Autoprogressive training of neural network constitutive models

Abstract

A new method, termed autoprogressive training, for training neural networks to learn complex stress-strain behaviour of materials using global load-deflection 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 finite element analysis of the test specimen in order to extract approximate, but gradually improving, stress-strain 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 load-deflection response recorded during a destructive compressive test of a [($45) ] 1 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) ] 1 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.

Explicit analysis technique for nonlinear inverse mechanics problems

“…Then, the present approach is used to solve a nonlinear elastic truss problem presented by Ghaboussi et al [1] for the sake of comparison between the two approaches. Finally, the present approach is used to solve a 2D nonlinear elastic finite element mesh subjected to uniaxial pressure.…”

“…In this example, the present approach is compared to the approach developed by Ghaboussi et al [1]. This comparison is accomplished by solving the same example presented by Zhang [14].…”

“…Two groups of researchers ( [1,14] and [10][11][12]) have tried to use pre-defined global structural response at specific points to back-predict the local stress-strain relationship. They formulated their procedures based on a combined finite element and neural network analysis.…”

“…Furthermore, the solution strategies followed have resulted in different levels of success in convergence at different convergence rates or computational effort. Ghaboussi et al [1] used a dual load and displacementcontrol analysis to incrementally-iteratively obtain sets of improved stress-strain data at all integration points for a certain load step. Then, they added these sets of data points to the data sets of the neural network, trained up to that load step, for retraining.…”

“…This requires repeating the entire procedure through a number of passes over all load step iterations to improve convergence. Ghaboussi et al [1] used a Conjugate Gradient Method to solve for the incremental displacements by minimizing the derivatives of the total potential energy. All these factors make this approach computationally expensive to implement.…”