SECA: Strict-Elastic Compact Activation for Differentiable Elastoplastic Deformation

Abstract

Return mapping keeps an exact elastic domain but switches its response tangent at yield, while smoothing laws with a sub-yield tail admit plastic flow below the threshold. We present SECA, a Strict-Elastic Compact Activation method for differentiable elastoplastic simulation. SECA prescribes a bounded $C^2$ activation over a finite positive-overstress interval and integrates it into a Perzyna-type flow law, so the implicit update returns exactly zero plastic increment for sub-yield trials while smoothing the onset. For scalar and proportional isotropic $J_2$ updates we derive an exact decomposition of the plastic-increment discrepancy into finite-width and viscosity contributions, and an explicit algebraic budget for the transition width. The update is embedded in finite-deformation loading histories with contact and complete unloading, and differentiated to released equilibria. Controlled indentation results stay closely matched. In the tested coarse cube-indentation run, where the transition is crossed without intermediate increments, SECA reduces whole-run Newton iterations by 47% and backtracking halvings by 93% against return mapping. A four-method comparison evaluates released-shape error and computational cost across loading partitions, and on a contact scene the path derivative drives a bounded control task to its target in three iterations. Further examples show elastic recovery and residual deformation under compression, tension and bending.

arXiv comment69 pages, 24 figures, including appendices. Substantially revised version with a new title, SECA formulation, updated analysis, and additional experiments