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    Elastic Solution of a Polyhedral Particle With a Polynomial Eigenstrain and Particle Discretization

    Source: Journal of Applied Mechanics:;2021:;volume( 088 ):;issue: 012::page 0121001-1
    Author:
    Wu, Chunlin
    ,
    Zhang, Liangliang
    ,
    Yin, Huiming
    DOI: 10.1115/1.4051869
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: The paper extends the recent work (Wu, C., and Yin, H., 2021, “Elastic Solution of a Polygon-Shaped Inclusion With a Polynomial Eigenstrain,” ASME J. Appl. Mech., 88(6), p. 061002) of Eshelby’s tensors for polynomial eigenstrains from a two-dimensional (2D) to three-dimensional (3D) domain, which provides the solution to the elastic field with continuously distributed eigenstrain on a polyhedral inclusion approximated by the Taylor series of polynomials. Similarly, the polynomial eigenstrain is expanded at the centroid of the polyhedral inclusion with uniform, linear, and quadratic order terms, which provides tailorable accuracy of the elastic solutions of polyhedral inhomogeneity using Eshelby’s equivalent inclusion method. However, for both 2D and 3D cases, the stress distribution in the inhomogeneity exhibits a certain discrepancy from the finite element results at the neighborhood of the vertices due to the singularity of Eshelby’s tensors, which makes it inaccurate to use the Taylor series of polynomials at the centroid to catch the eigenstrain at the vertices. This paper formulates the domain discretization with tetrahedral elements to accurately solve for eigenstrain distribution and predict the stress field. With the eigenstrain determined at each node, the elastic field can be predicted with the closed-form domain integral of Green’s function. The parametric analysis shows the performance difference between the polynomial eigenstrain by the Taylor expansion at the centroid and the C0 continuous eigenstrain by particle discretization. Because the stress singularity is evaluated by the analytical form of Eshelby’s tensor, the elastic analysis is robust, stable, and efficient.
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      Elastic Solution of a Polyhedral Particle With a Polynomial Eigenstrain and Particle Discretization

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    contributor authorWu, Chunlin
    contributor authorZhang, Liangliang
    contributor authorYin, Huiming
    date accessioned2022-02-06T05:36:11Z
    date available2022-02-06T05:36:11Z
    date copyright8/10/2021 12:00:00 AM
    date issued2021
    identifier issn0021-8936
    identifier otherjam_88_12_121001.pdf
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4278374
    description abstractThe paper extends the recent work (Wu, C., and Yin, H., 2021, “Elastic Solution of a Polygon-Shaped Inclusion With a Polynomial Eigenstrain,” ASME J. Appl. Mech., 88(6), p. 061002) of Eshelby’s tensors for polynomial eigenstrains from a two-dimensional (2D) to three-dimensional (3D) domain, which provides the solution to the elastic field with continuously distributed eigenstrain on a polyhedral inclusion approximated by the Taylor series of polynomials. Similarly, the polynomial eigenstrain is expanded at the centroid of the polyhedral inclusion with uniform, linear, and quadratic order terms, which provides tailorable accuracy of the elastic solutions of polyhedral inhomogeneity using Eshelby’s equivalent inclusion method. However, for both 2D and 3D cases, the stress distribution in the inhomogeneity exhibits a certain discrepancy from the finite element results at the neighborhood of the vertices due to the singularity of Eshelby’s tensors, which makes it inaccurate to use the Taylor series of polynomials at the centroid to catch the eigenstrain at the vertices. This paper formulates the domain discretization with tetrahedral elements to accurately solve for eigenstrain distribution and predict the stress field. With the eigenstrain determined at each node, the elastic field can be predicted with the closed-form domain integral of Green’s function. The parametric analysis shows the performance difference between the polynomial eigenstrain by the Taylor expansion at the centroid and the C0 continuous eigenstrain by particle discretization. Because the stress singularity is evaluated by the analytical form of Eshelby’s tensor, the elastic analysis is robust, stable, and efficient.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleElastic Solution of a Polyhedral Particle With a Polynomial Eigenstrain and Particle Discretization
    typeJournal Paper
    journal volume88
    journal issue12
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.4051869
    journal fristpage0121001-1
    journal lastpage0121001-17
    page17
    treeJournal of Applied Mechanics:;2021:;volume( 088 ):;issue: 012
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
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