A data‐driven bond‐based peridynamic model derived from group method of data handling neural network with genetic algorithm

Abstract

AbstractIn the governing equation of motion of bond‐based peridynamics, the acceleration of a material point can be considered as the response function of all the displacements of material points in the horizon and a micro stiffness containing Young's modulus and length scale. A group method of data handling (GMDH) neural network is first developed to explicitly derive the discrete bond‐based peridynamic equation of motion based on measured data in this study rather than traditional complicated mathematical derivation. In order to discover the optimal structure more efficiently and to avoid exhaustive search, genetic algorithm is incorporated into GMDH structure. It is found that the prediction results obtained by GMDH model agree well with measured values both for training and testing data. Moreover, the derived equation of motion is expressed as the product of parameter composed of Young's modulus and length scale and linear combination of displacements of material points in the horizon, which is in accordance with the original bond‐based peridynamic formulation. Furthermore, numerical benchmarks associated with elastic deformation and crack problems are performed and compared with analytical solution or finite element analysis result to verify the validity and feasibility of the proposed model.