An efficient kernel learning-based constitutive model for cyclic plasticity in nonlinear finite element analysis

Machine learning-based data-driven constitutive models have shown promise in capturing behavior of elastoplastic materials. However, training these models is usually computationally expensive and can become even more time-consuming as the size of the training data set increases. To address this challenge, this paper proposes a novel efficient kernel learning-based constitutive (EKLC) model to learn constitutive relations for elastoplastic materials directly from stress-strain data. The proposed EKLC model, from a neural network (NN) perspective, consists of six layers: input, hysteresis, feature, basis, kernel and output. The hysteresis layer enables the learning of path-dependent behavior of elastoplastic materials, while the basis layer ensures computational efficiency by allowing for nonlinear mappings between hysteresis neurons and stress. The proposed EKLC model outperforms NN-based models in terms of computational efficiency, interpolation and extrapolation capabilities by thorough comparisons with numerical results obtained from learning two widely used elastoplastic constitutive models for steel materials and from experimental data sets. Furthermore, the EKLC model is successfully applied to the nonlinear finite element analysis with cyclic plasticity and to learning the multidimensional stress-strain relationships. Noteworthily, training the proposed EKLC model runs much faster than training NN-based models, with a maximum speedup of about 496000 times.