Parameter identification of the viscoelastic constitutive model for particle filled polymer composites based on physics-informed neural operator

The time-/temperature-dependent viscoelasticity behaviors in polymer composites are due to the memory decay effects, inducing various interesting phenomena, including the shape memory effects, the morphology evolution in living of organisms, temperature-dependent fracture behaviors, and so forth. To model those behaviors, various constitutive models based convolutional integrals have been developed for capturing viscoelasticity. However, the more refined model introduced a greater number of parameters and made the parameter identification more intricate, hardening their applications. To solve this problem, we developed a viscoelastic constitutive artificial neural network (VCANN) for automated parameter identification. Following the recently developed physics-informed neural operator, the activation functions of the network architecture were chosen to incorporate the physical knowledge in the standard viscoelastic model within the continuum mechanics framework. This VCANN is equivalent to the viscoelastic model, mapping the input variables (time, temperature, and deformation histories) to the stress responses, and the network node weights are equivalent to the model parameters. Therefore, the parameter identification problems are equivalently transformed into the training problem of the VCANN. To validate the parameter identification by this VCANN, we used the finite element (FE) simulation method to generate datasets of the mechanical responses in polymer composites under different strain states (uniaxial tension and equibiaxial tension) and different loading history (monotonic stretching, relaxation, and step loading). Six training scenarios indicate that as the dataset incorporates more diverse material deformation features, the parameters identified by VCANN become more precise. The datasets should include both uniaxial and biaxial tensile data to achieve the decoupled identification of bulk modulus and shear modulus. Overall, this developed method could reduce the application threshold of the viscoelastic constitutive model by establishing a bridge between the results of experiments and the input of parameters in FE simulations.