Homogenisation empowers the efficient macroscale system level prediction of physical problems with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of dynamics at the finite scale separation of real physics, with proven results underpinned by modern dynamical systems theory. The novel systematic approach removes most of the usual assumptions, whether implicit or explicit, of other methodologies. By no longer assuming averages the methodology constructs so-called multi-continuum or micromorphic homogenisations systematically based upon the microscale physics. The developed framework and approach enables a user to straightforwardly choose and create such homogenisations with clear physical and theoretical support, and of highly controllable accuracy and fidelity.

翻译：均匀化方法使得具有复杂微观结构的物理问题能够在宏观系统层面进行高效预测。本文提出了一种创新、强大、严谨且灵活的渐近均匀化框架，适用于真实物理中有限尺度分离下的动力学问题，其有效性由现代动力系统理论提供支撑。该新颖的系统性方法摒弃了其他方法中大多数常见的隐含或显式假设。通过不再依赖平均假设，该方法基于微观尺度物理系统地构建了所谓的多连续介质或微形态均匀化模型。所开发的框架和方法使用户能够直接选择并创建此类均匀化模型，这些模型具有清晰的物理和理论基础，并且具有高度可控的精度与保真度。