Bifurcation of elastic solids with sliding interfaces

Area of Science:

• Biomechanics
• Solid Mechanics
• Materials Science

Background:

• Lubricated sliding contact is critical in biomechanics and micro-engineering.
• Existing models for finite strain contact between soft solids are incomplete or erroneous.
• Accurate formulation is needed to understand phenomena like bifurcation.

Purpose of the Study:

• To correctly formulate the finite strain problem of lubricated sliding contact between two elastic nonlinear solids.
• To derive incremental equations and an exclusion condition for bifurcation.
• To demonstrate the necessity of an accurate interface model for predicting bifurcations.

Main Methods:

• Development of a novel finite strain formulation for lubricated sliding contact.
• Derivation of incremental equations and bifurcation exclusion conditions.
• Experimental validation of the theoretical model.

Main Results:

• The study provides a non-trivial, correct formulation of the lubricated sliding contact problem.
• Previous models based on frictionless or spring-type interfaces fail to predict bifurcations in tension.
• The proposed model accurately predicts bifurcations, confirmed by experimental results.

Conclusions:

• The correct formulation of lubricated sliding contact is essential for understanding soft solid interactions.
• Accurate interface modeling is crucial for predicting bifurcations and instabilities.
• The methodology presented enables the determination of bifurcations in lubricated sliding contacts.