Modeling the nanoindentation of elastoplastic materials with nonlinear adaptive springs (NASs)

In this paper, the β-material concept helps to elaborate and explore a new model for the indentation cycle of elastoplastic materials. The proposed approach takes into account the nonlinear behavior of homogeneous and isotropic materials. It uses the idea of a nonlinear adaptive spring (NAS) with changing properties according to the depth of penetration to accurately reproduce the material behavior in loading and unloading stages. The properties of the adopted NAS are included in its own stiffness function κ appearing in the form of an infinite sum of which the convergence and some properties are discussed in detail. This new model, which allows the indentation cycle to be reproduced whatever the penetration depth, permits at the same time a direct calculation of the involved energy terms. It also provides the possibility to perform separate analysis of the plastic energy, which allows distinguishing between different types of the material behavior and a better understanding of its nature. A validation is accomplished by applying the method to three different materials.