Autoprogressive training of neural network constitutive models

A new method, termed autoprogressive training, for training neural networks to learn complex stressÐstrain behaviour of materials using global loadÐdeßection response measured in a structural test is described. The richness of the constitutive information that is generally implicitly contained in the results of structural tests may in many cases make it possible to train a neural network material model from only a small number of such tests, thus overcoming one of the perceived limitations of a neural network approach to modelling of material behaviour; namely, that a voluminous amount of material test data is required. The method uses the partially-trained neural network in a central way in an iterative non-linear Þnite element analysis of the test specimen in order to extract approximate, but gradually improving, stressÐstrain information with which to train the neural network. An example is presented in which a simple neural network constitutive model of a T300/976 graphite/ epoxy unidirectional lamina is trained, using the loadÐdeßection response recorded during a destructive compressive test of a [($45)6]S laminated structural plate containing an open hole. The results of a subsequent forward analysis are also presented, in which the trained material model is used to simulate the response of a compressively loaded [($30)6]S structural laminate containing an open hole. Avenues for further improvement of the neural network model are also suggested. The proposed autoprogressive algorithm appears to have wide application in the general area of Non-Destructive Evaluation (NDE) and damage detection. Most NDE experiments can be viewed as structural tests and the proposed methodology can be used to determine certain damage indices, similar to the way in which constitutive models are determined