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)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. © 1998 John Wiley & Sons, Ltd.

Jamshid Ghaboussi

David A. Pecknold

Mingfu Zhang

Rami M. Haj-Ali

International Journal for Numerical Methods in Engineering

《国际工程数值方法杂志》发表了原创论文，描述了适用于工程问题的数值方法的重大、新颖的发展。该杂志以欢迎在计算工程广泛领域的贡献而闻名，包括模型简化中的计算问题，不确定性量化、验证和确认、逆分析和随机方法、优化、元素技术、求解技术和并行计算、损伤和断裂、微观和纳米尺度力学、低速流体动力学、流固耦合、电磁学、耦合扩散现象，以及误差估计和网格生成。需要强调的是，这绝不是一份详尽的清单，尤其欢迎有关多尺度、多物理或多学科问题以及新兴主题的论文。

The International Journal for Numerical Methods in Engineering publishes original papers that describe significant and novel developments in numerical methods applicable to engineering problems. The journal is known for welcoming contributions across a wide range of computational engineering fields, including computational issues in model simplification, uncertainty quantification, validation and verification, inverse analysis and stochastic methods, optimization, element techniques, solution techniques and parallel computing, damage and fracture, micromechanics and nanomechanics, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, as well as error estimation and mesh generation. It is important to emphasize that this is by no means an exhaustive list, and papers on multiscale, multiphysics, or interdisciplinary issues, as well as emerging topics, are especially encouraged.

《International Journal for Numerical Methods in Engineering》发表原创论文，介绍适用于工程问题的数值方法的重大和新颖发展。该杂志以欢迎计算工程广泛领域的贡献而闻名，包括模型简化中的计算问题、不确定性量化、验证与确认、逆分析和随机方法、优化、元素技术、求解技术与并行计算、损伤与断裂、微观和纳米尺度力学、低速流体动力学、流固耦合、电磁学、耦合扩散现象，以及误差估计和网格生成。需要强调的是，这并不是一份详尽的清单，尤其欢迎有关多尺度、多物理或多学科问题以及新兴主题的论文。

Autoprogressive training of neural network constitutive models

The proposed autoprogressive algorithm appears to have wide application in the general area of Non-Destructive Evaluation (NDE) and damage detection and the proposed methodology can be used to determine certain damage indices, similar to the way in which constitutive models are determined.

Category	Quartile
工程技术	3
工程技术, 工程综合	3
工程技术, 数学跨学科应用	3

Autoprogressive training of neural network constitutive models

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Category	Quartile
MATHEMATICS, INTERDISCIPLINARY APPLICATIONS	1