Multiscale modeling of multiple-cracking fracture behavior of engineered cementitious composite (ECC)

A hierarchical multiscale modeling method developed to facilitate the characterization of tensile behavior of ECC under both static and fatigue loading is presented. This multiscale modeling method has accounted for the essential characteristic features of ECC, including fiber bridging, multiple cracking, and material randomness. The crack bridging behavior and bridging stress fatigue degradation of an arbitrary fiber and those of a quantity of randomly distributed fibers are theoretically analyzed at the microscale and lower-mesoscale, respectively, while the joint response of uncracked matrix and multiple cracks with stochastic matrix cracking strength and fiber volume fraction is studied at the upper-mesoscale via representative volume element (RVE) modeling. In particular, the integrated cohesive zone model-extended finite element method (integrated CZM-XFEM) is developed with an emphasis on embedment of multiple cohesive cracks for ease of modeling indefinite cracks for ECC, and a hardening cohesive law is developed based on the crack bridging analysis at the microscale and lower-mesoscale which realizes the cross-scale interaction. Finally, a special four-node quadrilateral element with enriched degrees of freedom is developed on the basis of the integrated CZM-XFEM method, and it is implemented with the help of the user-element subroutine (UEL) in ABAQUS for the finite element analysis of the RVE model. The multiscale modeling method is demonstrated to simulate ECC's multiple-cracking and tensile strain-hardening behavior under static loading as well as bridging stress degradation under fatigue loading with great accuracy.