Fast inversion algorithm for identification of elastoplastic properties of power hardening materials from limited spherical indentation tests

An inverse problem of identification of the elastoplastic properties of power hardening engineering materials from limited spherical indentation measurements is studied. A fast algorithm for reconstruction of the Ramberg–Osgood curve σi=σ0(ei/e0)κσi=σ0(ei/e0)κ, with the strain hardening exponent κ∈(0,1)κ∈(0,1), is proposed. The main distinguished feature of this algorithm is that the only two output measured data 〈αi,Pi〉〈αi,Pi〉, i  =0,1, i.e. discrete values of the penetration depth (αiαi) and the loading force (PiPi), are required for the reconstruction of the unknown Ramberg–Osgood curve. The first measured data 〈α0,P0〉〈α0,P0〉 corresponds to pure elastic deformations, and the second one to one of the plastic deformations. The second advantage of the proposed algorithm is its well-conditionedness, different from parametrization algorithms proposed in previous studies. Numerical examples related to applicability and enough accuracy of the proposed approach are presented for the noise free and noisy data.

► A fast inversion algorithm is proposed for identifying elastoplastic properties for Ramberg–Osgood type engineering materials.
► The algorithm is well-conditioned and uses minimal number of measured indentation data.
► Numerical results demonstrate high accuracy of the algorithm for noise free as well as noise data.