Modeling axisymmetric contact problems within strain gradient elasticity

Experimental testings indicate that the effective hardness of materials, as measured in normal contacts, depends on the size of the indenter. While this effect cannot be described by classical continuum theories, such a size-dependence can be modeled with generalized continuum theories. In this study, the application of simplified strain gradient elasticity in describing frictionless normal contacts is investigated. Axisymmetric contact problems for indenters of different shape are modeled within the framework of simplified strain gradient elasticity using a rigid body penalty-based contact approach in isogeometric analysis. The numerical implementation is verified using an existing semi-analytical solution for strain gradient elasticity. This study reveals significant deviations from classical theory, particularly in the form of the pressure distribution under the indenters. It is shown that the stress singularity present in the classical solution to the indentation test of a flat cylinder vanishes in the case of strain gradient elasticity. Furthermore, the importance of gradient elasticity for describing scale effects of normal contacts with indenters is demonstrated.