Perturbation Methods in Indentation Problems

Asymptotic Thinking in Continuum Mechanics 
• Linearization around a known solution 
• Perturbations of geometry vs. material properties 
• Role of boundary conditions in asymptotic models 
Indentation of Graded Media 
• Indentation of homogeneous vs. graded materials 
• Identification of the perturbation parameter (weak grading) 
• Derivation of first-order corrections to contact stiffness 
Incremental Indentation Stiffness 
• Concept of effective modulus

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