Non-linear finite element constitutive modeling of mechanical properties of hard and superhard materials studied by indentation

We present a new method for finite element modeling of the indentations into materials of hardness ranging up to ultra-hard ceramic coatings that accounts for the pressure enhancement of both elastic moduli and yield strength. This modeling is based on a non-linear constitutive model that uses the universal binding energy relation (UBER). A comparison with classical linear elasticity, that uses constant, zero-pressure, values of the moduli and constant yield strength, shows that the enhancement of the elastic moduli and of the yield strength due to extreme high pressures that develop in material under the indenter has a significant effect in hard and superhard materials. This enhancement has to be accounted for if accurate modeling of the mechanical response of such materials with extreme properties is to be achieved.