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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]

The conventional first-order computational homogenization framework is restricted to problems where the macro characteristic length scale is much larger than the underlying Representative Volume Element (RVE). In the absence of a clear separation of length scales, higher-order enrichment is required to capture the influence of the underlying rapid fluctuations, otherwise neglected in the first-order framework. In this contribution, focusing on matrix-inclusion composites, a novel computational homogenization framework is proposed such that standard continuum models at the micro-scale translate onto the macro-scale to recover a micromorphic continuum. Departing from the conventional FE 2 framework where a macroscopic strain tensor characterizes the average deformation within the RVE, our formulation introduces an additional macro kinematic field to characterize the average strain in the inclusions. The two macro kinematic fields, each characterizing a particular aspect of deformation within the RVE, thus provide critical information on the underlying rapid fluctuations. The net effect of these fluctuations, as well as the interactions between RVEs, are next incorporated naturally into the macroscopic virtual power statement through the Hill-Mandel condition. The excellent predictive capability of the proposed homogenization framework is illustrated through three benchmark examples. It is shown that the homogenized micromorphic model adequately captures the material responses, even in the absence of a clear separation of length scales between macro and micro. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a fully coupled multi-scale finite element model for the constitutive description of an alumina/magnesium alloy/epoxy composite inspired in the mechanics and structure of the wall of wood cells. The mechanical response of the composite (the large scale continuum) is described by means of a representative volume element (RVE, corresponding to the intermediate scale) in which the fibre is represented as a periodic alternation of alumina and magnesium alloy fractions. Furthermore, at a lower scale the overall constitutive behavior of the alumina/magnesium alloy fibre is modelled as a single material defined by a large number of RVEs (the smallest material scale) at the Gauss point (intermediate) level. Numerical material tests show that this new composite maximises its toughness when the hierarchical design of wood cellulose fibres is replicated. The above results provide for the first time new clues into the understanding of how trees and plants optimise their microstructures at the cellulose level in order to absorb a large amount of strain energy before failure. These findings are likely to shed more light into natural materials and bio-inspired design strategies, which are still not well-understood at present. [Copyright &y& Elsevier]

A remarkably simple analytical expression for the sensitivity of the two-dimensional macroscopic elasticity tensor to topological microstructural changes of the underlying material is proposed. The derivation of the proposed formula relies on the concept of topological derivative, applied within a variational multi-scale constitutive framework where the macroscopic strain and stress at each point of the macroscopic continuum are volume averages of their microscopic counterparts over a representative volume element (RVE) of material associated with that point. The derived sensitivity—a symmetric fourth order tensor field over the RVE domain—measures how the estimated two-dimensional macroscopic elasticity tensor changes when a small circular hole is introduced at the microscale level. This information has potential use in the design and optimisation of microstructures. [Copyright &y& Elsevier]

Auxetic chiral structures exhibit many unique and enhanced mechanical properties, which emerge from the coupling of stretching and rotational mechanisms within the underlying unit cell. The standard first-order Computational Homogenization (CH) approach is inadequate in capturing this coupling effect. Moreover, a size effect arising from the interactions between micro and macro length scales cannot be accounted for. In this contribution, the micromorphic CH framework developed in Biswas and Poh (2017), Biswas et al. (2019), is reformulated for 2D tetra-chiral solids to address these limitations. Together with the standard macro-distortion tensor, an additional kinematic variable is introduced to characterize the deformation and rotation of the central ring. These two kinematic fields, each characterizing a particular aspect of the unit cell deformation, enable the micromorphic framework to adequately characterize the underlying dominant deformation modes. The predictive capability of the micromorphic CH framework is demonstrated through three benchmark problems in plane strain condition. Considering an axial loading problem, it is shown that the proposed micromorphic framework accurately captures the coupling between internal ring rotation and stretching of tangential ligaments. The predictive capability of the micromorphic approach is next demonstrated with a flat punch indentation problem in a regime without a clear separation of length scales. The homogenized micromorphic model predicts the correct global force-displacement response, as well as the underlying deformation mechanisms. Finally, the capability of the micromorphic framework in capturing both distortional and rotational modes of the central ring is demonstrated through the axial loading of a tapering plate. [ABSTRACT FROM AUTHOR]