Adhesion of large-deformation elastic spherical contact

This paper presents an explicit form of Tatara's theory for the large-deformation elastic spherical contact in the absence of adhesion and friction. In the case of the linear Young's modulus and neglecting the radial expansion of the contact surface, the Hertz's linear relationship between the contact radius and the power of 1/2 to the elastic displacement is modified by adding a term of the elastic displacement, while the Hertz's relationship between the applied load and the contact radius still holds. In the case of the nonlinear Young's modulus and considering the radial expansion of the contact surface, the relationship between the contact radius before the deformation and the elastic displacement is explicitly given by introducing a term of the power of 3/2 to the radius of the sphere into the Hertz's relationship. Utilizing this relationship, the explicit dependence of the applied load and the contact radius after the deformation on the contact radius and the elastic displacement are also obtained. Based on the Tatara et al.'s model for the large-deformation elastic spherical contact with a constant modulus and without the radial expansion of the contact surface, the extended JKR adhesion model is derived along Johnson et al.'s path. Introducing the DMT adhesion, the extended COS adhesion model is obtained along Schwarz's path. It provides a theoretical basis for studying the large-deformation elastic spherical contact.