![]() Secondly, the configuration obtained here is naturally characterised by a finite length scale associated with the resolution of fabrication. Firstly, smooth connectivity within graded microstructures is automatically guaranteed. The present framework also exhibits interesting features in several other aspects. Upon linearisation, the computational cost associated with the proposed formulation is found to be as low as that in existing asymptotic-analysis-based homogenisation approaches, where only spatially periodic microstructures are considered. ![]() For a given graded microstructure, the stress field and overall compliance computed by the proposed method are shown, both theoretically and numerically, to be consistent with the underlying fine-scale results. With the introduction of a mapping function which transforms an infill graded microstructure to a spatially-periodic configuration, the originally complicated cross-scale problem can be asymptotically decoupled into a macroscale problem within a homogenised media and a microscale problem within a representative unit cell. ![]() With the use of asymptotic analysis, we propose in this article a homogenisation framework to underpin the fast design of devices filled with quasi-periodic microstructures. Graded microstructures have demonstrated their values in various engineering fields, and their production becomes increasingly feasible with the development of modern fabrication techniques, such as additive manufacturing. ![]()
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