In the past few years, nonlinear metamaterials have attracted a lot of attention due to the exceptional qualities they possess and the potential applications they have in a variety of different domains, such as optics, acoustics, and electronics. These materials are engineered composites that exhibit unconventional behaviour not found in natural materials. By designing their structure at the micro- or nano-scale, researchers can manipulate the response of nonlinear metamaterials to external stimuli, leading to exotic phenomena such as negative refraction, cloaking, and nonlinear wave propagation (Smith, Pendry, & Wiltshire, 2004).
Nonlinear effects in metamaterials arise from the inherent nonlinearity of their constituent materials, as well as the engineered nonlinear response at the unit-cell level. These effects manifest as the dependence of material properties on the intensity or amplitude of the excitation signal. Common nonlinear phenomena observed in metamaterials include harmonic generation, parametric amplification, bistability, and self-focusing (Lapine et al., 2014; Liu et al., 2017).
The study and modelling of nonlinear metamaterials play a crucial role in understanding their behaviour and exploiting their unique characteristics for practical applications. Various analytical, numerical, and experimental techniques have been employed to investigate the nonlinear response of metamaterials. However, due to the complex and often non-intuitive nature of nonlinear effects, modelling nonlinear metamaterials remains a challenging task.
To address these challenges, this chapter explores the application of fuzzy logic modelling as an effective tool for capturing and understanding the nonlinear behaviour of metamaterials. Fuzzy logic offers a flexible and intuitive framework for handling imprecise or uncertain information, making it well-suited for modelling complex and nonlinear systems. By integrating fuzzy logic into the modelling process, researchers can gain insights into the nonlinear dynamics of metamaterials and predict their behaviour under various operating conditions (Alù & Engheta, 2017).