# Numerical Modeling Technique of Damage Behavior of
## 5 Conclusions  
In this paper, we presented the implementation procedure of finite element modeling within FEAP for the numerical analysis of masonry-infilled RC frames. In this modeling, XFEM is combined with interface elements to predict the complicated failure process of masonry-infilled RC frames, such as diagonal cracking, sliding and crushing in the infill wall, as well as the flexural and shear failure in RC frame members. The implementation is based on a user element subroutine; two user element subroutines with and without crack tip enrichment functions included within XFEM are built to model the nonlinear behavior of the concrete in RC frame members and the masonry blocks in the infill panel, respectively. Additionally, a macro command used to check the crack-propagation criterion and update the crack, and enrichment information is added to assist in the implementation of XFEM. Some critical and difficult issues related to the selection of enriched nodal degrees of freedom, input material parameters, information passing, numerical integration strategy, constitutive relations, assembly procedure of stiffness matrix and force vector, output for post-processing, and crack-propagation strategy are addressed.  
A quasi-static test of two RC frames with and without infill walls is analyzed to verify the capability of the proposed finite element modeling. It revealed that the relative errors of peak load, displacement corresponding to peak load and initial stiffness for the two specimens are relatively small, and the load-bearing capacity curves are accurately predicted. Meanwhile, the failure process of the test specimens is well represented, especially for the cracking propagation in the concrete material and masonry units. These findings sufficiently demonstrate the efficacy of the XFEM implementation in FEAP and the effectiveness of the proposed modeling for representing the complicated behavior of masonry-infilled RC frames.  
Further parametric studies using the proposed modeling can better understand the behavior of masonry-infilled RC frame buildings, which will contribute to the development of valuable seismic design advice and simplified approaches. Moreover, the proposed modeling is an effort to solve the fracture problems of practical structures using XFEM. The description of the implementation procedure will help readers to apply XFEM for a broader class of problems. The uncertainties in the mechanical properties of masonry units and mortar joints has a great impact on the performance of the infilled wall RC frame, and it is not considered in this study. In future research, the spatial variation in material properties in infill walls can be considered in the proposed finite element model to better understand the failure behavior of infilled wall RC frame structures.  
Conceptualization, B.L., C.L. and X.W.; methodology, B.L., X.W. and J.K.; software, B.L., X.W., J.K. and. Z.C.; validation, B.L, C.L. and J.K.; formal analysis, B.L., C.L. and X.W.; investigation, Z.C.; resources, C.L., X.W., J.K. and Z.C.; data curation, X.W. and Z.C.; writing--original draft preparation, B.L., C.L. and X.W.; writing--review and editing, B.L., C.L., J.K. and Z.C.; visualization, B.L., C.L. and J.K.; supervision, Z.C.; project administration, J.K.; funding acquisition, X.W., C.L. and J.K. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Nature Science Foundation of China (Nos. 51808478), and Natural Science Foundation of Heilongjiang Province of China (Nos. LH2022E122). These supports are greatly appreciated.  
Not applicable.  
Grateful acknowledgment is given to [PERSON] and [PERSON] at Institute of Engineering Mechanics, China Earthquake Administration for the guidance and suggestions on theoretical analyses.  
The authors declare no conflict of interest.