Analysis Methodology of Inelastic Constitutive Parameter Using State Space Method and Neural Network

Abstract

Background/Objectives: In this paper, we present a method for describing a set of variables of an inelastic constitutive equation based on state space method (SSM) and neural network (NN). The advantage of this method is that it can identify the appropriate parameters.

Methods/Statistical analysis: Two NNs based on SSM are proposed. One outputs the ratio of inelastic strain for the internal parameters of the material, and the other is the following state of the inelastic strain ratio and material internal variable. Both NNs were trained and successfully collected using input and output data generated by Chaboche 's model.

Findings: As a result, previous NNs have demonstrated their validity as a powerful material model. However, the training data for the proposed NN can’t be easily obtained from actual experimental data. Previous neural networks can reproduce the original stress-strain curves. The NNs also produced untrained curves to demonstrate interpolation capabilities. It was also found that the NNs can be estimated to be close to training data. The author defines the implicit constitutive model and proposes the implicit viscous constitutive model using NNs. In modeling, inelastic behavior is generalized in state space representation, and the state space form is constructed by NNs using an input-output data sets. The proposed model was first created from the pseudo-experimental data generated by one of the commonly used configuration models and has been found to be a good replacement for the model. The actual experimental data was then tested, and the proposed model showed the accuracy of its superiority over all existing specified models because the amount of model errors was negligible.

Improvements/Applications: The comparison between the NN constitutive laws   with the Chaboche’s model indicates that the NN constitutive law generated curves with less model errors than the experimental data, thereby indicating the superiority of the neural constitutive law to explicit constitutive laws as a material model.