Buckling of 2D nano hetero-structures with moire patterns

Moire pattern arises from the lattice mismatch between two different nanosheets. The discovery of the Moire pattern has resulted in breakthrough properties in 2D carbon-based nanostructures such as graphene. Here we investigate the impact of a Moire pattern on mechanical properties of bi-layer 2D nanosheets. In particular, buckling instability of 2D carbon-based nano hetero-structures is investigated using atomistic finite element approaches. Nano hetero-structures considered are graphene-hBN (hexagonal Boron Nitride) and graphene-MoS2 (Molybdenum disulphide). Bilayer graphene has also been considered in the buckling analysis, by orienting the individual sheets at moire angle. Atomistic simulation methodology uses elastic beams to represent intra-sheet atomic bonds and elastic springs to represent inter-sheet atomic interactions. The influence of different boundary conditions and sheet length on the buckling of nano hetero-structures has been investigated. The bridged nano hetero-structures are found be displaying higher buckling strength as compared to cantilever sheets

Thermal uncertainty quantification in frequency responses of laminated composite plates

The propagation of thermal uncertainty in composite structures has significant computational challenges. This paper presents the thermal, ply-level and material uncertainty propagation in frequency responses of laminated composite plates by employing surrogate model which is capable of dealing with both correlated and uncorrelated input parameters. The present approach introduces the generalized high dimensional model representation (GHDMR) wherein diffeomorphic modulation under observable response preserving homotopy (D-MORPH) regression is utilized to ensure the hierarchical orthogonality of high dimensional model representation component functions. The stochastic range of thermal field includes elevated temperatures up to 375 K and sub-zero temperatures up to cryogenic range of 125 K. Statistical analysis of the first three natural frequencies is presented to illustrate the results and its performance

Nonlocal Mechanics Based Computational Methods for Nano-mechanical Sensors (Keynote Address)

AbstractTechnology behind nano-scale mass sensor has been growing rapidly in the recent years. This paper outlines a non-local mechanics based computational approach by which using the frequency-shift of the fundamental vibration mode the mass on an attached object can be predicted. We develop new nonlocal frequency sensor equations utilizing energy principles. Two physically realistic configurations of the added mass, namely, point mass and distributed masses are considered. Exact closed-form expressions relating the frequency-shift and the added mass have been derived for both the cases. The proposed nonlocal sensor-equation is general in nature and depends on three non-dimensional calibrations constants namely, the stiffness calibration constant, the mass calibration constant and the nonlocal calibration constant. Explicit analytical expressions of these calibration constants are derived. An example of a single wall carbon nanotube with attached multiple strands of deoxythimidine is considered to illustrate the analytical results. Molecular mechanics simulation is used to validate the new nonlocal sensor equations. The optimal values of nonlocal parameter are obtained from the molecular mechanics simulation results. The nonlocal approach generally predicts the frequency shift accurately compared to the local approach. Numerical results show the importance of considering the distributed nature of the added mass while using the nonlocal theory

Inertial mass sensing with low Q-factor vibrating microcantilevers

Mass sensing using micromechanical cantilever oscillators has been established as a promising approach. The scientific principle underpinning this technique is the shift in the resonance frequency caused by the additional mass in the dynamic system. This approach relies on the fact that the Q-factor of the underlying oscillator is high enough so that it does not significantly affect the resonance frequencies. We consider the case when the Q-factor is low to the extent that the effect of damping is prominent. It is shown that the mass sensing can be achieved using a shift in the damping factor. We prove that the shift in the damping factor is of the same order as that of the resonance frequency. Based on this crucial observation, three new approaches have been proposed, namely, (a) mass sensing using frequency shifts in the complex plane, (b) mass sensing from damped free vibration response in the time domain, and (c) mass sensing from the steady-state response in the frequency domain. Explicit closed-form expressions relating absorbed mass with changes in the measured dynamic properties have been derived. The rationale behind each new method has been explained using non-dimensional graphical illustrations. The new mass sensing approaches using damped dynamic characteristics can expand the current horizon of micromechanical sensing by incorporating a wide range of additional measurements

Voltage-dependent modulation of elastic moduli in lattice metamaterials: Emergence of a programmable state-transition capability

Two-dimensional lattices are ideal candidate for developing artificially engineered materials and structures across different length-scales, leading to unprecedented multi-functional mechanical properties which can not be achieved in naturally occurring materials and systems. Characterization of effective elastic properties of these lattices is essential for their adoption as structural elements of various devices and systems. An enormous amount of research has been conducted on different geometry of lattices to identify and characterize various parameters which affect the elastic properties. However, till date we can not control the elastic properties actively for a lattice microstructure, meaning that the elastic properties of such lattices are not truly programmable. All the parameters that control the effective elastic properties are passive in nature. After manufacturing the lattice structure with a certain set of geometric or material-based parameters, there is no room to modulate the properties further. In this article, we propose a hybrid lattice micro-structure by integrating piezo-electric materials with the members of the lattice for active voltage-dependent modulation of elastic properties. A bottom-up multi-physics based analytical framework leading to closed-form formulae is derived for hexagonal lattices to demonstrate the concept of active lattices. It is noticed that the Young’s moduli are voltage-dependent, while the shear modulus and the Poisson’s ratios are not functions of the applied voltage. Thus, the compound mechanics of deformation induced by external mechanical stresses and electric field lead to an active control over the Young’s moduli as a function of voltage. Interestingly, it turns out that a programmable state-transition of the Young’s moduli from positive to negative values with a wide range can be achieved in such hybrid lattices. The physics-based analytical framework for active modulation of voltage-dependent elastic properties on the basis of operational demands provide the necessary physical insights and confidence for potential practical exploitation of the proposed concept in various futuristic multi-functional structural systems and devices across different length-scales

Equivalent in-plane elastic properties of irregular honeycombs: An analytical approach

An analytical formulation has been developed in this article for predicting the equivalent elastic properties of irregular honeycombs with spatially random variations in cell angles. Employing unit-cell based approaches, closed-form expressions of equivalent elastic properties of regular honeycombs are available. Closed-form expressions for equivalent elastic properties of irregular honeycombs are very scarce in available literature. In general, direct numerical simulation based methods are prevalent for this case. This paper proposes a novel analytical framework for predicting equivalent in-plane elastic moduli of irregular honeycombs using a representative unit cell element (RUCE) approach. Using this approach, closed-form expressions of equivalent in-plane elastic moduli (longitudinal and transverse Young’s modulus, shear modulus, Poisson’s ratios) have been derived. The expressions of longitudinal Young’s modulus, transverse Young’s modulus, and shear modulus are functions of both structural geometry and material properties of irregular honeycombs, while the Poisson’s ratios depend only on structural geometry of irregular honeycombs. The elastic moduli obtained for different degree of randomness following the proposed analytical approach are found to have close proximity to direct finite element simulation results

Modeling Spatially Varying Uncertainty in Composite Structures Using Lamination Parameters

An approach is presented for modeling spatially varying uncertainty in the ply orientations of composite structures. Lamination parameters are used with the aim of reducing the required number of random variables. Karhunen–Loève expansion is employed to decompose the uncertainty in each ply into a sum of random variables and spatially dependent functions. An intrusive polynomial chaos expansion is proposed to approximate the lamination parameters while preserving the separation of the random and spatial dependency. Closed-form expressions are derived for the expansion coefficients in two case studies; an initial example in which uncertainty is modeled using random variables, and a second random field example. The approach is compared against Monte Carlo simulation results for a variety of layups as well as closed-form expressions for the mean and covariance. By summing the polynomial chaos basis functions through the laminate thickness, the separation of the random and spatial dependency may be preserved at a laminate level and the number of random variables reduced for some minimum number of plies. The number of variables increases nonlinearly with the number of Karhunen–Loève expansion terms, and as such, the approach is only beneficial in low-order expansions using relatively few Karhunen–Loève expansion terms