Size effects and the existence of scalable materials and systems

Abstract

Size effects are particular types of scale effect, where the response of a material is dependent to some extent on its size. These types of behaviour manifest to a greater or lesser extent in all materials, and pose a problem for constitutive models, where material parameters determined through experimentation at one size are inapplicable at different sizes. The origin of size effects is microstructural, through defects and structures ranging from cracks, fibres, grains, porosity, dislocations, precipitates, etc., and which has led to the creation of a plethora of microscale and mesoscale models in an attempt to represent the phenomena. In this paper an entirely different approach is taken where metamaterial constitutive models are created that eliminate entirely particular types of size effect. Such an approach has only recently been made possible with the arrival of a new scaling theory called finite similitude, which from a material-model standpoint starts from the unlikely position that it is founded on transport equations defined on a trial-spacetime manifold (where the scaled experiment resides). The approach however features a countably infinite number of similitude rules that in principle can capture any scale effect. It is this feature that enables metamaterials and metasystems to be defined on a projection of the trial spacetime manifold to the scaling-space manifold, where all physical quantities are dependent on a single dimensional scaling parameter. Metasystem and metamaterial models are shown to exist on the scaling space that feature the extraordinary ability to represent behaviours over a range of length scales. Although the models created are idealised they nevertheless provide a practical approach through testing at different sizes and it is demonstrated in the paper how real-world size effects can be captured efficiently.