Generalised Phase Field Modelling of Fracture in Gyroid Structures: Numerical and Experimental Insights Using Additively Manufactured Polylactic Acid (PLA) Specimens

This study presents a three-dimensional cohesive phase field framework for simulating quasi-static fracture in Gyroid lattice structures. To the authors' knowledge, this is one of the first experimentally validated applications of a diffuse cohesive phase field model to describe damage and fracture evolution in additively manufactured polylactic acid (PLA) lattice specimens. Due to the softening-like mechanical behaviour exhibited by the 3D-printed PLA specimens, the present work employs a high-order cohesive generalised phase field model capable of capturing material softening once the maximum load-carrying capacity is reached and energy dissipation becomes dominant. This modelling choice is essential to reproduce the gradual post-peak degradation observed experimentally, which would not be adequately described by a purely brittle AT1/AT2-type formulation. After validation in a two-dimensional case, the approach is extended to the analysis of 3D-printed Gyroid specimens subjected to tensile and compressive loading. Different Gyroid configurations, including unit cells and (Formula presented.) clusters, were tested under tensile and compressive loading regimes using an in situ tensile/compression testing stage, with deformations and failure modes directly monitored through in situ imaging. Each experiment was recorded from multiple angles during tensile and compressive loading of the additively manufactured Gyroid specimens and compared frame by frame with simulation outputs, revealing good agreement in the prediction of crack initiation and propagation paths. The comparison between experimental and numerical results confirms the model's ability to capture the main tensile failure mechanisms and the softening-driven fracture evolution in architected PLA lattices, while the compressive response is interpreted with caution in the late post-peak regime due to mechanisms such as buckling, contact and densification. This versatile modelling framework lays the foundation for future studies incorporating additional physical phenomena—such as surface coatings, residual stresses, or micron-scale effects—and for extension to other triply periodic minimal surface (TPMS) topologies beyond the Gyroid.