Equivalent inclusion method is the basis for semi-analytical models in tackling inhomogeneity problems. Equivalent eigenstrains are obtained by solving the consistency equation system of the equivalent inclusion method and then stress disturbances caused by inhomogeneities are determined. The equivalent inclusion method equation system can only be solved numerically, but the current fixed-point iteration method may not be able to achieve deep convergence when the Young's modulus of inhomogeneity is lower than that of the matrix material. The most significant innovation of this paper is to reveal the non-convergence mechanism of the current method. Considering the limitation, the Jacobian-free Newton Krylov algorithm is selected to solve the equivalent inclusion method equation. Results indicate that the new algorithm has significant advantages of computing accuracy and efficiency compared with the classic method.

等效包含法是解决非均匀性问题的半分析模型的基础。通过求解等效包含方法的一致性方程组，获得等效特征应变，然后确定由不均匀性引起的应力扰动。当量包含法方程组只能用数值求解，但是当不均匀杨氏模量低于基体材料的杨氏模量时，当前的定点迭代法可能无法实现深度收敛。本文最重要的创新之处在于揭示了当前方法的非收敛机制。考虑到这一限制，选择了无雅可比的牛顿克雷洛夫算法来求解等效包含法方程。