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| On the Formulation of Isoparametric Triangular Thermal Inclusion for Numerical Determination of the Displacements |
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Abstract In material manufacturing and mechanical design, a key factor contributing to mechanical failure is due to the localized heat fluctuations. The thermal inclusion model has been widely applied in quantitatively exploring the underlying failure mechanisms. In previous works, Eshelby’s inclusion model considering uniform thermal eigenstrains has attracted considerable attention. However, due to the complexity of the theoretical derivations, thermal inclusion studies focusing on non-uniform eigenstrains have not been comprehensively documented in literature. In the present work, polygonal inclusion subjected to linearly distributed thermal eigenstrain is examined first through analytical approach. Based on the method of Green's function and contour integral formulation, closed-form solution of the displacements produced by a typical line element is presented. Consequently, the exact solution to an arbitrary polygonal inclusion subjected to linear thermal eigenstrains can be deduced directly, in light of the superposition principle. Inspired by the isoparametric element of the finite element method (FEM), an isoparametric triangular inclusion model is proposed for numerical determination of the displacements due to any two-dimensional Eshelby’s inclusion with arbitrarily distributed thermal eigenstrains. The present numerical scheme excels the traditional FEM in that the mesh generation is merely required inside the inclusion domain, leading to a significant enhancement of the computational efficiency. As confirmed by the benchmark examples, the novel isoparametric triangular inclusion model shows robust reliability and sufficient accuracy, even for problems involving complex thermal eigenstrains.
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Received: 17 October 2022
Published: 18 April 2023
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2023, Vol. 44 
