  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.
