A Smooth-Activation Maximum-History Elastoplastic Update for Graphics Simulation

Abstract

History-dependent graphics solids need material updates that preserve residual deformation while remaining practical in explicit simulation and inverse problems. We present a smooth candidate activation followed by an irreversible maximum-history projection and a closed-form branchwise energy derivative. A deviatoric plastic-strain tensor stores residual direction. The downstream variable D attenuates only inelastic work and is not measured stiffness damage; an optional separate state d models unloading-stiffness loss. The radial update targets isotropic proportional or nearly proportional loading. Material-point, reduced-order, and 192-tetrahedron FEM residual-shape inverse tasks converge from all five tested initial guesses, versus two for nonsmoothed J2; smoothed J2 also succeeds in all five, demonstrating a generic benefit of smooth activation. Full-FEM gradients agree with finite differences below 3.1e-11, while analytical J2 retains the lowest forward/backward cost. The proportional-path stress RMSE against CalculiX 2.22 is 0.0314% of yield stress. An every-step audit shows that 100.000% and 99.965% of activity-weighted history growth in cube and torus compression occurs at direction turns no larger than 30 degrees; same-path Smooth History/J2 stress-discrepancy RMS is 8.88% and 9.61% of yield stress. A controlled 90-degree turn nevertheless reaches 49.39% normalized stress error, and public reverse-loading steel data falsify general cyclic use. Corrected exact-mesh structural/contact comparisons give 1.30-1.50% reaction NRMSE. An optional stiffness-loss extension calibrated on nine public concrete cycles gives a 3.35-5.83% uncertainty range on complete held-out cylinder reactions, versus 9.22% without stiffness loss. The method is a scoped graphics update with inverse-design utility, not a general constitutive or fracture model.