Wednesday  |  Monongahela  |  09:00 AM–09:20 AM

#13355, Novel Physics-Informed Neural Network Approach for Large-Deformation Mechanics Constitutive Model Calibration

The Virtual Fields Method (VFM) and Finite Element Model Updating (FEMU), among other inverse problem methodologies, have shown success in calibrating constitutive model parameters for anisotropic and nonlinear materials. However, VFM faces difficulties when only ingesting full-field surface data for specimens where plane-stress assumptions break down, and FEMU remains challenging when calibrating complex models where computational inefficiencies of the inverse problem are intractable. In this work, we use emerging physics-informed machine learning techniques rather than traditional approaches to calibrate constitutive models in large deformation scenarios using full-field experimental data. Physics-informed neural networks (PINNs) can utilize measured data for model calibration while approximately maintaining the known physical laws of the system. PINNs as a computational tool are meshless, with collocation points that are unconnected, meaning there is no need for interpolation strategies between the full-field measurement grid and the computational grid. In a PINN inverse problem, the unknown material parameters are added to the solution basis like VFM. Rather than shape functions, the solution basis in the case of PINNs are the weights and biases of the neural network and the unknown material parameters are added as additional trainable neural network parameters. To minimize the error between the measured full-field displacement data and global force data, we formulate a physics-informed loss function; we use the principle of stationary potential energy (whose first variation is the principle of virtual work) as the physics-informed piece of our loss function and mean-squared errors for the full-field displacement data and the global force data. We demonstrate this approach using synthetic data, generated from finite element simulations, representative of full-field experimental data for an initial exemplar of a flexible polymer foam undergoing large heterogenous deformation to calibrate several hyperelastic constitutive models. These include a nearly incompressible Gent model that captures polymer chain lock-up, a phenomenological compressible foam model, and a simple hyperelastic-damage model, demonstrating the ability of our PINNs approach to calibrate constitutive models with state variables. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.

Craig Hamel   Sandia National Laboratories
Sharlotte Kramer   Sandia National Laboratories
Kevin Long   Sandia National Laboratories