“…Multiscale methods have a wide range of applications in material science. Many materials have the heterogeneous structures in nature or by fabrication, such as cement and concrete [37,46], crystalline alloys [18,36], bulk metallic glasses [17,29,47,48], shape memory composites [12,20,63] and reinforced polymers [19,67,68]. Cementitious materials can be modeled as lattice elements that consist of unhydrated cement and hydration products [49,56]; Cohesive zone model has been extensively applied to investigate the failure mechanism of alloys [26-28, 66, 69]; Modern homogenization techniques have been developed to study random composites [15,35,38] as well as heterogeneous materials such as biological tissues [30] and Neo-Hookean-type composites [23,54,65] with large deformations.…”