Due to its simplicity and robustness, smooth particle hydrodynamics (SPH) has been widely used in the modelling of solid and fluid mechanics problems. Through the years, various formulations and stabilisation techniques have been adopted to enhance it. Recently, the authors developed JST–SPH, a mixed formulation based on the SPH method. Originally devised for modelling (nearly) incompressible hyperelasticity, the JST–SPH formulation is mixed in the sense that linear momentum and a number of strain definitions, instead of the displacements, act as main unknowns of the problem. The resulting governing system of conservation laws conveniently enables the application of the Jameson–Schmidt–Turkel (JST) artificial dissipation term, commonly employed in computational fluid dynamics, to solid mechanics. Coupled with meshless SPH discretisation, this novel scheme eliminates the shortcomings encountered when implementing fast dynamics explicit codes using traditional mesh-based methods. This paper focuses on the applicability of the JST–SPH mixed formulation to the simulation of high-rate, large metal elastic–plastic deformations. Three applications—including the simulation of an industry-relevant metal forming process—are examined under different loading conditions, in order to demonstrate the reliability of the method. Results compare favourably with both data from the previous literature, and simulations performed with a commercial finite elements package. Most noticeably, these results demonstrate that the total Lagrangian framework of JST–SPH, fundamental to reduce the computational effort associated with the scheme, retains its accuracy in the presence of large distortions. Moreover, an algorithmic flow chart is included at the end of this document, to facilitate the computer implementation of the scheme.

中文翻译：

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一种有效且稳定的SPH方法，用于大应变金属塑性变形

由于其简单性和鲁棒性，光滑粒子流体动力学（SPH）已被广泛用于固体和流体力学问题的建模。多年来，已经采用了各种配方和稳定技术来增强它。最近，作者开发了基于SPH方法的混合配方JST–SPH。JST–SPH公式最初是为建模（几乎）不可压缩的超弹性而设计的，它的混合意义是线性动量和许多应变定义而不是位移是问题的主要未知数。由此产生的守恒定律控制系统可以方便地将通常在计算流体动力学中使用的Jameson-Schmidt-Turkel（JST）人工耗散术语应用于固体力学。加上无网格SPH离散化，这种新颖的方案消除了使用传统的基于网格的方法实现快速动态显式代码时遇到的缺点。本文着重介绍JST-SPH混合配方在高速率，大金属弹塑性变形模拟中的适用性。为了证明该方法的可靠性，在不同的负载条件下检查了三个应用程序，包括模拟与行业相关的金属成型过程。结果与先前文献中的两个数据以及使用商业有限元程序包进行的仿真均具有可比性。最值得注意的是，这些结果表明，JST-SPH的整个拉格朗日框架对于减少与该方案相关的计算工作是至关重要的，但在存在较大失真的情况下仍能保持其准确性。此外，