A new method for theoretical analysis of static indentation test

Area of Science:

• Solid Mechanics
• Mathematical Modeling
• Theory of Elasticity

Background:

• Indentation problems are crucial in material science and engineering.
• Existing methods often rely on complex integral equations.
• Analyzing infinite elastic layers on rigid foundations presents unique challenges.

Purpose of the Study:

• To develop a new mathematical method for analyzing the indentation of an infinite elastic layer on a rigid foundation.
• To provide a more efficient and accessible solution compared to existing integral equation methods.
• To derive closed-form solutions for indentation problems involving cylindrical or spherical indenters.

Main Methods:

• A novel mathematical approach was employed, avoiding traditional Fredholm integral equations.
• The problem was reformulated as a mixed boundary-value problem within the theory of elasticity.
• Solutions were derived using an infinite series expansion.

Main Results:

• Closed-form solutions were successfully obtained for the indentation problem.
• The new method demonstrates efficient convergence, typically requiring fewer than 10 terms of the series.
• The analysis considered both bonded and unbonded interfaces between the elastic layer and the rigid foundation.

Conclusions:

• The developed mathematical method offers a significant advancement in solving elastic layer indentation problems.
• This approach provides a computationally efficient and accurate alternative for analyzing material deformation under indentation.
• The findings are applicable to scenarios involving various indenter shapes and interface conditions.