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.