Learning 1D stress resultant plasticity from 2D continuum plasticity: a physics-informed neural network model reduction approach

Abstract

A physics-informed neural network (PINN) is developed to identify a closed-form moment–curvature constitutive law for elastoplastic Euler–Bernoulli beams. The fiber-level von Mises response integrated through the thickness is recast as a structural plasticity problem with a single yield surface in moment space. The primary novelty is the data-driven identification of the structural kinematic hardening closure, an emergent property of the dimensional reduction, absent from the local material law, embedded inside the exact algorithmic return mapping, enforcing algorithmic admissibility by construction rather than by penalty terms. A cyclic maturity indicator and architectural constraints ensure Masing-rule consistency between virgin and stabilized branches and positivity of the hardening modulus. Trained weights are extracted to explicit linear algebra, enabling microsecond-scale constitutive evaluation in standard finite element codes. Two boundary value problems validate the 1D model against 2D plane-stress references and closed-form analytical solutions, confirming quantitative agreement in force–displacement response and deflection profiles across cyclic loading–unloading. Computation times are orders of magnitude shorter than the plane-stress reference, demonstrating the practical efficiency of the model reduction.