Review of uniqueness challenge in inverse analysis of nanoindentation

Accurately obtaining the mechanical properties of materials is crucial for materials property evaluations and engineering designs. Nanoindentation technology has emerged as an advanced testing method due to its high precision and deep insight into the nano- and micro-mechanical properties of materials. It is widely used in fields such as thin films, semiconductor materials, and metals. However, uniquely determining the elastoplastic mechanical properties of materials from the applied load–penetration depth curve remains a significant technical challenge, which can affect the accuracy of material assessments and the reliability of engineering designs. This paper reviews the cutting-edge research progress on the inverse analysis uniqueness of nanoindentation. It examines the factors influencing uniqueness from both theoretical and experimental perspectives and explores various proposed methods, including dimensionless analysis, finite element methods, and machine learning. The integration of multi-indenter testing, residual morphology analysis, and advanced iterative algorithms significantly enhances the uniqueness of inverse analysis. Additionally, this paper discusses the mathematical complexities underlying the uniqueness problem, particularly the nonlinear relationships within constitutive models. Therefore, combining geometric mathematics with elastoplastic theory is expected to help overcome these challenges. The paper also analyzes the mathematical challenges encountered in dimensionless analysis and finite element methods. It suggests that evaluating the monotonicity of dimensionless functions is crucial for ensuring solution uniqueness. Furthermore, shape manifold techniques and statistical algorithms are proposed as potential solutions to the high-dimensional data processing challenges in finite element methods.