Macro-architectured cellular materials: Properties, characteristic modes, and prediction methods

doi:10.1007/s11465-018-0488-8

Front. Mech. Eng.

2018, Vol. 13

Issue (3) : 442-459 https://doi.org/10.1007/s11465-018-0488-8

RESEARCH ARTICLE

Macro-architectured cellular materials: Properties, characteristic modes, and prediction methods

Zheng-Dong MA(

)

The University of Michigan, Ann Arbor, MI 48109, USA

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Abstract

Macro-architectured cellular (MAC) material is defined as a class of engineered materials having configurable cells of relatively large (i.e., visible) size that can be architecturally designed to achieve various desired material properties. Two types of novel MAC materials, negative Poisson’s ratio material and biomimetic tendon reinforced material, were introduced in this study. To estimate the effective material properties for structural analyses and to optimally design such materials, a set of suitable homogenization methods was developed that provided an effective means for the multiscale modeling of MAC materials. First, a strain-based homogenization method was developed using an approach that separated the strain field into a homogenized strain field and a strain variation field in the local cellular domain superposed on the homogenized strain field. The principle of virtual displacements for the relationship between the strain variation field and the homogenized strain field was then used to condense the strain variation field onto the homogenized strain field. The new method was then extended to a stress-based homogenization process based on the principle of virtual forces and further applied to address the discrete systems represented by the beam or frame structures of the aforementioned MAC materials. The characteristic modes and the stress recovery process used to predict the stress distribution inside the cellular domain and thus determine the material strengths and failures at the local level are also discussed.

Keywords architectured material cellular materials multi-scale modeling homogenization method effective material properties computational method

Corresponding Author(s): Zheng-Dong MA

Just Accepted Date: 01 November 2017 Online First Date: 14 December 2017 Issue Date: 11 June 2018

Cite this article:

Zheng-Dong MA. Macro-architectured cellular materials: Properties, characteristic modes, and prediction methods[J]. Front. Mech. Eng., 2018, 13(3): 442-459.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-018-0488-8
https://academic.hep.com.cn/fme/EN/Y2018/V13/I3/442

Fig.1 Tendency of new material development. Left: Going to a smaller scale; right: Going to a larger scale

Fig.2 Roadmap of MAC materials

Fig.3 Example MAC materials

Fig.4 MAC materials by 3D printing (fabricated at MKP Structural Design Associates, Inc.)

Fig.5 Design variables in a 3D NPR material cell

Fig.6 Special properties of NPR materials. (a) Reaction to load (stiffening under pressure); (b) wide range of material property coverage; (c) able to be functionally graded and function-oriented designed; (d) excellent impact energy absorption capability

Fig.7 Design variables in a BTR material cell

Fig.8 Unit uniform strain field

e (i) (i = 1, 2, 3)

applied in the 2-dimensional cellular domain

Fig.9 Unit uniform stress field

e (i) (i = 1, 2, 3)

applied on the 2-dimensional cellular domain

Fig.10 Loading and boundary conditions for the homogenization of a 2D NPR cell structure

Fig.11 Analysis model for characteristic mode 1

Fig.12 Effective Young’s modulus (in black and GPa) for Mode 1

Fig.13 Effective Poisson’s ratio (in black and 100%) for Mode 1

Fig.14 Analysis model for characteristic Mode 2

Fig.15 Effective Young’s modulus (in black and GPa) for Mode 2

Fig.16 Effective Poisson’s ratio (in black and 100%) for Mode 2

Fig.17 Unit uniform strain field applied in the 2-dimesional cellular domain (top left: Characteristic Mode 1, top middle: Characteristic Mode 2, top right: Characteristic Mode 3)

Fig.18 Strain distribution of characteristic Mode 1 (left:

ε x

, middle:

ε y

, right:

γ x y

)

Fig.19 Strain distribution of characteristic Mode 2 (left:

ε x

, middle:

ε y

, right:

γ x y

)

Fig.20 Strain distribution of characteristic Mode 3 (left:

ε x

, middle:

ε y

, right:

γ x y

)

Fig.21 Strain modes of BTR cell. (a) In-plane tension; (b) out-plane compression; (c) pure bending

Fig.22 Normalized bending stiffness-normalized area density map

Fig.23 Normalized in-plane modulus-normalized area density map

Fig.24 Normalized out-of-plane compression modulus-normalized area density map

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