Multi-scale simulation of anisotropic fracture behavior in BaZrO₃

This paper presents a multi-scale numerical method to study the electrolyte material BaZrO₃ (BZO) and gives numerical implementations and results. At the microscopic level, molecular dynamics (MD) is used to model the atomic structure of BZO. At the macroscopic level, the finite element method is used for loading and numerical solution. To bridge the microscopic and macroscopic scales, the concept of coarse-grained and coupled algorithms was used to establish a relationship between the atomic mass and the number of nodes in a continuous medium by means of a weighted residual method. This approach takes into account the anisotropy of the atomic structure of BZO and determines an intrinsic nature law through detailed modelling of the microstructure. We first describe the principle of the Atom-to-Continuum (AtC) multiscale approach and verify the accuracy of the multiscale calculation method by comparing the stress–strain curves of BZO with a central crack under the AtC method and MD simulations. The mechanical response of the crack under macroscopic and microscopic calculations is then observed and discussed by combining it with finite element software. Under the finite element simulations, the crack extends forward in a cleavage manner, while in the MD simulations the results show a clear directional dependence: the (100) surface fracture involves in-plane slip, with the crack propagating forward perpendicular to the plane between Zr and O; in the (110) surface the crack is unstable as it extends, resulting in a zigzag crack extension path, with the final crack remaining in the same direction as the initial direction remains the same. Our study not only reveals the fracture mechanism of perovskite oxide BZO but also presents a multi-scale approach that allows for large-scale calculations, providing a new way of studying the material design and applications.