不连续应变法：准确表示疲劳和断裂
The Discontinuous Strain Method: accurately representing fatigue and failure
AI总结：
本文提出不连续应变法，通过引入不连续应变来解决传统塑性损伤模型在卸载时的非物理行为，实现裂前裂后阶段的连续描述，且具有网格无关性和低计算成本。
摘要：
疲劳模拟需要准确建模卸载和加载过程。然而，经典塑性损伤模型将完全失效后的变形视为不可恢复的，导致卸载时出现非物理行为。这种非物理行为源于失效后塑性应变的持续积累，导致裂纹闭合时应力状态不正确。为此，我们引入加性弹塑性应变分解中的不连续应变，吸收失效后的多余应变。这允许在完全连续的设定中表示裂前和裂后阶段，其中弹塑性响应到裂纹的过渡可在任意阶段平滑触发。此外，所提出的方法不表现出混合方法中观察到的虚假能量释放。此外，通过依赖于离散化分辨率的特征长度尺度，本方法保证了网格无关性。我们称这种新方法为不连续应变法。所提出的方法只需对传统塑性损伤程序进行微小修改。为了教学目的，首先讨论了一维和随后的二维/三维实现的算法修改。使用简单的塑性本构模型，不连续应变法在已建立的二维基准上得到验证。然而，该方法与所用本构模型无关。弹性、塑性和损伤模型可以任意选择。此外，与该方法相关的计算工作量很小，使其在准确表示低周疲劳方面具有优势，可能也适用于其他需要在塑性损伤框架内表示不连续性的场景。
英文摘要：
Fatigue simulation requires accurate modeling of unloading and reloading. However, classical ductile damage models treat deformations after complete failure as irrecoverable -- which leads to unphysical behavior during unloading. This unphysical behavior stems from the continued accumulation of plastic strains after failure, resulting in an incorrect stress state at crack closure. As a remedy, we introduce a discontinuity strain in the additive elasto-plastic strain decomposition, which absorbs the excess strain after failure. This allows representing pre- and post-cracking regimes in a fully continuous setting, wherein the transition from the elasto-plastic response to cracking can be triggered at any arbitrary stage in a completely smooth manner. Moreover, the presented methodology does not exhibit the spurious energy release observed in hybrid approaches. In addition, our approach guarantees mesh-independent results by relying on a characteristic length scale -- based on the discretization's resolution. We name this new methodology the discontinuous strain method. The proposed approach requires only minor modifications of conventional plastic-damage routines. To convey the method in a didactic manner, the algorithmic modifications are first discussed for one- and subsequently for two-/three-dimensional implementations. Using a simple ductile constitutive model, the discontinuous strain method is validated against established two-dimensional benchmarks. The method is, however, independent of the employed constitutive model. Elastic, plastic, and damage models may thus be chosen arbitrarily. Furthermore, computational efforts associated with the method are minimal, rendering it advantageous for accurately representing low-cycle fatigue but potentially also for other scenarios requiring a discontinuity representation within a plastic-damage framework.
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