On brittle fracture analysis of architected materials using a structural-level frame model

This study proposes a mesoscale model for the deformation and fracture of lattice-frame based architected structures. It is directly based on moment-curvature and stress-strain relationships of the individual frame elements, augmented by thermodynamically consistent fracture propagation criteria. By modeling dense frames directly and introducing two fracture probability parameters (for tensile and bending fracture), we are able to capture a wide variety of fracture behavior of architected lattice structures. The model is applied to study the fracture behavior of various two-dimensional lattice structures under different load conditions. The model demonstrates that the nature of the failure of architected materials is very sensitive to mesostructure, as expected. It is also able to capture the quasi-brittle post-failure softening behavior that is observed even though the material of the lattice is brittle. The results show that, depending upon the lattice structure, the local bending moment distribution (or local curvature distribution) can be very widespread, thus promoting quasi-brittle behavior. The framework is computationally efficient and accounts for the local discrete mesostructure that is not captured by classical continua. The present work is intended as a methodological framework and proof-of-concept; results are interpreted in terms of qualitative trends and relative mesostructural comparisons, with experimental validation identified as a direction for future work.