A novel phase-field damage model coupled with Timoshenko beam kinematics to simulate localized fracture in brittle architected lattice material

Abstract

Architected lattice materials (ALM) have gained significant attention due to their superior mechanical properties compared to conventional bulk metals. However, limited studies in the literature focus on modeling the fracture behavior of ALM structural elements, particularly using beam kinematics coupled with phase-field (PF) damage models to reduce computational costs than analyzing an equivalent 2D model. The present study develops a beam-based PF model using Timoshenko beam theory to simulate localized damage evolution in brittle ALM grids. The proposed model employs a homogenized damage function to capture the overall damage state across the beam cross-section, bypassing the need to resolve damage variations within the section. Two damage approximation functions, constant and parabolic, are explored to describe damage across the cross-section. Damage evolution is attributed to a combination of tensile axial energy, shear energy, and a fraction of flexural strain energy. A series of numerical simulations, from isolated beam tests to full-scale ALM grid analyses, demonstrate the efficacy of the proposed model. Results indicate that the fraction of flexural strain energy(\(\alpha \)) influencing damage evolution varies with the beam’s depth-to-length ratio, while boundary conditions show negligible impact on \(\alpha \) for a fixed ratio. Model validation through comparisons with 2D simulations and experimental data highlights accurate predictions of load-displacement responses and crack patterns. Moreover, the proposed approach achieves significant computational efficiency, reducing the degrees of freedom for the lattice system from 3.2 million in a 2D model to just 58,000. Correspondingly, computational time decreases from 14 hours and 43 minutes to only 7 minutes and 20 seconds. These results underscore the potential of the proposed beam-based PF model as a computationally efficient and accurate tool for analyzing damage behavior in ALM.