Broadband dynamic elastic moduli of honeycomb lattice materials: A generalized analytical approach

Adhikari, Sondipon; Mukhopadhyay, T.; Liu, X.

doi:10.1016/j.mechmat.2021.103796

Cited by 45 publications

(24 citation statements)

References 56 publications

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“…For the considered 3DCDL‐type unit cells,

υ_{z x}

can further be obtained using the same

{normalΦ}_{i}

as discussed in this section (refer to Section 6 of Supporting Information). Subsequently, based on the reciprocal theorems

E_{z} υ_{x z} = E_{x} υ_{z x}

and

E_{x} υ_{y x} = E_{y} υ_{x y}

, [ 84 ] it is further possible to get the expressions for

E_{x}

and

υ_{y x}

, respectively. Thus, we focus on

υ_{x z}

υ_{y z}

, and

E_{z}

(refer to Equations ()–()) in this article for presenting the analytical expressions and numerical results.…”

Section: Mixed‐mode Multidirectional Auxeticitymentioning

confidence: 99%

Mixed‐Mode Multidirectional Poisson's Ratio Modulation in Auxetic 3D Lattice Metamaterials

Mukhopadhyay

Kundu

2022

Adv Eng Mater

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If a conventional material is compressed in one direction, it tries to expand in the other two perpendicular directions and vice versa, indicating a positive Poisson's ratio. Recently auxetic materials with negative Poisson's ratios, which can be realized through artificial microstructuring, are attracting increasing attention due to enhanced mechanical performances in multiple applications. Most of the proposed auxetic materials show different degrees of in‐plane auxeticity depending on their microstructural configurations. However, this restricts harnessing the advantages of auxeticity in 3D systems and devices where multidirectional functionalities are warranted. Thus, there exists a strong rationale to develop microstructures that can exhibit auxeticity both in the in‐plane and out‐of‐plane directions. Herein, generic 3D connected double loop (3DCDL) type periodic microstructures are proposed for multi‐directional modulation of Poisson's ratios. Based on the bending dominated behavior of elementary beams with variable curvature, mixed‐mode auxeticity following the framework of multimaterial unit cells is demonstrated. The proposed 3DCDL unit cell and expanded unit cells formed based on their clusters are capable of achieving partially auxetic, purely auxetic, purely nonauxetic and nullauxetic behavior. Comprehensive numerical results are presented for the entire spectrum of combinations concerning the auxetic behavior in the in‐plane and out‐of‐plane directions including their relative degrees.

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“…For the considered 3DCDL‐type unit cells,

υ_{z x}

can further be obtained using the same

{normalΦ}_{i}

as discussed in this section (refer to Section 6 of Supporting Information). Subsequently, based on the reciprocal theorems

E_{z} υ_{x z} = E_{x} υ_{z x}

and

E_{x} υ_{y x} = E_{y} υ_{x y}

, [ 84 ] it is further possible to get the expressions for

E_{x}

and

υ_{y x}

, respectively. Thus, we focus on

υ_{x z}

υ_{y z}

, and

E_{z}

(refer to Equations ()–()) in this article for presenting the analytical expressions and numerical results.…”

Section: Mixed‐mode Multidirectional Auxeticitymentioning

confidence: 99%

Mixed‐Mode Multidirectional Poisson's Ratio Modulation in Auxetic 3D Lattice Metamaterials

Mukhopadhyay

Kundu

2022

Adv Eng Mater

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“…Some researchers [ 119 , 120 , 121 , 122 , 123 , 124 ] established 2D multi-cell models to investigate the mechanical properties of cellular media, as shown in Figure 7 . Sun [ 120 ] thought that entrapped gas hardly affects plateau stress, but it did affect the deformation modes.…”

Section: Microstructure Mechanical Models Of Cellular Mediummentioning

confidence: 99%

“…Mukhopadhyay [ 122 , 123 , 124 ] investigated the mechanical properties (Young’s modulus, Poisson’s ratio, and shear modulus) of 2D honeycomb material based on a regular hexagon-cell model and irregular hexagon-cell model. They considered the viscoelasticity and the irregularity of the model, and found that the Young’s modulus and shear modulus depend on the viscoelastic parameters, while the Poisson’s ratio was independent on the viscoelastic parameters and frequency.…”

Section: Microstructure Mechanical Models Of Cellular Mediummentioning

confidence: 99%

A Review on Mechanical Models for Cellular Media: Investigation on Material Characterization and Numerical Simulation

et al. 2021

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Cellular media materials are used for automobiles, aircrafts, energy-efficient buildings, transportation, and other fields due to their light weight, designability, and good impact resistance. To devise a buffer structure reasonably and avoid resource and economic loss, it is necessary to completely comprehend the constitutive relationship of the buffer structure. This paper introduces the progress on research of the mechanical properties characterization, constitutive equations, and numerical simulation of porous structures. Currently, various methods can be used to construct cellular media mechanical models including simplified phenomenological constitutive models, homogenization algorithm models, single cell models, and multi-cell models. This paper reviews current key mechanical models for cellular media, attempting to track their evolution from their inception to their latest development. These models are categorized in terms of their mechanical modeling methods. This paper focuses on the importance of constitutive relationships and microstructure models in studying mechanical properties and optimizing structural design. The key issues concerning this topic and future directions for research are also discussed.

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“…It has been found that by varying one or more material constants such as, bulk modulus, shear modulus, Poisson's ratio and elastic modulus, extraordinary materials such as, ultra light weight and high strength aerospace shells, functionally graded electromagnetic sensors and energy absorbing dampers can be secured 5,6 .For exploring such exciting possibilities of discovering new materials with extreme properties, determining their optimal configuration at the very conceptual micro-structural design stage is indispensable 7 . A recent works with multi-material lattices 8 , pre-stressed materials 9 and piezo-embedded damped lattice metamaterials 10,11 show some ways of achieving extreme homogeneous properties. In this scenario, topology optimization (TO) is well-known to be an effective computational analysis tool which renders greater design freedom and yields the best material layout given a prescribed design domain and boundary condition 12 .…”

mentioning

confidence: 99%

“…For exploring such exciting possibilities of discovering new materials with extreme properties, determining their optimal configuration at the very conceptual micro-structural design stage is indispensable 7 . A recent works with multi-material lattices 8 , pre-stressed materials 9 and piezo-embedded damped lattice metamaterials 10,11 show some ways of achieving extreme homogeneous properties. In this scenario, topology optimization (TO) is well-known to be an effective computational analysis tool which renders greater design freedom and yields the best material layout given a prescribed design domain and boundary condition 12 .…”

mentioning

confidence: 99%

Robust topological designs for extreme metamaterial micro-structures

Chatterjee

Chakraborty

Goswami

et al. 2021

Sci Rep

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We demonstrate that the consideration of material uncertainty can dramatically impact the optimal topological micro-structural configuration of mechanical metamaterials. The robust optimization problem is formulated in such a way that it facilitates the emergence of extreme mechanical properties of metamaterials. The algorithm is based on the bi-directional evolutionary topology optimization and energy-based homogenization approach. To simulate additive manufacturing uncertainty, combinations of spatial variation of the elastic modulus and/or, parametric variation of the Poisson’s ratio at the unit cell level are considered. Computationally parallel Monte Carlo simulations are performed to quantify the effect of input material uncertainty to the mechanical properties of interest. Results are shown for four configurations of extreme mechanical properties: (1) maximum bulk modulus (2) maximum shear modulus (3) minimum negative Poisson’s ratio (auxetic metamaterial) and (4) maximum equivalent elastic modulus. The study illustrates the importance of considering uncertainty for topology optimization of metamaterials with extreme mechanical performance. The results reveal that robust design leads to improvement in terms of (1) optimal mean performance (2) least sensitive design, and (3) elastic properties of the metamaterials compared to the corresponding deterministic design. Many interesting topological patterns have been obtained for guiding the extreme material robust design.

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Broadband dynamic elastic moduli of honeycomb lattice materials: A generalized analytical approach

Cited by 45 publications

References 56 publications

Mixed‐Mode Multidirectional Poisson's Ratio Modulation in Auxetic 3D Lattice Metamaterials

Mixed‐Mode Multidirectional Poisson's Ratio Modulation in Auxetic 3D Lattice Metamaterials

A Review on Mechanical Models for Cellular Media: Investigation on Material Characterization and Numerical Simulation

Robust topological designs for extreme metamaterial micro-structures

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