<p>The strain gradient effect can play an important role in microscale contact. On the basis of a simplified strain gradient elasticity theory suggested by Altan and Aifantis, this paper considers the cylindrical indentation of a linear elastic half-plane. With the surface Green’s function that accounts for strain gradient effect, the governing integral equation for this two-dimensional contact problem is derived and subsequently solved using the Gauss–Chebyshev method. The results reveal that the contact pressure distribution deviates significantly from the classical Hertzian pressure when the contact length is comparable to the material length scale parameter. In contrast to the classical Hertz theory, the presence of strain gradient effects results in the substrate performing stiffer and yields more uniform Cauchy stress distribution nearby the contact region. Furthermore, the dependence of indentation force on contact half-width is presented. Unlike previous studies that assumed the contact pressure following the classical one, the current solution provides a more accurate interpretation of contact size dependency.</p>

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Two-dimensional Hertzian contact problem based on a simplified strain gradient elasticity theory

  • Weike Yuan,
  • Gangfeng Wang

摘要

The strain gradient effect can play an important role in microscale contact. On the basis of a simplified strain gradient elasticity theory suggested by Altan and Aifantis, this paper considers the cylindrical indentation of a linear elastic half-plane. With the surface Green’s function that accounts for strain gradient effect, the governing integral equation for this two-dimensional contact problem is derived and subsequently solved using the Gauss–Chebyshev method. The results reveal that the contact pressure distribution deviates significantly from the classical Hertzian pressure when the contact length is comparable to the material length scale parameter. In contrast to the classical Hertz theory, the presence of strain gradient effects results in the substrate performing stiffer and yields more uniform Cauchy stress distribution nearby the contact region. Furthermore, the dependence of indentation force on contact half-width is presented. Unlike previous studies that assumed the contact pressure following the classical one, the current solution provides a more accurate interpretation of contact size dependency.