Reduced-dimensional phase-field theory for lattice fracture and its application in fracture toughness assessment of architected materials

Abstract

To develop an efficient numerical scheme for investigating the fracture characteristics of modern architected lattice materials, we present a phase-field fracture model for shallow beams, an assemblage of which forms the lattice. Our approach introduces a simple hypothesis for the variation of phase-field across the beam cross-section along with the standard Euler–Bernoulli type kinematic assumptions to reduce the three-dimensional problem to a one-dimensional one. A variationally consistent formulation based on these hypotheses leads to an overestimation of crack driving energy. Our proposition overcomes it by incorporating a correction within the popular hybrid framework of phase-field fracture. We establish the efficacy and accuracy of the proposed formulation by performing a series of numerical simulations of fracture in beams and comparing the one-dimensional predictions with two-dimensional responses. The beam fracture model is then utilized in several investigations pertaining to architected brittle lattice materials, e.g. direct numerical simulation of crack propagation in lattices, application to concurrent multiscale approach, and utility in sequential multiscale modelling via predicting the fracture toughness of the homogenized material.