Abstract In cold areas, freeze–thaw damage seriously affects the long-term use and safe operation of concrete structures. The constitutive model is an important foundation for predicting deformation and strength characteristics of concrete materials and for the non-linear analysis of concrete structures. This study is based on the elaboration of methods for the constitutive model of damaged materials by using damage mechanics and others. This study focuses on the existing constitutive model results of concrete under the static axial compression load, dynamic load, and coupling environmental load, and analyzing the problems in existing studies. Research has shown that segmented models exhibit higher fitting accuracy of concrete freeze–thaw constitutive model under static axial compression loads. By defining coupled damage variables, it is possible to approach the actual freeze–thaw damage of concrete under environmental coupling, and attention should be paid to the differences or interactions between damage factors. In order to meet the actual engineering needs of high altitude and cold areas needs to expand the temperature range of freeze–thaw tests and consider the dynamic loads impact on concrete damage, the establishment of constitutive model of concrete under the actual freeze–thaw damage is the focus of frost-resistant durability research of hydraulic concrete in cold regions.
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