General Equations Describing Elastic Indentation Depth and Normal Contact Stiffness versus Load

Area of Science:

• Solid Mechanics
• Materials Science
• Surface Science

Background:

• Existing models like JKR and DMT describe adhesive elastic contact but are limiting cases.
• The Maugis-Dugdale theory offers a more general solution but is complex for experimental data analysis.
• Scanning Force Microscopy (SFM) generates experimental data requiring accessible models.

Purpose of the Study:

• To develop a generalized equation for elastic indentation depth and load in adhesive contact.
• To create a generalized equation for normal contact stiffness and load for force modulation microscopy.
• To provide a method for easily fitting experimental data to determine interfacial energy and elastic modulus.

Main Methods:

• Developed a generalized analytical equation approximating the Maugis-Dugdale solution.
• Derived a second generalized equation relating normal contact stiffness to load.
• Proposed a framework for fitting these equations to experimental contact mechanics data.

Main Results:

• The proposed generalized equation closely approximates Maugis' solution for adhesive elastic contact.
• The derived equations are easily fitted to experimental data, including force modulation microscopy.
• Successful determination of interfacial energy and elastic modulus from experimental data is demonstrated.

Conclusions:

• The generalized equations offer a practical and accurate approach to analyzing adhesive elastic contact.
• This work simplifies the interpretation of experimental data from techniques like SFM.
• The method allows for straightforward determination of key material properties at the contact interface.