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The present research focuses on a continuum description of stratified metamaterials achieved through the superposition of layers with alternating chirality. Each layer is constructed as a periodic assembly of centre-symmetric periodic cells, formed by a recurring arrangement of rigid circular discs connected by elastic ligaments. The layers are interconnected through elastic pins passing through the centres of aligned discs, allowing for either restrained or free relative rotation. A micropolar continuum model is used to describe each individual layer. The overall response of the metamaterials to in-plane forces is derived using a multi-field non-local model, expressed in terms of the average and difference of displacement and rotational fields. The overall micropolar and standard (Cauchy) constitutive tensors have been determined in closed form. The validity of the equivalent generalized micropolar model has been confirmed through comparison with discrete Lagrangian solutions of representative examples. In addition, a detailed analysis of a pseudo-indentation test has been carried out. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.
Bacigalupo et al. (2024) studied this question.