Determining constitutive models from conical indentation: Sensitivity analysis

Several procedures have previously been advanced for extracting constitutive relations from the force–displacement curves obtained from indentation. This work addresses the specific problem of determining the elastic modulus E, yield stress Y, and hardening exponent n, which define the isotropic strain-hardening model from a single force–displacement curve with a sharp conical tip. The sensitivity of the inversion process was tested through a series of finite element calculations using ABAQUS. Different magnitudes of normally distributed noise were superimposed on a calculated force–displacement curve to simulate hypothetical data sets for specific values of E, Y, and n. The sensitivity of the parameter confidence intervals to noise was determined using the χ²-curvature matrix, statistical Monte Carlo simulations, and a conjugate gradient algorithm that explicitly searches the global parameter space. All three approaches demonstrate that 1% noise levels preclude the accurate determination of the strain-hardening parameters based on a single force–displacement curve.