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Efficient modeling of multiphase solids using high-order ellipsoidal elements and eigenstrain BIEs
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DOI：10.1016/j.enganabound.2026.106867.png)
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Abstract
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This study aims to develop a unified and highly efficient computational framework for generalized multiphase solids containing inclusions, pores, and defects. The specific objective is to overcome the explicit interface treatment and high computational cost commonly encountered in conventional multi-domain BEM formulations by combining the Boundary Element Method (BEM) with eigenstrain-based boundary integral equations (BIEs) and high-order smooth ellipsoidal elements. The proposed approach enables each heterogeneous phase to be represented by a single element with very few nodes, thereby significantly reducing the size of local Eshelby matrices while maintaining accuracy. In addition, the eigenstrain BIE formulation avoids explicit interface unknowns, leading to a compact system matrix that is assembled only once. All local Eshelby matrices are also computed only once, resulting in a substantial reduction in computational cost. Numerical examples demonstrate excellent agreement with analytical solutions and conventional quadratic elements, while achieving markedly improved efficiency, especially for large-scale problems. The proposed method provides an accurate and scalable tool for modeling multiphase materials with complex microstructures.
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