We are pleased to share our recent JMPS paper, “Graph-Field Framework for Fracture Mechanics of Architected Lattice Materials.” (link: 10.1016/j.jmps.2026.106729)
Fracture in architected lattices cannot be fully described by classical homogenization or standard LEFM, because crack-tip fields are strongly governed by discrete topology, strut bending, nodal rotations, and non-affine deformation. To address this issue, we develop a Graph-Field (GF) framework that maps discrete nodal equilibrium directly into continuum field equations.
The method starts from a graph representation of the lattice unit cell, identifies primary and secondary nodes, condenses internal degrees of freedom through local equilibrium, and derives topology-explicit PDEs through a vanishing-cell-size limit. Without empirical fitting, the GF framework captures anomalous crack-tip kinematics missed by conventional orthotropic models.
We further propose a parameter-free crack-path criterion based on the maximum principal strain field and derive a path-independent crack driving force using Eshelby’s configurational mechanics. The results show that standard ASTM-type fracture tests may overestimate the true toughness of highly constrained lattices.
This work provides a topology-explicit continuum foundation for fracture analysis and inverse design of architected lattice materials.