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Physics-informed neural network (PINN) has recently gained increasing interest in computational mechanics. This work extends the PINN to computational solid mechanics problems. Our focus will be on the investigation of various formulation and programming techniques, when governing equations of solid mechanics are implemented. Two prevailingly used physics-informed loss functions for PINN-based computational solid mechanics are implemented and examined. Numerical examples ranging from 1D to 3D solid problems are presented to show the performance of PINN-based computational solid mechanics. The programs are built via Python with TensorFlow library with step-by-step explanations and can be extended for more challenging applications. This work aims to help the researchers who are interested in the PINN-based solid mechanics solver to have a clear insight into this emerging area. The programs for all the numerical examples presented in this work are available at https://github.com/JinshuaiBai/PINN_Comp_Mech. [ABSTRACT FROM AUTHOR]

Despite its rapid development, Physics-Informed Neural Network (PINN)-based computational solid mechanics is still in its infancy. In PINN, the loss function plays a critical role that significantly influences the performance of the predictions. In this paper, by using the Least Squares Weighted Residual (LSWR) method, we proposed a modified loss function, namely the LSWR loss function, which is tailored to a dimensionless form with only one manually determined parameter. Based on the LSWR loss function, an advanced PINN technique is developed for computational 2D and 3D solid mechanics. The performance of the proposed PINN technique with the LSWR loss function is tested through 2D and 3D (geometrically nonlinear) problems. Thoroughly studies and comparisons are conducted between the two existing loss functions, the energy-based loss function and the collocation loss function, and the proposed LSWR loss function. Through numerical experiments, we show that the PINN based on the LSWR loss function is effective, robust, and accurate for predicting both the displacement and stress fields. The source codes for the numerical examples in this work are available at https://github.com/JinshuaiBai/LSWR_loss_function_PINN/. [ABSTRACT FROM AUTHOR]

• A new data-driven topology optimization (DDTO) framework is proposed. • Sensitivity analysis for discrete noisy material data sets is developed. • Verification of the new DDTO framework by truss structure designs. The application of structural topology optimization with complex engineering materials is largely hindered due to the complexity in phenomenological or physical constitutive modeling from experimental or computational material data sets. In this paper, we propose a new data-driven topology optimization (DDTO) framework to break through the limitation with the direct usage of discrete material data sets in lieu of constitutive models to describe the material behaviors. This new DDTO framework employs the recently developed data-driven computational mechanics for structural analysis which integrates prescribed material data sets into the computational formulations. Sensitivity analysis is formulated by applying the adjoint method where the tangent modulus of prescribed uniaxial stress-strain data is evaluated by means of moving least square approximation. The validity of the proposed framework is well demonstrated by the truss topology optimization examples. The proposed DDTO framework will provide a great flexibility in structural design for real applications. [ABSTRACT FROM AUTHOR]