Physics-informed neural networks (PINNs) are a data-driven method for solving forward and inverse problems of ordinary and partial differential equations, based on sparse, noisy and unstructured data-points. The methods turn out to be effective in tackling inverse problems in computational fluid mechanics, and we extend the PINNs to inverse problems in hyperelastic solid mechanics. There have been very few reports in literature on these problems. To demonstrate the ability to handle the nonlinearity in hyperelasticity, we first employ PINNs to solve forward boundary value problems. We observe that PINNs can accurately solve for the displacement and stress fields compared to the reference solution computed by the finite element method. We then focus on inverse problems of identifying geometric and material parameters, where we consider a chunk of 2D incompressible hyperelastic solid under uniaxial/biaxial tension, with inhomogeneity of three different cases: (1) one elliptical hole, (2) two circular holes, and (3) one circular inclusion. We solve the parameter estimation problem based on the displacement observations on the boundaries of the solid body. For the first two cases, we surprisingly find that PINNs can accurately identify the location, size, and shape of the hole(s). For the inclusion case, all the parameters are well recovered except for the Young’s modulus of the inclusion. The inaccurate estimate of Young’s modulus could arise from the ill-posedness of the parameter estimation problem. One attractive feature of the PINNs is that being essentially meshless PINNs are easily applied to geometric identification problems with unknown boundary location. The finite element method, however, requires repeated re-meshing in each optimization iteration, which could be time-consuming for complex geometries.
2021-04-07 08:00:00
