🤖 AI Summary
This work addresses the challenge in computational solid mechanics of simultaneously preserving irreversible plastic deformation and continuous damage evolution during complex loading–unloading–reloading cycles. To this end, the authors propose a compact, vectorizable explicit update algorithm that couples elastoplasticity and damage. The method employs a softplus-based equivalent plastic strain combined with a maximum historical projection to enforce irreversibility, and introduces an exponential scalar degradation variable to track damage evolution. Within a unified energy framework, both active and frozen solution branches are resolved analytically, thereby eliminating the need for local Newton iterations. Numerical experiments demonstrate high accuracy under proportional or near-proportional loading (with only 1.53% error), implementation simplicity, and gradient consistency. Although error increases under large path-angle reversals, the approach achieves enhanced smoothness and algorithmic robustness at minimal additional computational cost.
📝 Abstract
History-dependent solids require material updates that preserve irreversible deformation and progressive degradation during loading, unloading, and reloading. We present a compact, vectorizable elastoplastic-damage update for explicit graphics simulation, designed for smooth activation and closed-form evaluation rather than exact yield-surface enforcement. A softplus function generates a candidate equivalent plastic strain, a maximum-history projection enforces irreversibility, and a deviatoric plastic-strain tensor retains the residual direction. An exponential scalar degradation variable is driven by the stored history. The active and frozen branches are evaluated analytically from one response energy without a local Newton solve.
We evaluate the method using one-dimensional cyclic tension, two-dimensional cantilever bending, controlled three-dimensional platen compression, and a genus-one torus. The results verify residual deformation, monotone internal variables, branchwise energy-gradient agreement, and mesh-resolution sensitivity. An analytical J2 radial-return baseline is compared both as a vectorized kernel and within the same structural solver. The baseline is 1.51--3.08 times faster as a kernel and 1.69 times faster in the structural material update, showing that our contribution is smoothness and implementation simplicity rather than raw speed. A path-direction sweep gives 1.53% normalized equivalent-stress error under proportional loading but 49.39% for a fixed-magnitude 90-degree turn. This quantifies the method's intended restriction to isotropic, proportional or nearly proportional loading; it is not a replacement for general return mapping, anisotropic damage, or phase-field fracture.