A data-driven process for estimating nonlinear material models

Driven by the wide range of new material properties offered by multi-material 3D printing, there is emerging need to create predictive material models for these materials. A data driven process for estimating nonlinear material model is presented in this paper. In contrast with classical methods which derive the engineering stress-strain relationship assuming constant cross-section area and fixed length of a specimen, the proposed approach takes full advantage of 3D geometry of the specimen to estimate the material models. Give a hypothetical material model, virtual tensile tests are performed using Finite Element Analysis (FEA) method, and the parameters of the material model are estimated by minimizing the discrepancies of the virtual responses and the experimental results. The detailed material models, numerical algorithms as well as the optimization approaches are presented and finally preliminary results are offered. Introduction Driven by the wide range of new material properties offered by multi-material 3D printing, there is emerging need to create predictive material models for these materials. Tensile tests are one of the most widely used mechanical tests to derive such material properties as Young’s modulus and yield stress. The output of the tensile test is a force-elongation curve, which is usually converted to the stress-strain curve for estimation of material properties. In such a conversion, it is usually assumed that the cross-section area and the length of the specimen are constant in the entire tensile test. The derived stress/strain is referred to as engineering stress/strain. Because of its simplicity and satisfactory accuracy in modeling metallic materials, it has been widely used in the past. For metallic materials, such engineering stress-strain based parameter estimation proves to be effective, since metals are significantly stiff and the change in the cross-section of the specimen is usually negligible. For polymer materials, such simplifications may introduce significant errors in the estimated parameters. In lieu of such classical approaches, there have been many targeted approaches that tries to get the true stress-strain from tensile tests. Arriaga et al [1] proposed empirical formulae to convert engineering stress-strain to true Cauchy stress. Grytten et al [2] used Digital Image Correlation (DIC) to measure local strain values in the tensile test of ductile thermoplastic materials. In this paper, a different data-driven approach is proposed to estimate the material models. We propose different hypothetical material models, and for each material model, the parameters are estimated by minimizing an objective function which relates the model parameters to the discrepancies of the virtual and experimental tensile test data.