Inverse parameter identification with finite element simulations using knowledge-based descriptors

Material parameters can be determined from complex engineering processes by inverse methods: A simulation model (usually using finite elements) of the process is used, and its parameters are varied systematically until agreement between simulation and experiment is achieved. Using standard methods like the Levenberg–Marquardt algorithm or evolutionary techniques has the disadvantage of needing a large number of simulations. Here we present a new method to solve the problem of inverse identification. The material behaviour is described using auxilliary quantities, called descriptors, that are closely related to observable quantities, for example the force in a deformation process. Choosing appropriate descriptors allows to determine them rapidly using a scaling procedure. Calculating material parameters from descriptors involves inverse parameter identification methods, but no finite element simulations are needed for this step. The method is described theoretically and is numerically investigated using two examples: Forging of an elasto-plastic specimen and deformation of a hyperfoam material. The number of finite element simulations needed to identify material parameters and the total computing time are strongly reduced compared to standard methods.