51. An isoparametric inclusion model for determining the thermo-elastic fields produced by varying Eigen-temperature gradients.
- Author
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Li, Pu, Li, Jinran, Borodich, Feodor, Li, Dongfeng, and Jin, Xiaoqing
- Subjects
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STEADY state conduction , *HEAT conduction , *FINITE element method , *STRESS concentration , *MATERIALS science , *GREEN'S functions - Abstract
• A mathematical analogy established between steady-state heat conduction and thermal inclusion in plane elasticity. • A complete set of Eshelby tensors for thermal and elastic fields expressed in explicit analytical form. • All the closed-form solutions elegantly unified in an algebraic expression for both interior and exterior fields. • Present model is flexible, effective and versatile for arbitrarily shaped inclusions with any eigen-temperature gradients. • The heat and stress concentrations investigated around the inclusion boundary. The existence of inclusions or inhomogeneities may disrupt heat flow, resulting in increased stresses and temperature fluctuations at the material interface. Analyzing the thermo-elastic fields surrounding such microstructures is crucial for unveiling the intricate failure mechanisms within materials. Based on the method of Green's function and contour integral, this work presents a complete set of explicit analytical solutions for thermal and elastic fields of an arbitrary polygonal inclusion subjected to linearly varying eigen-temperature gradients or thermal eigenstrains. In contrast to the previous studies on potentials showing analogy with anti-plane elasticity, a mathematical analogy of Green's functions between steady-state heat conduction and thermal inclusion for plane elasticity is accordingly established. By employing the linear interpolation of the nodal eigen-temperature gradients or eigenstrains, the work further extends the traditional isoparametric element idea to the thermos-elastic inclusions, and proposes a novel isoparametric inclusion model to solve arbitrarily shaped inclusions with any distributed eigen-temperature gradients. Unlike the finite element method, which requires meshing for both the matrix and inclusion, the present model exhibits efficiency, flexibility, and versatility with the mesh discretization only conducted inside the inclusion domain. The inclusion based isoparametric method may have potential applications in mechanical engineering and material science for analyzing the thermo-structural behavior of various microstructures. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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