A Monte Carlo simulation-based approach to realistic modelling of additively manufactured lattice structures

Abstract

Lattice structures fabricated via Additive Manufacturing (AM) offer improved performance over traditional manufacturing methods, however, predicting their mechanical behaviour both accurately and with acceptable computational efficiency remains a challenge. AM associated defects combined with multiple high aspect-ratio strut elements require fine 3D finite-element (FE) meshes; resulting in high computational complexity that limits the number of lattice unit cells that can be practically simulated. Alternatively, Euler-Bernoulli or Timoshenko beam elements can be specified to reduce computational complexity. However, these beam elements are typically based on idealised representations that exclude AM associated defects. This research proposes a novel method which combines data driven AM defect modelling, Markov Chains and Monte Carlo (MCS) simulation techniques to predict the stiffness of an AM lattice structure. Furthermore, this method accommodates stochastic distributions of AM associated defects within computationally effective beam models; thereby enabling the simulation of large-scale lattice structures at a relatively low computational cost. The proposed method is aimed at reliability analysis or a probabilistic approach to structural analysis of AM lattice structures. The combination of generating AM strut digital realisations and MCS, resulted in a variety of possible strut deformation shapes and effective diameters under axial compression. The propagation of effective diameter variability to the lattice-scale level displayed the possible variation in the mechanical response of AM lattice structure. Simulations are validated and insight into how a lattice structures unit cell topology affects simulation accuracy is discussed.