采用改进的基于键的变形梯度的全拉格朗日光滑粒子流体动力学方法用于大应变固体动力学
Total Lagrangian Smoothed Particle Hydrodynamics with An Improved Bond-Based Deformation Gradient for Large Strain Solid Dynamics
AI总结：
本文针对TLSPH在极大应变固体模拟中的零能量模式不稳定问题，提出了一种改进的基于键的变形梯度计算方法，通过核光滑和自键修正提高精度与稳定性，并在二维和三维算例中验证了其在极端伸长下的鲁棒性。
摘要：
全拉格朗日光滑粒子流体动力学（TLSPH）是SPH的一种变体，其中变量使用固定的参考构型和拉格朗日光滑核进行描述。当不涉及拓扑变化时，TLSPH提高了标准SPH的计算效率，并且缓解了SPH格式在拉伸载荷下的稳定性问题。然而，与伪模式或沙漏/零能量模式相关的不稳定性仍然存在，并且经常影响经历极大应变的固体的模拟。本工作提出了一种替代公式来计算变形梯度，具有更高的精度，从而最小化遇到零能量模式的可能性。具体来说，我们利用由核光滑化的基于键的（或成对的）变形梯度的局部离散计算。此外，考虑粒子与自身的键以保持核修正方案所施加的多项式再现性。我们使用一个二维基准示例展示了该方法的收敛性。此外，在各种二维和三维示例中评估了所提出方法的精度、鲁棒性和稳定性，重点展示了稳定性的改进，使得固体动力学模拟能够承受更极端的伸长。
英文摘要：
Total Lagrangian Smoothed Particle Hydrodynamics (TLSPH) is one variant of SPH where the variables are described using the fixed reference configuration and a Lagrangian smoothing kernel. TLSPH elevates the computational efficiency of the standard SPH when no topological change is involved, and it alleviates the stability of SPH scheme with respect to tensile loading. However, instabilities associated with spurious mode, or hourglass/zero-energy mode, persists and often affects the simulation of solids undergoing extremely large strain. This work proposes an alternative formulation to compute deformation gradient with improved accuracy and therefore minimising the possibility of encountering the zero-energy mode. Specifically, we leverage the local discrete computation of bond-based (or pairwise) deformation gradient smoothed by the kernel. Additionally, the bond of a particle with itself is considered to preserve the polynomial reproducibility imposed by the kernel correction scheme. We showcase the convergence of the approach using a two-dimensional benchmark example. Furthermore, the accuracy, robustness, and stability of the proposed approach are assessed in various two- and three-dimensional examples, highlighting on the stability improvement that allows for solid dynamic simulations with more extreme elongation.
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