A discrete Lagrangian approach is the basis for modelling the macroscale elastic response of a solid material, which can be homogeneous as well as a periodic composite. The basic topology is a square “heuristic molecule” that is an assemblage of four rigid bodies with a definite shape bonded by elastic springs. This is the minimum unit cell, UC, that contains all the macroscopic mechanical properties of the solid material, object of study. The paper presents 4 unit cells, in progression from a basic molecule bonded by 2 types of central forces, to a refined “Cosserat-auxetic” molecule that is connected by 4 types of shear and central bond-springs. The emphasis is given to the isotropic response in relation to the value of the macroscopic Poisson ratio, and the four examples of UC topologies are presented showing their relationship to different materials at the macro-scale: from a “rari-constant” continuum, through a standard isotropic Cauchy continuum, up to an isotropic centre-symmetric auxetic Cosserat solid.

离散拉格朗日方法是对固体材料的宏观弹性响应建模的基础，该材料可以是均匀的，也可以是周期性的复合材料。基本拓扑是一个正方形的“启发式分子”，它是由四个弹性体组成的组合，具有通过弹性弹簧粘结的确定形状。这是最小的单位晶胞UC，其中包含固体材料（研究对象）的所有宏观力学性能。该论文提出了4个单位细胞，从通过2种类型的中心力键合的基本分子到通过4种类型的剪切力和中心键合弹簧连接的精制的“ Cosserat-auxetic”分子，逐步发展起来。重点是与宏观泊松比值有关的各向同性响应，