For decades, aspects of the topological architecture, and of the mechanical as well as other physical behaviors of periodic lattice truss materials (PLTMs) have been massively studied. Their approximate infinite design space presents a double-edged sword, implying on one hand dramatic designability in fulfilling the requirement of various performance, but on the other hand unexpected intractability in determining the best candidate with tailoring properties. In recent years, the development of additive manufacturing and artificial intelligence spurs an explosion in the methods exploring the design space and searching its boundaries. However, regrettably, a normative description with sufficient information of PLTMs applying to machine learning has not yet been constructed, which confines the inverse design to some discrete and small scrutinized space. In the current paper, we develop a system of canonical descriptors for PLTMs, encoding not only the geometrical configurations but also mechanical properties into matrix forms to establish good quantitative correlations between structures and mechanical behaviors. The system mainly consists of the geometry matrix for the lattice node configuration, density, stretching and bending stiffness matrices for the lattice strut properties, as well as packing matrix for the principal periodic orientation. All these matrices are theoretically derived based on the intrinsic nature of PLTMs, leading to concise descriptions and sufficient information. The characteristics, including the completeness and uniqueness, of the descriptors are analyzed. In addition, we discuss how the current system of descriptors can be applied to the database construction and material discovery, and indicate the possible open problems.

翻译：数十年来，周期性晶格桁架材料（PLTMs）的拓扑结构、力学及物理特性已得到广泛研究。其近乎无限的设计空间是一把双刃剑：一方面赋予材料通过性能定制满足各类需求的巨大可设计性，另一方面却导致在确定具有定制属性的最优候选结构时面临难以处理的复杂性。近年来，增材制造与人工智能技术的发展催生了探索设计空间及其边界的方法爆炸式增长。然而遗憾的是，适用于机器学习的PLTMs标准化信息描述体系尚未建立，这制约了逆设计仅能局限于离散且微小的可探测空间。本文针对PLTMs构建了一套规范描述符系统，不仅将几何构型编码为矩阵形式，更将力学性能纳入其中，从而建立结构与力学行为间的定量关联。该系统主要由以下矩阵构成：晶格节点构型的几何矩阵、晶格支柱属性的密度矩阵、拉伸与弯曲刚度矩阵，以及主周期取向的堆积矩阵。所有矩阵均基于PLTMs内在属性进行理论推导，既实现简洁描述又包含充分信息。我们分析了描述符的完备性与唯一性等特征，并探讨了当前描述符系统在数据库构建和材料发现中的应用，同时指出可能存在的开放性问题。