  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.
