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Analytical Solution of Thermo-Mechanical Properties of Functionally Graded Materials by Asymptotic Homogenization Method

Materials, 2022-04, Vol.15 (9), p.3073 [Peer Reviewed Journal]

2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. ;2022 by the authors. 2022 ;ISSN: 1996-1944 ;EISSN: 1996-1944 ;DOI: 10.3390/ma15093073 ;PMID: 35591408

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  • Title:
    Analytical Solution of Thermo-Mechanical Properties of Functionally Graded Materials by Asymptotic Homogenization Method
  • Author: Chen, Dan ; Liu, Lisheng ; Chu, Liangliang ; Liu, Qiwen
  • Subjects: Accuracy ; Algorithms ; asymptotic homogenization method ; Asymptotic methods ; Asymptotic properties ; Boundary conditions ; Boundary value problems ; Composite materials ; Constituents ; Design optimization ; effective properties ; Exact solutions ; functionally graded materials ; Functionally gradient materials ; Homogenization ; Material properties ; Mathematical models ; Mechanical properties ; Methods ; Segmentation ; Tensors ; thermo–mechanical coupling ; Viscoelasticity ; Zirconium carbide
  • Is Part Of: Materials, 2022-04, Vol.15 (9), p.3073
  • Description: In this work, a general mathematical model for functionally graded heterogeneous equilibrium boundary value problems is considered. A methodology to find the local problems and the effective properties of functionally graded materials (FGMs) with generalized periodicity is presented, using the asymptotic homogenization method (AHM). The present models consist of the matrix metal Mo and the reinforced phase ceramic ZrC, the constituent ratios and the property gradation profiles of which can be described by the designed volume fraction. Firstly, a new threshold segmentation method is proposed to construct the gradient structure of the FGMs, which lays the groundwork for the subsequent research on the properties of materials. Further, a study of FGMs varied along a certain direction and the influence of the varied constituents and graded structures in the behavior of heterogeneous structures are investigated by the AHM. Consequently, the closed-form formulas for the effective thermo-mechanical coupling tensors are obtained, based on the solutions of local problems of FGMs with the periodic boundary conditions. These formulas provide information for the understanding of the traditional homogenized structure, and the results also be verified the correctness by the Mori-Tanaka method and AHM numerical solution. The results show that the designed structure profiles have great influence on the effective properties of the present inhomogeneous heterogeneous models. This research will be of great reference significance for the future material optimization design.
  • Publisher: Switzerland: MDPI AG
  • Language: English
  • Identifier: ISSN: 1996-1944
    EISSN: 1996-1944
    DOI: 10.3390/ma15093073
    PMID: 35591408
  • Source: Directory of Open Access Scholarly Resources (ROAD)
    Open Access: PubMed Central
    AUTh Library subscriptions: ProQuest Central
    GFMER Free Medical Journals
    DOAJ Directory of Open Access Journals
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