Investigation of effective elastic properties of frame-like periodic cellular solids by strain-energy-based homogenization

Name: Kasem Theerakittayakorn

keyword: Periodic cellular solid

; Homogenization

; Effective elastic property

; Euler beam element

Abstract: Periodic cellular solids are used in various applications such as tissue-engineering scaffolds, lightweight structural sandwich panels, energy absorption devices, and thermal insulating containers. When periodic cellular solids are used as load-bearing structures, the effective elastic properties of periodic cellular solids are of significant interest, and are among the main considerations of cellular solid design. The desired effective elastic properties of a periodic cellular solid can be obtained by appropriate selection of the base material and the topology of its unit cell. Homogenization methods can be used to calculate the effective elastic properties of a periodic cellular solid from its unit-cell structure and the finite element method can be used to analyze the unit cell. Many useful periodic cellular solids are frame-like structures. For such periodic cellular solids, beam elements can be used to accurately model their struts. In this study, the exact forms of the effective elastic constants of arbitrary frame-like periodic cellular solids that can be modelled accurately by Euler beams are analytically derived by using the homogenization method based on equivalent strain energy. The exact forms are obtained in terms of some dimensionless factors, the characteristic length and volume of the unit cell, the area and moment of inertia of the struts, and Young’s modulus of the base material. In general, the dimensionless factors can be functions of the area and moment of inertia of the struts. However, in many practical cases, these factors are constant. When the dimensionless factors are constant, they can be determined by exact curve fitting using finite element results with different areas and moments of inertia of the struts. In these cases, the closed-form solutions of the effective elastic constants will be obtained from exact curve fitting. By using the closed-form effective elastic constants obtained from exact curve fitting, mechanical characteristics of periodic cellular solids with various unit-cell topologies can be determined. This allows advantages and disadvantages of different unit-cell topologies to be studied. The closed-form effective elastic constants also allow the effect of strut sectional properties on the effective elastic constants to be thoroughly investigated. In addition to the closed-form effective elastic constants obtained from the exact forms with exact curve fitting, the closed-form effective elastic constants can also be derived in a symbolic computation platform. In summary, by using the closed-form effective elastic constants, unit-cell topologies and strut sectional properties can be appropriately chosen to suit different applications

Thammasat University. Thammasat University Library

Address: BANGKOK

Email: preserv@tu.ac.th

Name: Pruettha Nanakorn

Role: advisor

Name: Kriskrai Sitthiseripratip

Role: co-advisor

Created: 2015

Modified: 2021-10-04

Issued: 2021-10-04

วิทยานิพนธ์/Thesis

application/pdf

DOI: 10.14457/TU.the.2015.449

eng

DegreeName: Doctor of Philosophy

Level: Doctoral Degree

Descipline: Engineering

Grantor: Thammasat University

©copyrights Thammasat University

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