The contact of hyperelastic solids like rubber is ubiquitous in everyday life and industrial production, encompassing applications such as tires, seals, cables, and more [1]. It is worth noting that the nonlinear behavior of hyperelastic materials would be magnified by stress concentration due to microscale contacts and render the study of hyperelastic solid contact behavior significantly more complex. So far, investigating the impact of hyperelasticity on contact behavior represents a crucial challenge within academic fields [2–5].

Incorporating surface roughness into contact models presents a formidable challenge due to the intricate nature of randomness and features over multiple scales. Currently, two primary characterizations of rough surface morphology prevail: statistical description and fractal description. In the early stages of research, Greenwood and Williamson [6] established the classical statistical contact model in 1996, known as the GW model. This model was groundbreaking in establishing a linear relationship between contact load and actual contact area by employing Hertz's solution. Based on the GW model, various statistical models have since emerged, each incorporating different hypotheses. These hypotheses include considerations for nonuniform asperity radii [7–9], elliptic paraboloidal asperities [10], and anisotropic topographies [11]. As to fractal description, in 1982, Mandelbrot [12] found, most rough surfaces in the nature can be described as self-affine fractals. This self-affinity property signifies that these surfaces maintain statistical equivalence when their height (*h*) and lateral coordinates (*x* and *y*) are rescaled by varying factors. Building upon fractal theory, Persson [13] created a theory for rough surface contact utilizing power spectral density (PSD) and assuming the elasticity of rubber materials. Recently, Wang [14] adopted a deterministic description of rough surface and put forward an incremental contact model for rough surfaces. This model was validated by the finite element method[14, 15] (FEM) and experiments [16], focusing on contact area fractions within the 15% range. These aforementioned contact theories could contribute to the realization in mechanism of rough surfaces.

Besides morphology descriptions and contact mechanism, the property of materials is one of crucial factors affecting the contact response [17]. In many studies, FEM simulations offer an alternative and convenient method to investigate rough surface contact considering complex influencing factors, for example the nonlinearity of materials. Song et al. [18], Zhang et al. [19] and Jiang et al. [20] studied the contact behaviors of rough surfaces by taking the size dependence into account. Zhang and Yang [21] noted that the indentation behaviors of hyperelastic spheres primarily depend on the combined influences of substantial deformation and material nonlinearity. By introducing the instantaneous tangent modulus *E**t*, Jiang et al. [22] extended the incremental model into the hyperelasytic materials and this extension was subsequently validated through FEM. Similarly, Lengiewicz et al. [23] emphasized that hyperelasticity introduces notable differences in the contact deformation process under high loads, as observed through FEM analysis. All these researches indicate the nonlinearity of materials plays as a significant role in deformation. Therefore, considering hyperelasticity in the context of rough surface contact seems to be a reasonable approach.

In addition to theoretical investigations and numerical simulations, the evolution of interfacial contact can also be gleaned through experimental observations. The physical technologies, such as thermal resistance [24], electric resistance [25], and X-ray examination [26], and ultrasound reflection [27–29] at the contact interface, can exhibit noteworthy changes in response to variations in actual contact area at the interfaces. In addition to abovementioned methods, the optical technique [30–34] have also been utilized to investigate the rough surface contact with the advantage of in-site measurement and direct observation. Liang et al [16] and Li et al. [34] utilized the frustrated total internal reflection technique (FTIR) for studying the elastoplastic deformation of metals which possess super catoptric performance. As an alternative optical technique, Hertz pioneered the use of interferometric techniques to measure surface separation and established the foundation for the field of contact mechanics [35]. For polymer materials, Krick et al. [31] employed the 0th order interference fringe to identify the actual contact regions, and Benz et al. [36] utilized optical interferometric analysis to measure polymer deformation at the contact interface. Compared to FTIR, the application of optical interferometric technique results in reduced light pollution and enhances the detection of small contact regions.

In this paper, we have conducted uniaxial tensile (UT), planar tensile (PT), and biaxial tensile (BT) experiments to comprehensively determine the mechanical property of the hyperelastic material. And, the 6th-order-Ogden constitutive model was selected and fitted in commercial software ABAQUS with the experimental data. Subsequently, rough surface contact experiments were conducted using an interferometric method and compared with the incremental model for hyperelastic materials [22] and both results reach great agreement within a contact fraction range of 90%. Furthermore, it is found that the incremental model demonstrated a strong predictive capability for the contact behavior of hyperelastic rough surface. At the same time, the application of tangent modulus introduced the nonlinearity of material. The ratio of the tangent modulus to the linear elastic modulus varies with contact stresses and consistently falls within the range of approximately 2.2 ~ 3, which aligns with the FEM results presented in the reference [22]. This research experimentally demonstrates that the influence of the material's nonlinearity on contact behavior, driven by stress concentration at the contact surface, enhances the instantaneous tangent modulus of the material at the contact interfaces.