## 3 Materials and Methods  
The methodology followed in this study is presented in Figure 2. Given a certain geometry and [PERSON]'s modulus and Poisson's ratio values obtained through an experimental compression test--without friction between sample and loading plates--a simulation of the compression behaviour considering a frictional contact can be performed through Finite Element Analysis (FEA). The results obtained from the numerical analysis can then be used for determining a relationship between the two testing configurations. A detailed description of the methodology steps is given below.  
Regarding experimental methods, two compression tests were performed, considering frictionless and frictional contact between sample and loading plates. To simulate frictionless contact, lubricated plates were used. The value of [PERSON]'s modulus was calculated based on load-displacement data from that experiment. Poisson's ratio of cork-rubber materials was also determined based on an internal experimental procedure. This value was obtained through the measurement of lateral deformation, using a probe indicator until a maximum of 20% axial strain. In this study, assuming an isotropic material behaviour, the Poisson's ratio obtained for the cork-rubber composites had a value of 0.31. About the experimental testing with frictional contact, no lubricant or rough surface was applied between the sample and compression plates. All the samples tested have the same square cross-section, differing only in thickness.  
Based on the values of Young's modulus obtained by experimental tests, the compression behaviour of different geometries of a cork-rubber compound was simulated, employing finite element analysis. Simulations were performed using ANSYS Mechanical. The experimental setup and 3-D finite element model are presented in Figure 3. The finite element model was composed of a solid block, representing the cork-rubber specimen, placed between two surfaces. The numerical analysis consisted of simulating the compression machine displacement in contact with one of the surfaces of a cork-rubber block, recording as output the reaction force on the opposite surface. For that, rigid joints were employed on each surface: one with a fixed condition on all degrees of freedom, and another with only free translation on the load direction. Two contact options--rough and frictionless--were also employed to simulate the experimental method, according to the respective testing condition.  
In this study, to model the compression behaviour of cork rubber composites, Hooke's Law was considered, since these materials present a linear region at small strains [22]. These values of deformation usually correspond to the application range of the cork-rubber vibration isolation pads, which simplifies the problem under study. However, at higher strains, the use of non-linear models is recommended [4; 7; 20]. The value of Poisson's ratio used as an input for numerical analysis was the same for all simulations performed since all tested materials presented similar results for that parameter  
Figure 2: Methodology scheme.  
With the results from the numerical analysis of frictional contact between surfaces-stress and strain data, the apparent compression modulus was calculated for different geometries, using Equation (10):  
\[E_{c}=\frac{\sigma}{\varepsilon} \tag{10}\]  
where \(\sigma\) is stress and \(\varepsilon\) is strain. Then, the apparent compression modulus was related to [PERSON]'s modulus for each shape factor.  
Finally, for validation purposes, the results obtained by FEA for frictional contact were compared to samples tested experimentally. In addition, the results concerning the application of the methodology proposed in this article were compared against results obtained by the application of [PERSON] [16] and [PERSON] [20] models.