Harvesting Deformation Modes for Micromorphic Homogenization from Experiments on Mechanical Metamaterials

TL;DR

This paper introduces an experimental method using digital image correlation to identify and decompose deformation modes in mechanical metamaterials, enhancing micromorphic homogenization models for better material behavior prediction.

Contribution

It develops a full-field micromorphic IDIC technique for experimentally extracting deformation components in cellular metamaterials, bridging the gap between theory and real-world data.

Findings

Successfully applied to simulated and experimental images

Enabled decomposition of deformation into macro, meso, micro components

Improved understanding of patterning effects in metamaterials

Abstract

A micromorphic computational homogenization framework has recently been developed to deal with materials showing long-range correlated interactions, i.e. displaying patterning modes. Typical examples of such materials are elastomeric mechanical metamaterials, in which patterning emerges from local buckling of the underlying microstructure. Because pattern transformations significantly influence the resulting effective behaviour, it is vital to distinguish them from the overall deformation. To this end, the following kinematic decomposition into three parts was introduced in the micromorphic scheme: (i) a smooth mean displacement field, corresponding to the slowly varying deformation at the macro-scale, (ii) a long-range correlated fluctuation field, related to the buckling pattern at the meso-scale, and (iii) the remaining uncorrelated local microfluctuation field at the micro-scale. The micromorphic framework has proven to be capable of predicting relevant mechanical behaviour, including size effects and spatial as well as temporal mixing of patterns in elastomeric metamaterials, making it a powerful tool to design metamaterials for engineering applications. The long-range correlated fluctuation fields need to be, however, provided a priori as input parameters. The main goal of this study is experimental identification of the decomposed kinematics in cellular metamaterials based on the three-part ansatz. To this end, a full-field micromorphic Integrated Digital Image Correlation (IDIC) technique has been developed. The methodology is formulated for finite-size cellular elastomeric metamaterial specimens deformed in (i) virtually generated images and (ii) experimental images attained during in-situ compression of specimens with millimetre sized microstructure using optical microscopy.