Keywords: neural networks, genetic algorithm, viscoplasticity, stress relaxation composites.

Fiber-reinforced polymer-matrix composites (PMCs) exhibit both time- and rate dependent nonlinear behaviour under thermomechanical loading. Therefore, it is crucial to develop a constitutive model for describing the time-, rate- and temperature-dependent behaviour of PMCs. Viscoplastic constitutive equations can describe the time and rate dependence of PMCs [1]. These models are written explicitly and they involve many parameters that depend on the materials and the service temperatures. Under conditions of high stress, strain rate and high temperature, to secure more accurate results, the model has to become more complicated in the mathematical formulation, but the problem of parameter identification of the material parameters will introduce more numerical errors and instabilities to the model.

As an alternative to traditional explicit constitutive modelling, we propose using implicit constitutive modelling based on artificial neural networks (ANN) to predict the stress relaxation behaviour of PMCS. ANN can directly map the behaviour of a viscoplastic material; for example creep behaviour [2]. The difficulty in constructing these ANN implicit viscoplastic models stems from the uncertainty in constructing the neural network itself; i.e. number of layers and number of neurons in each layer.

The current work resolves the uncertainty in the ANN structure by employing genetic algorithm (GA) to optimize the number of neurons and the connections in or between the ANN hidden layers. A synthetic GA method is used. This method is a combination of both constructive algorithm and pruning based on a genetic algorithm. The method includes the following steps: a dynamic constructive method is adopted to train the initial networks; the genetic algorithm is then used to prune the trained network; then the global optimal solution can be obtained rapidly due to the good initial solution. Upon reaching an optimal ANN structure, we utilized several training algorithm to train the neural network to predict the stress relaxation behaviour of the composite based on learning different load relaxation tests performed at different temperature/strain levels. Training the ANN Quasi-Newton (BFGS) method outperformed several training algorithms such as steepest descent and conjugate gradient methods in terms of convergence rate and accuracy.

Comparison of the ANN model results to those of phenomenological approach is provided to test the ANN predictive capability for inelastic phenomena. Unlike the explicit viscoplastic model, the neural network model utilizing the Quasi- Newton algorithm predicted more accurate results at different stress-temperature conditions. Moreover, in building the neural network stress relaxation model, only one type of data is required, that is stress relaxation data at different thermomechanical histories, while viscoplastic model requires both tensile tests data together with load relaxation data.

1

M. Al-Haik, M.Vaghar, M. Shahaway, H. Garmestani, "Viscoplastic analysis of structural polymer composites using stress-relaxation and creep data", Composites B, vol. 32, pp. 165-170, 2001. doi:10.1016/S1359-8368(00)00042-1

2

M.S. Al-Haik, H. Garmestani, A. Savran, "Explicit and implicit viscoplastic models for polymeric composite", Int. J. Plasticity, vol. 20, pp. 1875-1907, 2004. doi:10.1016/j.ijplas.2003.11.017

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