  Indentation tests are largely exploited in experiments to characterize the
mechanical and fracture properties of the materials from the resulting crack
patterns. This work proposes an efficient theoretical and computational
framework, whose implementation is detailed for 2D axisymmetric and 3D
geometries, to simulate indentation-induced cracking phenomena caused by
non-conforming contacts with indenter profiles of arbitrary shape. The
formulation hinges on the coupling of the MPJR (eMbedded Profile for Joint
Roughness) interface finite elements which embed the indenter profile to solve
the contact problem between non-planar bodies efficiently and the phase-field
for brittle fracture to simulate crack evolution and nonlocal damage in the
substrate. The novel framework is applied to predict cone-crack formation in
the case of indentation tests with smooth spherical indenters, with validation
against experimental data. Then, the methodology is employed for the very first
time in the literature to assess the effect of surface roughness superimposed
on the shape of the smooth spherical indenter. In terms of physical insights,
numerical predictions quantify the dependencies of the critical load for crack
nucleation and the crack radius on the amplitude of roughness in comparison
with the behavior of smooth indenters. Again, the consistency with available
experimental trends is noticed.
