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• The polyhedral formula of the Cosserat theory has been derived. • The precision of the proposed method can approach that of quadratic elements. • The meshing performance is enhanced benefiting efficient octree techniques. The Cosserat continuum offers high accuracy in micro-structure analysis and stress concentration simulation due to its consideration of mechanical factors such as coupled stress and internal length scale. However, existing methods are mainly developed based on the isoparametric conventional continuum framework, with relatively simple element shapes and weak adaptability to complex geometries. Therefore, this paper proposes an improved Cosserat continuum theory based on the three-dimensional (3D) polyhedral scale boundary finite element method (PSBFEM). The main work is as follows: (1) The Cosserat continuum theory formula is deduced within the SBFEM framework by integrating a polygon mean-value shape function; (2) The analytical accuracy of the proposed method is examined through classical micro-structure test examples; (3) An efficient octree algorithm is introduced to evaluate the comprehensive performance of the proposed method for the analysis of complex structures, and the selection and impact of the internal length scale are discussed. The results indicate that the proposed method incorporates the good performance of SBFEM and the Cosserat continuum, and its accuracy can approach the traditional quadratic Cosserat continuum elements; The stress concentration problem can be effectively addressed, leading to a more accurate representation of structural stress characteristics. Additionally, complex polyhedral elements can be directly calculated, and the element library of traditional Cosserat theory has been greatly expanded. [ABSTRACT FROM AUTHOR]

This paper uses a multi-scale crystal plasticity modelling approach to investigate the role of microstructure in the damage of Sn-3Ag-0.5Cu (wt%, SAC305) solder joints subject to thermal cycling. Faithful microstructure modelling has been developed to explicitly represent the complex microstructure characterized in the experiments. The mechanisms for the experimental finding that single crystal joints systematically outperform interlaced and beachball joints, in terms of damage development during thermal cycling, are found to be the localization of stored energy due to the grain boundaries. Interlaced regions, however, benefit the lifetime of solder joints versus a beachball microstructure by virtue of energy diffusion. The modelling results, together with experimental characterization, provide practical suggestions on how the microstructure could be designed to optimize the in-service lifetime of solder joints subject to thermal fatigue. [Display omitted] [ABSTRACT FROM AUTHOR]