Abstract
Neural networks provide a potentially viable alternative to a differential equation based constitutive models. Here, a neural network model is developed to describe the large deformation response of a Levy-von Mises sheet material with isotropic strain hardening. Using a conventional return-mapping scheme, virtual experiments are performed to generate stress-strain data for random monotonic biaxial loading paths (up to strains of 0.2). Subsequently, a basic feedforward neural network model is trained and validated using the results from virtual experiments. The results for a shallow network with only two hidden layers show remarkably good agreement with all experimental data. The identified neural network model is implemented into a user material subroutine and used in basic structural simulations such as uniaxial tensile and notched tension experiments. In addition to demonstrating the potential of neural networks for modeling the rate-independent plasticity of metals, their application to more complex problems involving strain-rate and temperature effects is discussed.
Highlights
Proper identifying a material model in finite element analysis – to predict the strain and stress distribution and failure and fracture – is often an extensive and tedious task when a complex material model needs to be studied
Virtual Experiments made by Zerilli–Armstrong Model The well-known Zerilli–Armstrong constitutive relations is widely used to characterize the hardening of material at different temperature and strain rate hardening
In this research, we showed that an artificial neural network is an alternative tool that can assist in modeling a material response and predicting plasticity in metal forming applications
Summary
Proper identifying a material model in finite element analysis – to predict the strain and stress distribution and failure and fracture – is often an extensive and tedious task when a complex material model needs to be studied. Mechanical characterization of material is mainly determined through the high number of experiments and applying the hybrid experimental-numerical approach [1,2,3,4,5]; it is emerging to employ a fully automated testing system (that will be soon available) to perform experiments. We show the machine learning (here the neural network) as an alternative method for a differential equation based constitutive model.
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