用于图形模拟的光滑显式弹塑性损伤更新
SECA: Strict-Elastic Compact Activation for Differentiable Elastoplastic Deformation
- Shanghai Jiao Tong University（上海交通大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究针对历史相关固体在图形模拟中的材料更新问题，提出紧凑可矢量化的弹塑性损伤更新方法，通过特定函数和张量确保相关特性，经多种模型评估验证了有效性，与基线比较显示其优势及适用加载限制。
AI中文摘要：
历史相关固体在加载、卸载和重新加载过程中需要进行能保留不可逆变形和渐进退化的材料更新。本文提出一种紧凑、可矢量化的弹塑性损伤更新用于显式图形模拟，旨在实现光滑激活和闭式评估而非精确屈服面强制。通过软加函数生成候选等效塑性应变，最大历史投影确保不可逆性，偏塑性应变张量保留残余方向，指数标量退化变量由存储历史驱动。通过一维循环拉伸、二维悬臂弯曲、三维压板压缩和环面等模型评估该方法，结果验证了残余变形、单调内部变量、分支能量梯度一致性和网格分辨率敏感性。与解析J2径向返回基线比较，结果表明本文方法贡献在于光滑性和实现简单性而非原始速度。路径方向扫描在比例加载下归一化等效应力误差为1.53%，但在固定大小90度转弯时为49.39%，这量化了该方法对各向同性、比例或近似比例加载的预期限制，它不能替代一般返回映射、各向异性损伤或相场断裂。
英文摘要：
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.
