A two-dimensional molecular model is presented for the elastic non-linear modelling and design of meta-materials. The fundamental unit-cell, based on a heuristic molecule (HM) approach, is composed of atoms that interact through centred and non-centred spring-based bonds. The kinematics formulation allows to consider large displacements and finite strains while the specific topology of the HM can be parametrized to modify the shape of the rigid atoms and the size of the bonds. The HM is frame indifferent and provides a remarkable quasi-isotropic elastic response for both deviatoric and volumetric large deformation modes. At a macro-scale, the relationship with different continuum materials is given through a standard isotropic Cauchy up to an isotropic Cosserat solid. Evidence on the interest of the model as a calculation tool is provided by studying the elastic response of standard and auxetic materials subjected to a non-homogeneous deformation field, as well as the response of auxetic foams under large deformations. Aside the numerical agreement, it is highlighted how the tailoring of the HM topology can be effective to approximate the non-linear geometric effects that occur at finer scales of auxetic foams. In perspective, we address how the exotic mechanical properties provided by the HM, together with the assumed physical-driven framework, can foster the engineering application and the design of new meta-materials.

提出了一种二维分子模型，用于超材料的弹性非线性建模和设计。基于启发式分子 (HM) 方法的基本晶胞由通过中心和非中心弹簧键相互作用的原子组成。运动学公式允许考虑大位移和有限应变，而 HM 的特定拓扑结构可以参数化以修改刚性原子的形状和键的大小。HM 是框架无关的，并为偏量和体积大变形模式提供显着的准各向同性弹性响应。在宏观尺度上，与不同连续体材料的关系通过标准各向同性柯西到各向同性 Cosserat 固体给出。通过研究标准和拉胀材料在非均匀变形场下的弹性响应，以及拉胀泡沫在大变形下的响应，提供了模型作为计算工具的兴趣的证据。除了数值一致性之外，还强调了 HM 拓扑的定制如何有效地近似在拉胀泡沫的更精细尺度上发生的非线性几何效应。从长远来看，我们讨论了 HM 提供的奇异机械特性以及假设的物理驱动框架如何促进工程应用和新超材料的设计。除了数值一致性之外，还强调了 HM 拓扑的定制如何有效地近似在拉胀泡沫的更精细尺度上发生的非线性几何效应。从长远来看，我们讨论了 HM 提供的奇异机械特性以及假设的物理驱动框架如何促进工程应用和新超材料的设计。除了数值一致性之外，还强调了 HM 拓扑的定制如何有效地近似在拉胀泡沫的更精细尺度上发生的非线性几何效应。从长远来看，我们讨论了 HM 提供的奇异机械特性以及假设的物理驱动框架如何促进工程应用和新超材料的设计。