Since the tension instability was discovered in updated Lagrangian smoothed particle hydrodynamics (ULSPH) at the end of the 20th century, researchers have made considerable efforts to suppress its occurrence. However, up to the present day, this problem has not been fundamentally resolved. In this paper, the concept of hourglass modes is firstly introduced into ULSPH, and the inherent causes of tension instability in elastic dynamics are clarified based on this brand-new perspective. Specifically, we present an essentially non-hourglass formulation by decomposing the shear acceleration with the Laplacian operator, and a comprehensive set of challenging benchmark cases for elastic dynamics is used to showcase that our method can completely eliminate tensile instability by resolving hourglass modes. The present results reveal the true origin of tension instability and challenge the traditional understanding of its sources, i.e., hourglass modes are the real culprit behind inducing this instability in tension zones rather that the tension itself. Furthermore, a time integration scheme known as dual-criteria time stepping is adopted into the simulation of solids for the first time, to significantly enhance computational efficiency.

翻译：自20世纪末在更新拉格朗日光滑粒子流体动力学（ULSPH）中发现拉伸不稳定现象以来，研究者们为抑制其发生付出了巨大努力。然而至今，该问题仍未得到根本解决。本文首次将沙漏模态的概念引入ULSPH，并基于这一全新视角阐明了弹性动力学中拉伸不稳定性的内在根源。具体而言，我们通过拉普拉斯算子分解剪切加速度，提出了一种本质上无沙漏的公式体系，并利用一系列具有挑战性的弹性动力学基准案例证明，该方法可通过消除沙漏模态完全消除拉伸不稳定性。本文结果揭示了拉伸不稳定性的真正起源，挑战了对其成因的传统认知：即在拉伸区域中，沙漏模态才是诱发不稳定性的真正元凶，而非拉伸本身。此外，本文首次将双判据时间步长这一时间积分方案引入固体模拟，显著提升了计算效率。