Kármán model for graphene

Davini, Cesare; Favata, Antonino; Paroni, Roberto

doi:10.1016/j.ijnonlinmec.2019.07.011

Cited by 5 publications

(1 citation statement)

References 38 publications

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“…Here, we use the Föppl-von Karman approach by introducing some novelty elements: first, we apply the macroscopic elastic model to the relatively new context of nanoscale deformations of ultrathin shells of 2D materials (MoS 2 bulged domes). [55][56][57] Second, we consider a modified formulation of the Föppl-von Karman equation (in the membrane limit), including the action of two loading forces: the internal gas pressure and the local indentation force. [54,57] Finally, we apply the Föppl-von Karman theoretical formulation to interpret the findings of AFM nanoindentation experiments on two different systems, i.e., the spontaneously formed and the engineered clamped domes.…”

Section: Introductionmentioning

confidence: 99%

Nanoscale Measurements of Elastic Properties and Hydrostatic Pressure in H₂‐Bulged MoS₂ Membranes

Giorgio

Blundo

Pettinari

et al. 2020

Adv Materials Inter

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defects, and intercalations, [14-18] charge carrier doping, [19-21] charge transfer, [22,23] and pressure. [24] In addition to this, due to its intrinsic atomically smooth surface, it has been regarded as an ideal barrier for tunneling junctions. [25] Single-layer MoS 2 has been theoretically predicted to withstand a critical intrinsic stress and strain of σ c ≈ 24GPa and ε c ≈ 20% for biaxial tensile deformations (and higher for uniaxial), by employing first-principle calculations and investigating the stress-strain (σ − ε) relations up to the failure point. [26,27] On the other hand, experimental estimates of ε c in MoS 2 sheets subjected to nanoindentation (which has the effect of a biaxial tensile stress), lead to lower values, ε c = 6%-13%, [27,28] for measured σ c close to the expected one. The discrepancy in the experimental value of ε c is caused by the use of a linear σ − ε relation, σ = Yε, where Y is the material Young's modulus, in a no-longer linear regime (close to the breaking point). Recently, the excellent robustness and flexibility of MoS 2 and other 2D crystals has led to a keen interest into 2D-material-blisters, such as bubbles, wrinkles, and tents. Their spontaneous formation has been observed after transferring 2D materials on top of a substrate, or on stacks of van der Waals (vdW) heterostructures, and it has been attributed to the trapping of adsorbed water and/or hydrocarbons inevitably present on the individual layers before assembly. [29-31] Moreover, The combination of extremely high stiffness and bending flexibility with tunable electrical and optical properties makes van der Waals transition metal dichalcogenides appealing both for fundamental science and applied research. By taking advantage of localized H 2-bulged MoS 2 membranes, an innovative approach, based on atomic force microscopy nanoindentation, is demostrated and discussed here, aiming at measuring elastic and thermodynamic properties of nanoblisters made of 2D materials. The results, interpreted in the membrane limit of the Föppl-von Karman equation, lead to the quantification of the internal pressure and mole number of the trapped H 2 gas, as well as of the stretching modulus and adhesion energy of the MoS 2 membrane. The latter is discussed in the limit of strong (clamped and fully bonded interlayer interface) shear, as experimentally achieved in the investigated H 2-bulged 2D blisters. Moreover, this approach allows to quantify the stress, and consequently the strain, locally imposed to the MoS 2 membrane by the bulging of the domes.

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Section: Introductionmentioning

confidence: 99%

Nanoscale Measurements of Elastic Properties and Hydrostatic Pressure in H₂‐Bulged MoS₂ Membranes

Giorgio

Blundo

Pettinari

et al. 2020

Adv Materials Inter

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A mixed variational principle for the Föppl–von Kármán equations

Brunetti

Favata

Paolone

et al. 2020

Applied Mathematical Modelling

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Foreword to the special issue “Mathematics & Mechanics: Natural Philosophy in the 21st Century”

Saccomandi

Schlömerkemper

Tomassetti

2020

International Journal of Non-Linear Mechanics

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An atomistic-based Föppl–von Kármán model for graphene

Cited by 5 publications

References 38 publications

Nanoscale Measurements of Elastic Properties and Hydrostatic Pressure in H₂‐Bulged MoS₂ Membranes

Nanoscale Measurements of Elastic Properties and Hydrostatic Pressure in H₂‐Bulged MoS₂ Membranes

A mixed variational principle for the Föppl–von Kármán equations

Foreword to the special issue “Mathematics & Mechanics: Natural Philosophy in the 21st Century”

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An atomistic-based Föppl–von Kármán model for graphene

Cited by 5 publications

References 38 publications

Nanoscale Measurements of Elastic Properties and Hydrostatic Pressure in H2‐Bulged MoS2 Membranes

Nanoscale Measurements of Elastic Properties and Hydrostatic Pressure in H2‐Bulged MoS2 Membranes

A mixed variational principle for the Föppl–von Kármán equations

Foreword to the special issue “Mathematics & Mechanics: Natural Philosophy in the 21st Century”

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Nanoscale Measurements of Elastic Properties and Hydrostatic Pressure in H₂‐Bulged MoS₂ Membranes

Nanoscale Measurements of Elastic Properties and Hydrostatic Pressure in H₂‐Bulged MoS₂ Membranes