The material point method can be regarded as a meshfree extension of the finite element method. This fact has two interesting consequences. On the one hand, this puts a vast literature at our disposal. On the other hand, many of this inheritance has been adopted without questioning it. A clear example of it is the use of the Voigt algebra, which introduces an artificial break point between the formulation of the continuum problem and its discretized counterpart. In the authors' opinion, the use of the Voigt rules leads to a cumbersome formulation where the physical sense of the operations is obscured since the well-known algebra rules are lost. And with them, the intuition about how stresses and strains are related. To illustrate it, we will describe gently and meticulously the whole process to solve the nonlinear governing equations for isothermal finite strain elastodynamics, concluding with a compact set of expressions ready to be implemented effortless. In addition, the classic Newmark-$\beta$ algorithm has been accommodated to the local maximum-entropy material point method framework by means of an incremental formulation.

中文翻译：

---

在无 B 方法中的有限应变下的局部最大熵材料点方法

质点法可以看作是有限元法的无网格扩展。这个事实有两个有趣的后果。一方面，这为我们提供了大量文献。另一方面，许多这种继承都被采用而没有质疑。一个明显的例子是 Voigt 代数的使用，它在连续统问题的表述与其离散化对应物之间引入了一个人为的断点。在作者看来，Voigt 规则的使用导致了一个繁琐的公式，其中由于众所周知的代数规则丢失，操作的物理意义变得模糊。与它们有关的直觉是关于压力和应变之间的关系。为了说明，我们将温和而细致地描述求解等温有限应变弹性动力学非线性控制方程的整个过程，并以一组易于实现的紧凑表达式结束。此外，经典的纽马克-$\beta$算法已通过增量公式适应局部最大熵材料点方法框架。