AI summaryⓘ
The authors developed a new way to simulate materials that remember how they were stretched or damaged over time, especially when forces are applied repeatedly. Their method updates material properties in a smooth and simple way to capture irreversible changes without needing complex calculations every step. They tested it on different shapes and loading conditions, showing it works well for certain types of loading but is not suitable for all cases like sharp directional changes or more complex damage. They also compared it to a traditional method, finding it slower but easier to implement and smoother. Overall, their approach is designed for specific simulations where smoothness and simplicity are more important than speed or extreme generality.
elastoplasticitydamage mechanicsplastic strainirreversibilityexplicit simulationyield surfacereturn mappingisotropic loadingenergy gradientvectorization
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.