Contact of a spherical probe with a stretched rubber substrate

Area of Science:

• Solid Mechanics
• Materials Science
• Contact Mechanics

Background:

• Understanding the mechanical behavior of soft materials under contact is crucial for various applications.
• Neo-Hookean materials are a common model for rubber-like elastomers, but their accuracy under large deformations needs validation.
• Contact mechanics of prestressed materials presents unique challenges due to altered strain fields.

Purpose of the Study:

• To develop and validate a theoretical model for the normal contact of stretched neo-Hookean substrates with rigid spherical probes.
• To predict contact area shape, load, and stiffness as functions of substrate in-plane stretch ratios.
• To experimentally assess the model's accuracy using silicone rubber under uniaxial stretching.

Main Methods:

• Derivation of a contact model based on surface Green's functions for incremental displacements.
• Formulation of both adhesive and non-adhesive contact scenarios.
• Experimental validation using uniaxial tensile testing of silicone rubber and analysis of contact parameters.

Main Results:

• The derived model successfully predicts contact area, load, and stiffness for neo-Hookean substrates under moderate stretching (stretch ratio < 1.25).
• Experimental results show good agreement with theoretical predictions within this range.
• Deviations between the model and experimental data emerge at higher stretch ratios (> 1.25) due to the material's nonlinear elastic behavior.

Conclusions:

• The neo-Hookean model provides a reliable framework for analyzing the contact mechanics of stretched elastomers at low to moderate strains.
• The study highlights the limitations of the neo-Hookean assumption for highly deformed silicone rubber.
• Further research may involve exploring more advanced constitutive models to capture the behavior of elastomers under large deformations.