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. 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 strainstress relationship on the strain level is taken into consideration by taking the first order derivative with respect to spatial coordinates of the first DNN as an input 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 effectiveness of the proposed framework on a low pressure turbine disc design problem.

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