## 1 Introduction  
One of the application areas of cork-rubber-composites is vibration isolation. This type of elastomers is composed of a rubber matrix filled with granules of cork, which can be utilised as isolation pads for systems subjected to the presence of dynamic loads, such as buildings, industrial machines and floating floors [1; 2]. Cork is a natural origin material that is mostly used in wine stoppers. The insertion of cork granules into a rubber compound contributes to its recovery improvement when submitted to compression loads [3]. The use of numerical methods, such as finite element analysis (FEA), has proven to be an advantageous tool to predict the mechanical behaviour of many materials. The application of FEA related to elastomers and other cork composites has been utilised to access static, dynamic loading and impact behaviour [4; 5; 6; 7; 8]. One of the first requirements for the application of isolation pads is to evaluate their capacity to support static loadings. Regarding elastomers, one of the crucial steps during FEA is the definition of material properties [9]. Typically for large strains, elastomer's properties are defined through the application of non-linear models. However, if a linear stress-strain relationship, at small strains, is observed, Hooke's Law can be adopted for that strain range [10]. Concerning rubber materials, the compression behaviour of a specimen between bonded surfaces can be quantified using apparent compression modulus (\(E_{c}\)) [9; 11]. This parameter is associated with the rubber sample's geometry. In the case of compression without bonded surfaces, the rubber block presents axial and uniform lateral deformation, as depicted in Figure 0(a). With a bonded condition, the lateral surfaces deform, assuming a barrel shape due to incompressibility, as presented in Figure 0(b). The compression of rubber materials, considering friction between specimen and loading instrument surfaces, will also cause a similar shape effect. However, the rubber's stiffness will be smaller when compared to a bonded block due to some slippage of the edges [9]. For example, considering frictional contact compression on two blocks with the same area and different thicknesses, the sample with lower thickness will present higher stiffness. This effect is related to the ratio between loaded area and total free area, also known as shape factor [10; 12]. For disks and rectangular blocks, it can be determined by Equations (1) and (2), respectively:  
\[f_{disk}=\frac{D}{4T} \tag{1}\]  
\[f_{block}=\frac{LW}{2T(L+W)} \tag{2}\]  
with \(L\) and \(W\) are the length and width of a block, \(T\) corresponds to the thickness and \(D\) to the diameter of a cylinder. Another aspect that has been considered by several authors is the effect of the rubber's hardness. A softer material presents higher deformation at a certain load level compared with a material with higher hardness. To describe this effect, mathematical relationships between hardness and Young's modulus (\(E_{0}\)) have been developed by several authors with applications on different types of rubbers [13; 14; 15]. Mathematical models relating the compression behaviour with bonded contact and Young's modulus can also be found in the literature. Several works present different types of expressions for the approximated solution of the relation between apparent compression and Young's moduli [12; 16; 17; 18; 19; 20; 21]. Some of these studies are described in the literature review section. However, most of the analytical models developed only focus on disk geometry and/or assume a condition of material incompressibility, restricting its application to cork-rubber materials. The existence of a relation between moduli can be useful, for example, to estimate Young's modulus value of a cork-rubber material and use it to evaluate the performance of an isolation pad with other dimensions, reducing the need of several experimental testing.