Similarity measures for identifying material parameters from hysteresis loops using inverse analysis

Sum-of-square based error formulations may be difficult to implement on an inverse analysis consisting of multiple tension-compression hysteresis loops. Five alternative measures of similarity between curves are investigated as useful tools to help identify parameters from hysteresis loops with inverse analyses. A new algorithm is presented to calculate the area between curves. Four additional methods are presented from literature, which include the Partial Curve Mapping value, discrete Frechet distance, Dynamic Time Warping, and Curve Length approach. These similarity measures are compared by solving a non-linear regression problem resembling a single load-unload cycle. The measures are then used to solve more complicated inverse analysis, where material parameters are identified for a kinematic hardening transversely anisotropic material model. The inverse analysis finds material parameters such that a non-linear FE model reproduces the behavior from five experimental hysteresis loops. Each method was shown to find useful parameters for these problems, and should be considered a viable alternative when sum-of-square based methods may be difficult to implement. It is important to consider multiple similarity measures in cases when it is impossible to obtain a perfect match.