## 1 Introduction  
The application of incremental bulk metal forming processes is gaining growing interest in the current industry. These processes are being investigated due to their advantages, widely discussed in literature by different authors [1; 2; 3; 4; 5; 6]. The incremental method is frequently used since it offers load reductions and workability increments in comparison with other processes. It also allows forging materials that present high resistance to deformation, obtaining large final shapes. Another important issue is the tools simplicity--normally a simple punch--and their exchangeable capability. This gives flexibility to the production, a very important feature nowadays. Finally, the high smoothness of the final workpiece deformed by these processes, the material economy and the aptitude for a complete management with Computer Numerical Control (CNC) machines can also be noted. To this end, having these processes implemented in the current industry plays an important role in achieving a competitive production. Consequently, the indentation case study as a fundamental part of these incremental bulk metal forming processes, is considered as a necessary step in the metalworking industries. Applying indentation to a workpiece, the final shape is progressively obtained by repetitive compressions. Thus, the indentation process is no longer considered as a secondary manufacturing process. On the contrary, it is presented as an alternative to traditional plastic deformation processes. It is not difficult to find works that extensively explore possible applications related with indentation processes,like the Single Point Incremental Forming (SPIF) or the localized-incremental forging processes. These processes achieve the final shape as a result of discrete indentations throughout the whole workpiece [7; 8]. Another example can be found with the Multiple Indentation processes, when a concatenation of elementary indentations is applied [9]. These new indentation based processes allow big deformation with less compression forces. Thus, the singular case study in this paper enables achieving an approximation to these new incremental processes referenced. Several studies show that the final workpiece shape depends on the geometry of the punch employed. In addition, other process parameters can have an effect, like the step over, feed rate or penetration [10; 11; 12]. The purpose of this paper is twofold: first, it aims to characterize the workpiece behaviour under different punch geometries. Second, it proposes an analytical solution that can be easily applied to estimate the necessary force needed to generate plastic deformation by indentation. Thus, different punch shapes are examined under the Finite Element Method (FEM) and the Upper Bound Theorem (UBT), in order to determine the force pick value for each of the geometries considered and compare the versatility of the methods applied. We propose a general UBT application that seeks a simplification of the analysis approached. Due to its efficiency, it is presented as an alternative to other current methods. The Upper Bound Theorem is considered one of the main analytical solutions for the metal forming process modelling. It is usually found applied in investigations of deformation processes like incremental forging, extrusion, Equal Channel Angular Extrusion/Pressing (ECAE/ECAP), orbital forming and others [13; 14; 15; 16]. On general terms and under a plain strain hypothesis, the UBT can be expressed as <<... The work realized by the superficial strengths of real traction (or compression) on a rigid-perfect plastic body is lower or the same as that realized by the superficial strengths of traction (or compression) corresponding to any other field of admissible kinematic velocities... >>[17].