An Event-Driven Framework for Accelerating Constitutive Integration in Multiaxial Plasticity

The local integration of elastoplastic constitutive equations is one of the most frequently repeated numerical operations in nonlinear finite element analysis. In conventional practice, the same high-fidelity return-mapping procedure is invoked at every integration point and at every load increment, regardless of whether the local state actually demands it. This work introduces an event-driven constitutive integration framework for multiaxial small-strain $J_2$ plasticity with nonlinear isotropic hardening that replaces this uniform treatment with a selective routing strategy. At each material point and each increment, three inexpensive indicators, including trial overstress, strain-increment magnitude, and directional reversal, classify the local update as elastic, mildly plastic, or severely plastic. Elastic and mild events are handled by an elastic shortcut or a single-step linearised correction, respectively, while only severe events invoke the full Newton-based radial return map. This approach ensures that the exact constitutive model is never replaced, instead is reserved for the sparse subset of increments where it is genuinely needed. The framework is implemented in a fully vectorised GPU-accelerated form and benchmarked on synthetic multiaxial cyclic strain histories applied to 12\,000 material points over 900 increments. The event-driven solver achieves a speedup of approximately $3.2\times$ in the multiaxial benchmark (and exceeding $5\times$ in a uniaxial proof-of-concept) relative to the dense exact baseline, while maintaining a mean relative stress error below $0.05\%$ and pathwise agreement that is visually indistinguishable from the exact solution across representative points spanning low to maximum plasticity. It is further realised that only $8.72\%$ of all local updates require the full exact correction. Stated otherwise, the results demonstrate that the constitutive integration loop contains substantial exploitable redundancy and that the present event-driven strategy can convert this redundancy into meaningful computational savings without sacrificing the underlying constitutive physics.