Convolution-compatible modeling of elastic fields induced by inclusions with linearly varying eigenstrains - Ma, Ningning; Li, Pu; Luo, Xiaowu; Zhou, Qinghua; Zhu, Hao; Liu, Yanmin; Zhang, Qiang (Mechanics of materials, 2025)
Modeling the elastic fields induced by inclusions with complex shapes and non-uniform eigenstrains remains a classical challenge in solid mechanics and materials science. This study addresses the case of linearly varying eigenstrains by reorganizing Green's function into a convolution-compatible formulation, where the effect of the eigenstrains is decomposed into two parts: a linear-coordinate weighted form of the integral corresponding to uniform eigenstrains, and an additional integral unique to the linear variation. Based on this structure, explicit analytical tensors for the displacement, strain, and stress fields of rectangular inclusions are derived. A general and efficient computational method is further proposed by integrating primitive function formulations with fast Fourier transform (FFT) algorithms, enabling rapid evaluation of inclusions with arbitrary shapes and linearly varying eigenstrains. The derived solutions degenerate to classical ones when the eigenstrains are uniform, highlighting the consistency and broader applicability. Comparisons with finite element simulations and the direct superposition method validate the accuracy and efficiency of the proposed approach across various scenarios, including linearly distributed eigenstrains, multiple inclusions, and complex geometries. The present analytical formulation provides a fundamental basis for modeling elastic fields induced by thermal loads in heterogeneous materials. •A efficient convolution-compatible formulation is proposed for precise modeling of linearly varying eigenstrains.•Closed-form solutions for displacement, strain, and stress in rectangular inclusions are derived.•Combing primitive functions with FFT allows efficient analysis of inclusions of arbitrary shape and linear eigenstrains.