Analysis of the effect of a compliant layer on indentation of an elastic material

• The indentation deformation of an elastic cylinder surrounding by a thin film was analyzed.
• Analytical relationships between the indentation load and the indentation depth were derived.
• The deformation of the elastic film changes the indentation load–displacement relationship.

Considering the possible effect of the thin protein-rich sheath on the indentation deformation of an enamel rod, we analyzed the indentation response of an elastic cylinder with a compliant layer between the cylinder and rigid-surrounding material. For the film thickness much less than the characteristic dimension of the cylinder, closed-form solutions were obtained between the indentation load and the indentation depth, which depends on the film thickness and the ratio of the Young's modulus of the cylinder to the Young's modulus of the film. The finite element results supported the relationships for the ratio of the film thickness to the characteristic dimension of the cylinder less than or equal to 1/3. The indentation load required to produce the same indentation displacement decreases with increasing the ratio of the Young's modulus of the cylinder to the Young's modulus of the film for compressible-elastic films. Incompressible-elastic films have no significant effect on the indentation response of the elastic cylinder.

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