Elastic Solution of a Polyhedral Particle With a Polynomial Eigenstrain and Particle Discretization
Elastic Solution of a Polyhedral Particle With a Polynomial Eigenstrain and Particle Discretization
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DOI：
10.1115/1.4051869
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发表时间：
2021-12
期刊：
影响因子：
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通讯作者：
Chunling Wu;Liangliang Zhang;H. Yin
中科院分区：
文献类型：
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作者：
Chunling Wu;Liangliang Zhang;H. Yin
本文扩展了最近的工作（吴，C.，和Yin，H.，2021，“具有多项式本征应变的多边形夹杂物的弹性解”，ASME J. Appl. Mech.，88（6），p.061002）的Eshelby张量的多项式本征应变从二维（2D）到三维（3D）域，它提供了弹性场的解决方案，具有连续分布的本征应变的多面体夹杂物近似的泰勒级数的多项式。同样，多项式特征应变展开的多面体夹杂物的质心与均匀，线性和二次阶项，这提供了裁剪精度的弹性解决方案的多面体不均匀性使用Eshelby的等效包含方法。然而，由于Eshelby张量的奇异性，无论是二维还是三维情况，在顶点附近，非均匀体中的应力分布与有限元结果有一定的差异，这使得在质心处用泰勒多项式级数来捕捉顶点处的本征应变是不准确的。本文采用四面体单元进行区域离散，以精确求解本征应变分布和预测应力场。在确定了各节点的本征应变后，可以用绿色函数的封闭形式的区域积分来预测弹性场。参数分析表明多项式特征应变的泰勒展开在质心和C0连续特征应变的颗粒离散化之间的性能差异。由于应力奇异性是由Eshelby张量的解析形式来计算的，因此弹性分析是鲁棒的、稳定的和有效的。
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.