In a previous work we considered a two-dimensional lattice of particles and calculated its time evolution by using an interaction law based on the spatial position of the particles themselves. The model reproduced the behaviour of deformable bodies both according to the standard Cauchy model and second gradient theory; this success led us to use this method in more complex cases. This work is intended as the natural evolution of the previous one in which we shall consider both energy aspects, coherence with the principle of Saint Venant and we start to manage a more general tool that can be adapted to different physical phenomena, supporting complex effects like lateral contraction, anisotropy or elastoplasticity.

中文翻译：

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粒子系统的基于位置的动力学：一种可配置的算法，用于描述从群体机器人开始的连续材料的复杂行为

在之前的工作中，我们考虑了粒子的二维晶格，并通过使用基于粒子本身空间位置的相互作用定律来计算其时间演化。该模型根据标准柯西模型和第二梯度理论再现了可变形体的行为；这一成功促使我们在更复杂的情况下使用这种方法。这项工作旨在作为前一项工作的自然演变，其中我们将考虑能量方面，与圣维南原则的一致性，我们开始管理一个更通用的工具，可以适应不同的物理现象，支持复杂的效果，如横向收缩、各向异性或弹塑性。