Multiscale analysis, a critical aspect of materials science and engineering, involves understanding and predicting material behaviours across different scales, from microscopic to macroscopic levels. This approach is particularly essential for advanced materials like complex composite structures, where properties at one scale significantly influence the overall performance. This thesis contributes by introducing new computational methods to improve multiscale analysis and prediction, including a black-box meta-modelling based multiscale scheme and an FFT-based method for white-box multiscale simulations.

The first method presents a dynamic coupling strategy between macro and micro scales. It employs meta-modelling informed by homogenisation theory and machine learning to adeptly manage constitutive information across these scales. This approach is shown to excel at facilitating efficient multiscale modelling of complex structures, but exhibits black-box characteristics due to the reliance on machine learning-based surrogate modelling. Next, a novel homogenisation framework using Fast Fourier Transform (FFT) for analysing micro-structures in plate models, is presented. This technique is paired with a multiscale analysis for plate structures, improving modelling efficiency and outperforming traditional methods in computational effectiveness, while maintaining clear, white-box simulations at both micro and macro levels. The effectiveness of the two methods is demonstrated through several case studies, including the analysis of perforated plates and woven composites among others, highlighting their alignment with macro-scale simulations and enhanced efficiency over conventional multiscale methods. The contributions guide readers in selecting the appropriate method based on their preference for efficiency or transparent, white-box models.