## 1 Introduction  
Currently, hot melt bonding methods are significantly influential in the market, with the hot melt adhesives industry expected to increase from USD 10.07 billion in 2024 to USD 13.42 billion by 2032, reflecting a 4.33% annual growth rate during the forecast period [1]. Hot melt adhesives, glues made of polymers that are melted before application, transition from liquid to solid over a narrow temperature range. After cooling, the hot melt solidifies and forms a sticky bond between two chosen surfaces [2]. Hot melt adhesives are advantageous for bulk production at a low cost because of their easy application, fast bonding, and the ability to bond with just one component, eliminating the need for extra materials or catalysts. Hot melts can adhere to various materials including plastics, paper, wood, metal, and fabrics, leading to a variety of application possibilities. Conventional bonding techniques with hot melts may include thermal, electrical, or laser methods, either individually or in combination [3]. The electromagnetic field-activated adhesive bonding technology is a unique and modern alternative to the current thermal bonding methods utilized in various manufacturing industries. The primary benefit of this is the preheating of the hot melt prior to heating the surfaces being bonded, ensuring the thorough heating of the hot melt. A more recent technique involves utilizing microwave radiation at frequencies over 1 GHz [4, 5, 6], but this addresses mainly fluid hot melts, with limited applicability. The difficulty with microwave technologies lies in creating new solid hot melt materials and related bonding processes that are multifunctional, highly reliable, and can create a strong, energy-efficient joint. On the other hand, the joints should be able to be disassembled by a specific electromagnetic field trigger too, allowing for a reversible bonding process in line with the circular economy concept [7; 8]. Developing new hot melt adhesives with specialized micro-/nanosized fillers can enhance the mechanical strength of adhesives, improve joint performance, increase adhesion to various substrates, and accelerate heating through electromagnetic fields. Different materials have been extensively researched as inserts in dielectrics due to their current application in microwave absorber technology [9; 10; 11; 12], or for their impact on electromagnetic energy [13; 14; 15], particularly by enhancing absorption in the microwave frequency range. But there is no current research on using MW-activatable adhesives with metallic functional particles, and the present study demonstrates, by modeling with specialized software, that adding metal particles to thermo-plastic formulations may create MW-activatable adhesives with lower energy usage. The main focus of this paper is on developing the concept of polyethylene-based hot melt adhesives with metallic inserts of Al and Fe, which may offer advantages like long-term stability, improved heat resistance, a broader range of bonding capabilities, and no potential for charring or producing unpleasant odors. Analytical methods were initially used to determine the parameters of a material with inserts from another material, [PERSON] and [PERSON], cited in [16; 17], being among the first to investigate these issues. The interest in theoretical approaches has remained constant as new dielectric/insert combinations have been found to obtain adequate behavior at microwave frequencies [18; 19; 20; 21]. However, analytical approaches have only been successful for simple structures and are generally ineffective in the microwave frequency range where the wavelength starts to become comparable to the interparticle distances and/or particle size. To estimate the electrical parameters, some methods for estimating the relative permittivity of a composite material, e.g., the Kraszewski, Landau, Lifshitz, Looyenga, and Lichtenecker equations are available [22].