Construct accurate multi-continuum micromorphic homogenisations in multi-D space-time with computer algebra

TL;DR

This paper introduces a rigorous, flexible framework for asymptotic homogenisation of dynamic systems with finite scale separation, enabling the systematic creation of multi-continuum models informed by microscale physics.

Contribution

It develops a novel, assumption-light homogenisation methodology for dynamics, grounded in modern dynamical systems theory, allowing customizable and accurate multi-continuum homogenisations.

Findings

Framework proven under modern dynamical systems theory

Removes most assumptions of previous methods

Enables straightforward creation of physically informed homogenisations

Abstract

Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of dynamics at the \emph{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 informed by 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.