## 1 Introduction  
In 1903, [PERSON] first noted that the contact area can decrease under the application of load [1]. In the case of a beam situated on a frictionless, smooth, rigid plane and subjected to an isolated load, he demonstrated correctly that at a specific distance from the point of force application, the sides of the beam are lifted. Such contacts are referred to as \"receding contacts\", in contrast to, e.g., Hertzian contact demonstrating a monotonic increase in contact area with increasing force, which is referred to as an \"advancing contact\" [2]. This terminology was first introduced by [PERSON] [3]. Receding contacts can be observed even in well-engineered machines and structures with meticulously assembled components. The occurrence of gaps between these individual parts is a consequence of their distortion under the influence of external loads [4]. Contact problems are inherently nonlinear, as the extent of the contact area is determined by Signorini inequalities. [PERSON], however, showed that for a receding contact, the contact area is independent of the magnitude of applied force. The contact jumps to the reduced area as soon as an infinitesimally small force is applied and remains unchanged when the force increases. Furthermore, since the contact area remains unchanged in receding contacts, the overall stress and displacement field are proportional to the applied force [2]. [PERSON] and [PERSON] considered inhomogeneous materials and examined the role of elastic constants [5]. They concluded that for receding contacts, whether between contacting bodies of the same material or of different materials, the stresses within the material are proportional to the applied tractions and the extent of the contact area remains independent of the load [5]. In addition to the aforementioned example of a thin elastic beam pressed against a half space, one may also consider a cylindrical pin with radius \(R\) that is pressed into a hole of the same radius in an infinite elastic matrix. In the unloaded state, the border of the pin makes contact with the matrix at each point on the circumference of the pin. If the pin is subjected to a load, an arc section of the boundary between the pin and the matrix will be separated [6]. It is of interest to find the exact arc of contact and the pressure along that arc. A solution for contact bodies of the same material was found in [6; 7], where it was found that the angle of contact is independent of the elastic properties. It has to be noted that the original description of receding contacts was limited to frictionless problems. It, however, can be shown that the solution can be extended to frictional problems when the external tractions increase monotonically. The contact area \(\Gamma_{C}\) now has to be divided into a slip region \(\Gamma_{S}\) and a stick region \(\Gamma_{C}-\Gamma_{S}\), where the tangential tractions must satisfy different conditions [4]. Apart from friction or the effect of loading and material properties, the effect of adhesion on frictionless receding contacts has been investigated [8]. The study of this problem is of great practical interest, as receding contacts are a common feature in a wide range of applications. An example, which is omnipresent in the industry, is the method of bolted joints to assemble composite structures [9]. This method is used due to its high load-carrying capacity, ease of assembly, and therefore, relatively low cost. Bolted joints are employed in a number of industries, including automotive, aerospace, and railway track construction [10]. Note that in industry, hybrid connections which combine adhesive bonding and bolts are also used [11]. Receding contacts are common features in complex elastic structures composed of several elastic layers with different elastic properties [12; 13]. Receding contact is observed in widely used technological applications, for example, in different steel connections in buildings [14; 15].