Coupling physics-informed neural networks and constitutive relation error concept to solve a parameter identification problem

Identification of material model parameters using full-field measurement is a common process both in industry and research. The constitutive equation gap method (CEGM) is a very powerful strategy for developing dedicated inverse methods, but suffers from the difficulty of building the admissible stress field. In this work, we present a new technique based on physics-informed neural networks (PINNs) to implement a CEGM optimization process. The main interest is to easily construct the admissible stress thanks to automatic differentiation (AD) associated with PINNs. This new method combines the high quality of the CEGM with the numerical effectivity of the PINNs and realizes the identification of material properties in a more concise way. We compare two variants of the developed method with the classical identification strategies on simple two-dimensional (2D) cases and illustrate its effectiveness in three-dimensional (3D) problems, which is of interest when dealing with tomographic images. The results indicate that the proposed method has good performance while avoiding complex calculation procedures, showing its great potential for practical applications.