Identification of material properties using indentation test and shape manifold learning approach

• We construct a lower-dimensional space in which a smooth manifold is approximated.
• We develop a family of algorithms to identify material properties in the shape space.
• Our protocol is verified by a real indentation test starting from different initial points.

The conventional approach for the identification of the work hardening properties of a material by an indentation test usually relies on the force–displacement curve. However, finite element modeling of the indenter–specimen system is a complex task, and the unicity of the solution to the inverse problem of identifying material parameters using the force–displacement curve is not always guaranteed. Also, the precise measurement of the displacement of the indenter tip requires the determination of the indenter frame compliance and indenter tip deformation. To alleviate these problems, we propose in this work an approach based solely on the 3D indentation imprint shape measured after indenter withdrawal, rather than relying on the minimization of the pointwise discrepancy between the experimental and simulated indentation curve. We first build a mathematical “shape space” of indentation shapes in which a lower-dimensional manifold of imprints admissible according to a postulated material constitutive law is approximated. Then, we solve the inverse problem by using a series of predictor–corrector algorithms minimizing the distance between the estimated solution and the experimental imprint in this shape space. We finally apply the proposed approach to indentation tests using a spherical tip indenter on two different materials: a C100 steel specimen and a specimen of the AU4G (AA2017) aluminum alloy.