Q2BSTUDIO is a company specialized in the development and provision of technological services, offering innovative solutions for various industries. In this article, we present an inertia-augmented relaxed micromorphic model, which enriches the model previously developed by the authors by introducing a Curl P? term in the kinetic energy density. This enhanced model allows for a more precise adjustment of dispersion curves and offers the ability to describe modes with negative group velocity, which are related to negative refraction effects.
Additionally, the model allows greater flexibility in the values of the asymptotes corresponding to the cutoff points, eliminating a restriction present in previous versions. Although the curve fitting obtained is of high quality in general terms, it is still necessary to achieve a perfect quantitative match for very small wavelengths, close to the size of the unit cell.
Metamaterials are materials whose mechanical properties go beyond those of conventional materials due to their heterogeneous microstructure. These can exhibit unusual responses such as negative Poisson's ratio, cloaking, wave focusing, channeling, negative refraction, among others. The operating frequency of each metamaterial largely depends on the size and geometry of its unit cell, as well as the base material used.
In this article, a labyrinth-type metamaterial based on polymers is presented, whose optimized mass distribution within the unit cell allows generating a wide band of acoustic absorption on a size scale on the order of centimeters. Finite element modeling of structures built with this metamaterial is unfeasible due to the extremely dense mesh required to correctly represent the thin strips of material within each cell. For this reason, the need for a homogenized model that allows using this innovative metamaterial in real engineering designs becomes evident.
Various homogenization techniques have been developed with the aim of rigorously predicting the macroscopic mechanical behavior of metamaterials. However, many of these techniques are inadequate for treating finite-size metamaterials, as they are based on scaling approaches suitable only for media without defined boundaries. As a result, finite-size metamaterial structures are often analyzed through finite element simulations that directly use the microstructured material, which entails high computational costs.
To overcome this challenge and enable the design of complex structures using the presented metamaterial, the use of an inertia-augmented relaxed micromorphic model is proposed. This model, based on the previously developed relaxed micromorphic model, has been expanded with a new inertia term that incorporates coupled space-time derivatives of the microdistortion tensor. This model has proven effective in describing the behavior of numerous infinite and finite-size metamaterials, and in this article it is extended to represent negative group velocities, which was not possible in previous versions.
It will be shown that the proposed model is capable of adequately describing the response of the labyrinth metamaterial over a wide range of frequencies and wave numbers, including values close to the unit cell size and for all propagation directions, using a limited set of constitutive parameters independent of frequency and scale. Likewise, it will be shown how the new inertia term is capable of generating modes with negative group velocities, associated with negative refraction phenomena.
In this context, at Q2BSTUDIO we are committed to technological innovation and the development of advanced solutions in the field of material modeling and computational simulations. Our team works with cutting-edge methodologies to offer precise and efficient tools that allow optimizing the design and implementation of new materials with unique properties.
In the last section of this article, new designs of finite-size labyrinth metamaterial structures will be presented, which can be used for elastic energy control in the acoustic regime and their application in various industries.
