Effective in-plane elastic moduli of quasi-random spatially irregular hexagonal lattices

Abstract

An analytical framework is developed for predicting the eective in-plane elastic moduli (longitudinal and transverse Young's modulus, Poisson's ratios and shear modulus) of irregular hexagonal lattices with generalized form of spatially random structural geometry. On the basis of a mechanics based bottom-up multi-step approach, computationally ecient closed-form formulae are derived in this article. As a special case when there is no irregularity, the derived analytical expressions reduce to the respective well known formulae of regular honeycombs available in literature. Previous analytical investigations include the derivation of eective in-plane elastic moduli for hexagonal lattices with spatially random variation of cell angles, which is a special case of the generalized form of irregularity in material and structural attributes considered in this paper. The present study also includes development of a highly generalized nite element code for obtaining equivalent elastic properties of random lattices, which is employed to validate the proposed analytical formulae. The statistical results of elastic moduli obtained using the developed analytical expressions and using direct nite element simulations are noticed to be in good agreement arming the accuracy and validity of the proposed analytical framework. All the in-plane elastic moduli are found to be signicantly inuenced by spatially random irregularity resulting in a decrease of the mean values for the two Young's moduli and two Poisson's ratios, while an increase of the mean value for the shear modulus.

Design and Optimization Lattice Endoprosthesis for Long Bones: Manufacturing and Clinical Experiment

“…), different forces act on the bone. Hexagonal bipyramid was chosen for an elementary cell of the lattice endoprosthesis [7,10]. Such geometry allows containing a sufficient amount of bone material, which potentially can improve bone tissue growth [13,22,23].…”

“…However, problems appear because of melting: A manifestation of brittle properties and geometry deviations [4][5][6][7]. Different materials and melting modes are investigated to improve the quality of constructions [8][9][10]. Nowadays there are papers with a wide review focuses on three-dimensional-printed technics and related composite systems were performed [11].…”

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

“…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].…”

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

“…The elastic moduli with spatially random structural and material attributes have been derived in a previous paper (Mukhopadhyay and Adhikari, 2017a) which correspond to a generalization of the elastic moduli for perfectly periodic lattices (Gibson and Ashby, 1999), are given below:…”

“…In the present analysis of spatially irregular lattices with spatially varying viscoelastic properties, the scheme for introducing structural irregularity is explained in figure 1(a), where it can be noticed that each node of a regular lattice is simultaneously perturbed with a certain bound (defined by degree of irregularity) for each of the realizations (Mukhopadhyay and Adhikari, 2017a).…”