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Abstract
To accommodate the rising demand in identifying material properties of polymer thin films using the indentation test, an automated, systematic and efficient analysis methodology is proposed. This method includes experimental design, finite element analysis, design sensitivity analysis, and optimization techniques. The identification of material properties is treated as an optimization problem, minimizing the difference between the numerical simulation results and the experimental data.
Finite element analysis is the bottleneck in the optimization procedure since it takes a large portion of the total computational time. The modeling of the indentation test is simplified as an axisymmetric, small deformation problem with frictionless, small sliding contact. The formulations of the response and sensitivity analysis with contact are presented. The governing equations of the response and sensitivity analysis have the same tangent stiffness. The inclusion of the contact does not change this favorable property. Verifications have been performed on the implemented finite element code comparing both the theoretical results and ABAQUS simulation results. Good agreement has been achieved for both responses and sensitivities.
The implemented finite element code provides the function evaluation routine for the optimization process. To reduce the computational cost, it is essential that the number of iterations is as small as possible. Significant effort has been put on the estimation of the material constants. A good estimation will be close to the optimal point; and therefore can avoid being trapped into a remote minima region. The implemented estimation method is based on both theoretical solutions and empirical relations. In this thesis, the behavior of a polymer material is described by a 3-parameter rheological model, which includes a dashpot in parallel with an elasto-plastic spring. This spring represents a linear hardening plastic response. The analytical solution of viscoelastic indentation helps determine the viscosity of the dashpot and the elasto-plastic modulus. The remaining parameter in the model is obtained through curve fitting, which requires one finite element run.
The proposed estimation method provides an excellent estimation of the material constants. More accurate results are obtained through numerical optimization with the estimation as the starting point. The BFGS method is chosen as the optimization algorithm with slight modification to accommodate the simple bounds. Fast convergence is achieved using this modified BFGS method. Normally, 7 iterations are needed for convergence.
