# Fracture of disordered and stochastic lattice materials

## TL;DR

This paper develops a probabilistic framework to analyze how disorder and stochastic properties influence failure and fracture behavior in lattice mechanical metamaterials, validated through finite element analysis.

## Contribution

It introduces a novel probabilistic approach that couples stochastic failure and geometric disorder to predict failure in disordered lattice materials.

## Key findings

- Disorder and stochasticity reduce average failure loads.
- Variance in failure loads increases with disorder.
- Fracture length and volume size constraints are identified.

## Abstract

The failure of mechanical metamaterials is a function of the interplay between the properties of the base material and the microstructural geometry. Stochastic failure properties of the base material and disordered microstructural geometries can contribute to variations in the global failure mechanics that are not captured in traditional analyses of ordered, deterministic architected materials. We present a probabilistic framework that couples stochastic material failure and geometric disorder to predict failure in lattice mechanical metamaterials. These predictions are verified through finite element analysis, which confirm that disorder and stochasticity affect both the mean and variance of the damage initiation load in a lattice, with average failure loads being generally reduced and variance increasing with higher levels of disorder and stochasticity. The fracto-cohesive length and representative volume element size are also predicted and constrain the minimum defect and lattice sizes, respectively, for failure to be considered a fracture process. The framework is extended to consider the fracture behavior of the lattice, the development of damage zones, and their impact on the steady-state fracture toughness.