Calibration of the Nonlocal Dynamic Deformation Model of a Flexural Beam Based on Numerical Experiment Results

In this paper, the problem of numerical modeling of the dynamic behavior of bending beams made of the materials with a developed internal structure is considered. The simulation is performed taking into account the non-local elastic properties of the material in time. According to the principals of nonlocal mechanics, it is assumed that elastic forces in a structure depend on the entire history of its deformation, and not only on the instantaneous deformed state. The proposed dynamic deformation model is proposed as an alternative to detailed three-dimensional models. The nonlocal dynamic deformation model is integrated into the algorithm of the FEA method to make it applicable to solving applied engineering problems. The numerical implementation of the model is performed in Python. A technique for selecting the scale parameter of a non-local model based on experimental data using the least squares method and the dichotomy method has also been developed and implemented. To identify the possibility of extrapolation of the scale parameter values determined according to the developed methodology, a series of numerical experiments were conducted, on the basis of which scale parameters for beams of different lengths were obtained and the stability of the nonlocal model was evaluated.