Prediction of Non-Linear Mechanical Behavior With Deep Neural Network: Application on Low Pressure Turbine Disc

High-fidelity simulations are capable to provide accurate description of physical phenomena. Meanwhile, the calculation accuracy is always gained at the expense of numerical cost. This gap prevents utilization of such simulations in highly iterative design optimization process. To address this problem, surrogate models, which approximate the high-fidelity models, are introduced for the purpose of realizing design acceleration. Thanks to the increase of computational capacity and the diversification of computational means, deep learning techniques have shown great successes in learning representations from data in the past decade. Following this trend, efforts have been made in the literature to apply Deep Neural Network (DNN) as surrogate model. Common practice consists in utilizing a single DNN to predict a certain physical property given input design parameters, and the DNN is trained by corresponding simulation results. However, most of the complex high-fidelity simulations involve nonlinear physical laws, e.g. elasto-plasticity, which cannot be explicitly depicted by the applied single DNN model. As a consequence, different physical quantities, that are physically related, need to be predicted separately, and the corresponding physical law is not necessarily respected. In the present work, static mechanical simulation with nonlinear constitutive law is addressed with a novel approach in a deep learning framework. We approximate the displacement and the nonlinear constitutive law by two deep neural networks. The first DNN acts as a prior on the unknown displacement field, while the second network aims at describing the nonlinear strain-stress relationship. The dependence of the strain-stress relationship on the strain level is taken into consideration by taking the first order derivatives with respect to spatial coordinates of the first DNN as inputs of the second network. A new loss model combining the error in displacement field prediction and constitutive law description is proposed to train the two DNNs together. We demonstrate the accuracy and efficiency of the proposed framework on a low pressure turbine disc design problem. Static mechanical finite element simulations considering an elasto-plastic constitutive law are performed by altering design parameters and boundary conditions. The displacement, strain and stress values on the finite element mesh nodes are utilized as training data. Once trained, the first DNN provides directly the prediction of the displacement field and its first-order spatial derivatives are used to calculate the strain field. The stress field is obtained with the second DNN and the calculated strain field. Taken together, with the proposed approach, we are able to predict the displacement, strain and stress fields by taking into account the applied constitutive law given input design parameters and boundary conditions on the turbine disc.