Advances in materials processing have enabled development of artificial metamaterials with exceptional properties derived from their microstructures. Being a hybrid-multiscale, the field of metamaterials has been recently extended to realize practical devices out of the various exotic properties. Even though the exotic properties of metamaterials have been experimentally determined using various methods, it is good to note that their optimal design has not been fully met due to the limited knowledge about the relationship between the macroscopic behavior and microstructure of metamaterials. Furthermore, there is still need to develop models of metamaterials that include the effects of microscopic fields, e.g., micro-deformations and micro-rotations, on their mechanics.
Recently, Dr. Mohamed Shaat from Abu Dhabi University in collaboration with Dr. El Dhaba from the Damanhour University investigated the equivalent shear modulus of metamaterials. In particular, they comprehensively explored the mechanism by which the equivalent shear modulus of metamaterials would be negative and/or giant. The work is currently published in the journal, Composites Part B: Engineering.
In brief, the authors commenced their work by developing a micromorphic model for the equivalent shear modulus of metamaterials. The model assumed a multiscale metamaterial exhibiting microstructural strain field that is independent of the macroscopic strain field. Then, the equivalent shear modulus was derived based on the microstructure topology and material sample size. They established the conditions of the microstructure topology at which the shear modulus would be zero, positive and negative. In addition, the conditions that would give a composite metamaterial with a giant shear modulus were determined. These conditions were defined with evaluations of the changes in the material stability with the shear modulus change.
Metamaterials being a composition of a large number of unit cells capable of moving and deforming, the shear modulus was found to depend on the material size and microstructure topology provided that the micro-strain field remained significant and different from the macro-strain field. To define the conditions favorable for material stability, a unique parameter was introduced. A metamaterial with negative shear modulus was observed to be stable as the square of the parameter remained less than zero.
To validate the feasibility of the proposed micromorphic model, it was used to determine the equivalent shear modulus of composite metamaterials with coated inclusions embedded in a matrix of linear elastic material. Composite metamaterials with negative shear moduli were realized by using coated inclusions of modulus lower than that of the matrix phase. To obtain a relatively large (i.e., giant) shear modulus, either one phase of a negative modulus or an interfacial layer between the inclusion and the matrix was employed.
In summary, the authors noted that the implementation of the interface between the inclusion and the matrix gave a composite metamaterial with negative shear modulus. The study findings were in agreement with the previous findings of the stability of the material. Therefore, in a statement to Advances in Engineering, Dr. Shaat – the lead author – stated that the study will pave the way for the development of advanced metamaterials with negative or giant shear modulus for various applications.
Shaat, M., & El Dhaba, A. (2019). On the equivalent shear modulus of composite metamaterials. Composites Part B: Engineering, 172, 506-515.