The total Lagrangian material point method (TLMPM) is a recent modification to the conventional material point method (MPM). It poses the weak form in the undeformed configuration, and has shown great potential in solid mechanics applications because it seamlessly eliminates the so-called cell-crossing instability and overcomes numerical fracture. Despite its promise, it has not been widely adopted by the MPM community yet, and only a handful of research groups have employed it. At the same time, due to TLMPM’s recent appearance, there are open research questions, such as the subject of near-incompressibility that has not been thoroughly studied within its context. In this paper we attempt to strengthen TLMPM’s position in the field by providing an independent assessment of the method in a set of benchmark problems. Furthermore, we evaluate the need of using higher order spline shape functions, which have been shown to be crucial for the success of the conventional MPM. Finally, we present a simple projection technique for addressing solid mechanics problems that fall within the near-incompressible regime. The numerical results show that TLMPM is indeed a strong alternative to conventional MPM, whereas our near-incompressibility approach produces solutions that are free of volumetric locking and pressure oscillations, while introducing very minor modifications to existing codes.

总拉格朗日质点法(TLMPM) 是对传统材料点法 (MPM) 的最新修改。它在未变形配置中提出了弱形式，并且在固体力学应用中显示出巨大的潜力，因为它无缝地消除了所谓的细胞交叉不稳定性并克服了数值断裂。尽管它很有前途，但它还没有被 MPM 社区广泛采用，只有少数研究小组使用了它。同时，由于 TLMPM 最近的出现，存在一些开放的研究问题，例如在其背景下尚未深入研究的近不可压缩性主题。在本文中，我们试图通过在一组基准问题中对该方法进行独立评估来加强 TLMPM 在该领域的地位。此外，我们评估了使用高阶样条形状函数的需求，这已被证明对传统 MPM 的成功至关重要。最后，我们提出了一种简单的投影技术来解决属于近不可压缩范围内的固体力学问题。数值结果表明，TLMPM 确实是传统 MPM 的有力替代方案，而我们的近不可压缩性方法产生的解决方案没有体积锁定和压力振荡，同时对现有代码进行非常小的修改。