时空规范理论用于建模延性损伤及其NOSB近场动力学实现
A space-time gauge theory for modeling ductile damage and its NOSB peridynamic implementation
AI总结：
本文提出一种基于时空局部平移和标度对称性的规范理论，用于建模金属延性损伤，并通过NOSB近场动力学实现，能重现应变率锁定等实验现象。
摘要：
利用时空中的局部平移和标度对称性，对金属和合金在宽应变率和温度范围内的延性损伤进行建模。通过施加类Weyl条件，基于规范不变的曲率张量构造了与延性变形对应的不变能量密度。塑性变形的能量学通过由局部平移产生的规范补偿场引入。通过最小替换的时空规范协变算子，保持了能量密度在局部平移和标度作用下的不变性。最小替换引入了两个非平凡的规范补偿场，分别对应于局部平移和标度。这些场用于描述延性损伤，包括材料中的塑性流动和微裂纹演化。使用时空伪黎曼度量在有限变形框架下描述运动学。借鉴经典粘塑性理论中的现有见解，我们还建立了空间平移对应的规范补偿场与Kröner变形梯度乘法分解之间的联系。通过适当的退化函数，确保了粘塑性与延性损伤之间的热力学一致耦合。数值实现采用非普通状态基（NOSB）近场动力学（PD）离散化。该模型的可行性通过重现一些实验已知事实得到检验，即应力-应变响应中的应变率锁定，其起源可追溯到由时空平移对称性产生的非线性微观惯性项。最后，我们求解了二维和轴对称变形问题，以定性验证模型的可行性。还提出了有限变形框架下的NOSB近场动力学轴对称公式。
英文摘要：
Local translational and scaling symmetries in space-time is exploited for modelling ductile damage in metals and alloys over wide ranges of strain rate and temperature. The invariant energy density corresponding to the ductile deformation is constructed through the gauge invariant curvature tensor by imposing the Weyl like condition. The energetics of the plastic deformation is brought in through the gauge compensating field emerged due to local translation. Invariance of the energy density under the local action of translation and scaling is preserved through minimally replaced space-time gauge covariant operators. Minimal replacement introduces two non-trivial gauge compensating fields pertaining to local translation and scaling. These are used to describe ductile damage, including plastic flow and micro-crack evolution in the material. A space-time pseudo-Riemannian metric is used to lay out the kinematics in a finite-deformation setting. Recognizing the available insights in classical theories of viscoplasticity, we also establish a correspondence of the gauge compensating field due to spatial translation with Kröner's multiplicative decomposition of the deformation gradient. Thermodynamically consistent coupling between viscoplasticity and ductile damage is ensured through an appropriate degradation function. Non-ordinary state-based (NOSB) peridynamics (PD) discretization of the model is used for numerical implementation. The model's viability is tested in reproducing a few experimentally known facts, viz., strain rate locking in the stress-strain response, whose origin is traced to a nonlinear microscopic inertia term arising out of the space-time translation symmetry. Finally, we solved 2D and axisymmetric deformation problems for qualitatively validating the model's viability. NOSB peridynamics axisymmetric formulation in finite deformation setup is also presented.
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