This paper presents a concise state-of-the-art review along with an exhaustive comparative investigation on surrogate models for critical comparative assessment of uncertainty in natural frequencies of composite plates on the basis of computational efficiency and accuracy. Both individual and combined variations of input parameters have been considered to account for the effect of low and high dimensional input parameter spaces in the surrogate based uncertainty quantification algorithms including the rate of convergence. Probabilistic characterization of the first three stochastic natural frequencies is carried out by using a finite element model that includes the effects of transverse shear deformation based on Mindlin's theory in conjunction with a layer-wise random variable approach. The results obtained by different metamodels have been compared with the results of traditional Monte Carlo simulation (MCS) method for high fidelity uncertainty quantification. The crucial issue regarding influence of sampling techniques on the performance of metamodel based uncertainty quantification has been addressed as an integral part of this article.

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A generalized analytical approach is presented to derive closed-form formulae for the elastic moduli of hexagonal multiplanar nano-structures. Hexagonal nano-structural forms are common for various materials. Four dierent classes of materials (single layer) from a structural point of view are proposed to demonstrate the validity and prospective application of the developed formulae. For example, graphene, an allotrope of carbon, consists of only carbon atoms to form a honeycomb like hexagonal lattice in a single plane, while hexagonal boron nitride (hBN) consists of boron and nitrogen atoms to form the hexagonal lattice in a single plane. Unlike graphene and hBN, there are plenty of other materials with hexagonal nano-structures that have the atoms placed in multiple planes such as stanene (consists of only Sn atoms) and molybdenum disulde (consists of two dierent atoms: Mo and S). The physics based high-delity analytical model developed in this article are capable of obtaining the elastic properties in a computationally ecient manner for wide range of such materials with hexagonal nano-structures that are broadly classied in four classes from structural viewpoint. Results are provided for materials belonging to all the four classes, wherein a good agreement between the elastic moduli obtained using the proposed formulae and available scientic literature is observed.

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights • Equivalent elastic moduli of irregular auxetic honeycombs are analysed. • Closed-form analytical formulae are presented. • Spatially random cell angles have been considered.

This paper develops an origami based mechanical metamaterial with programmable deformationdependent stiffness and shape modulation, leading to the realization of a distant actuation feature.Through computational and experimental analyses, we have uncovered that a waterbomb based tubular metamaterial can undergo mixed mode of deformations involving both rigid origami motion and structural deformation. Besides the capability of achieving a near-zero stiffness, a contact phase is identified that initiates a substantial increase in the stiffness with programmable features during deformation of the metamaterial. Initiation of the contact phase as a function of the applied global load can be designed based on the microstructural geometry of the waterbomb bases and their assembly. The tubular metamaterial can exhibit a unique deformation dependent spatially varying mixed mode Poisson's ratio, which is achievable from a uniform initial configuration of the metamaterial. The spatial profile of the metamaterial can be modulated as a function of the applied far-field global force, and the configuration and assembly of the waterbomb bases. This creates a new possibility of developing a distant actuation feature in the metamaterial enabling us to achieve controlled local actuation through the application of a single far-field force. The distant actuation feature eliminates the need of installing embedded complex network of sensors, actuators and controllers in the material. The fundamental programmable features of the origami metamaterial unravelled in this paper can find wide range of applications in soft robotics, aerospace, biomedical devices and various other advanced physical systems.

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The eect of stochasticity in mechanical behaviour of metamaterials is quantied in a probabilistic framework. The stochasticity has been accounted in the form of random material distribution and structural irregularity, which are often encountered due to manufacturing and operational uncertainties. An analytical framework has been developed for analysing the eective stochastic in-plane elastic properties of irregular hexagonal structural forms with spatially random variations of cell angles and intrinsic material properties. Probabilistic distributions of the in-plane elastic moduli have been presented considering both randomly homogeneous and randomly inhomogeneous stochasticity in the system, followed by an insightful comparative discussion. The ergodic behaviour in spatially irregular lattices is investigated as a part of this study. It is found that the eect of random micro-structural variability in structural and material distribution has considerable inuence on mechanical behaviour of metamaterials.