## 1 Introduction  
Flexible wearable wireless devices are gaining significant attention because of their characteristics of light weight and low cost, low power consumption, high flexibility combined with robustness, and compact size. These wearable devices have become essential for many wireless applications. In recent decades, flexible sensors such as antennas and RFID tags have been designed for WLAN, GPS, military, and biomedical related applications [1; 2; 3; 4; 5]. Presently, as a result of the exponential development of wearable sensors and devices, and the high demand for the flexible electronic systems, various new challenges have arisen because of the unconventional performance requirements. Traditional antennas are customarily made of conductive wires or by etching metal patterns on rigid substrates. When subjected to stretching, folding, or twisting, these types of antennas become permanently deformed, if not broken, which renders them incompatible for applications that require high flexibility/bendability and are subject to this continuous deformation. Therefore, it is very important for the flexible sensors to be lightweight, small,durable, moist and heat resistant, and, most importantly, highly flexible without distorting radiation characteristics. Flexible antennas have gained significant attention in recent years due to their advantage of high flexibility, which directly addresses the above problem, in addition to their convenient integration with other microwave components [6], light weight, energy efficiency, reduced fabrication complexity, easy mountability on conformal surfaces, low cost, and abundant availability in the form of substrate films [7]. For this reason, this investigation focuses on the flexibility and seamless integrity of flexible antennas for wearable/IoT applications. To achieve the aforementioned characteristics for flexible antennas, conventional conductors and substrate materials such as metals and ceramics are not essentially appropriate. This is because these materials are usually rigid, costly, and lack flexibility and mechanical resilience. A large amount of research has previously explored numerous materials that exhibit suitable properties as a substrate for conductive materials for flexible antennas, including conductive polymers, conductive threads, and conductive textile. For dielectric materials, Polyimide (PI), Polyethylene Terephthalalate (PET), Polydimethylsiloxane (PDMS), Polytetrafluoroethylene (PTFE), and Liquid Crystal polymers (LCPs) have been explored. A detailed review of these conductive and polymer-based substrate materials is presented in our recent study in [1]. Wearable devices, such as flexible antennas, and RFID sensors and tags, are critically affected by bending, twisting, and crumpling [1; 3; 8; 9]. These deformative actions are sometimes inevitable, resulting in detrimental changes in the radiation performance of the flexible device. To ensure the robustness and durability of these flexible devices under flex conditions, a few important parameters for flexible devices are required to be tested for performance, such as shifts in resonant frequency, return loss, and signal degradation [8; 9]. Although radiation patterns, directivity, and gain are all factors that can be affected by bending [10], one of the major impacts of bending is on the resonant frequency and return losses, because the curvature on the device is prone to shift the resonant frequency either towards higher components or lower components of the resonant frequency and cause a change in its signal strength. The process of applied bending is predisposed to creating a mismatch in the impedance of the Transmission Line (TL) and the feedline, and changing the capacitance between the resonators and causing a modification in the effective length of the radiation element [10]. Therefore, the most reliable flexible antennas are considered to be those that tolerate the application of a certain level of bending to limit the adverse impacts on their radiation efficiency.