Indentation of transversely isotropic power-law hardening materials: computational modelling of the forward and reverse problems

Using a combination of dimensional analysis and large deformation finite element simulations of triple indentations of 120 materials, a framework for capturing the indentation response of transversely isotropic materials is developed. By considering 4800 combinations of material properties within the bounds of the original set of 120 materials, forward algorithms that predict the indentation response of materials and reverse algorithms that predict the materials’ elastic and plastic properties from experimentally measured indentation responses are formulated for both longitudinal and transverse indentations. Issues of accuracy, reversibility, uniqueness and sensitivity within the context of the indentation of transversely isotropic materials are addressed carefully. Using 1400 combinations of material properties, it is demonstrated that there is perfect reversibility between the material properties and their indentation responses as predicted by the forward and reverse algorithms. On average, the differences between the results of the finite element analysis and those predicted by the forward algorithms for longitudinal or transverse indentations are less than 1%, thus demonstrating the high accuracy and uniqueness of the forward analysis. For longitudinal and transverse indentations, the reverse algorithms provide accurate results in most cases with an average error of 3 and 6%, respectively. A sensitivity analysis with a ±2% variation in the material properties in the forward algorithm and ±2% variation in the indentation responses in the reverse algorithms demonstrated the robustness of the algorithms developed in the present study, with the longitudinal indentations providing relatively less sensitivity to variability in indentation responses as compared to the transverse indentations.