Physics-informed neural network frameworks in strong and weak forms for elastoplastic analysis

Physics-informed neural networks have recently achieved remarkable success in solving elastic problems by embedding governing equations into the training of neural networks. Building upon these advances, this study extends physics-informed neural networks to material nonlinearity and develops two computational frameworks for small-strain von Mises elastoplasticity. The strong-form framework enforces governing equations through pointwise residual minimization, enabling unified forward–inverse modeling of field variables and unknown material parameters. In contrast, the weak-form framework derived from total potential energy minimization allows data-free learning of elastoplastic evolution through incremental loading, yielding stable and physically consistent predictions. The recently developed Kolmogorov–Arnold network is further incorporated and compared with the conventional multilayer perceptron. Results show that the Kolmogorov–Arnold network alleviates the gradient oscillation and convergence instability in the weak-form framework but performs less effectively in the strong form. Furthermore, validations against reference solutions from conventional numerical methods demonstrate the potential of the developed physics-informed neural network frameworks as mesh-free surrogates for elastoplastic analysis.