论文标题
总拉格朗日平滑粒子流体动力学的无沙漏配方
An hourglass-free formulation for total Lagrangian smoothed particle hydrodynamics
论文作者
论文摘要
用于弹性固体动力学的总拉格朗日平滑颗粒流体动力学（TL-SPH）具有沙漏模式，可能会增长并导致模拟失败，以免发生较大变形的问题。为了解决这个长期存在的问题，我们提出了一种基于体积效应应力分解的无沙漏配方。受到沙漏模式诱导的非物理锯齿形颗粒分布的伪像的启发，主要以剪切变形为特征，以及在Navier-Stokes方程（NS）方程中的粘性期限的标准SPH离散化，目前的配方在直接通过laplacian的剪切应力来计算剪切应力，而不是由laplacian shipelect sheale vers shear sheargence sheargence of shergence of shergence of shorgence vilivergence。模拟了一组综合的具有挑战性的基准案例，以证明，在提高准确性和计算效率的同时，目前的配方能够消除沙漏模式，并通过单个一般有效参数实现非常好的数值稳定性。另外，模拟了实际相关支架结构的变形，以证明本生物力学领域的本方法的潜力。
The total Lagrangian smoothed particle hydrodynamics (TL-SPH) for elastic solid dynamics suffers from hourglass modes which can grow and lead to the failure of simulation for problems with large deformation. To address this long-standing issue, we present an hourglass-free formulation based on volumetric-devioatric stress decomposition. Inspired by the fact that the artifact of nonphysical zigzag particle distribution induced by the hourglass modes is mainly characterized by shear deformation and the standard SPH discretization for the viscous term in the Navier-Stokes (NS) equation, the present formulation computes the action of shear stress directly through the Laplacian of displacement other than from the divergence of shear stress. A comprehensive set of challenging benchmark cases are simulated to demonstrate that, while improving accuracy and computational efficiency, the present formulation is able to eliminate the hourglass modes and achieves very good numerical stability with a single general effective parameter. In addition, the deformation of a practically relevant stent structure is simulated to demonstrate the potential of the present method in the field of biomechanics.
