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| A multi-scale elastoplastic constitutive model of porous rock based on incremental variational theory |
| ZHAO Lunyang1，2，LAI Yuanming1，3，NIU Fujun1，2，ZHU Qizhi4，SHAO Jianfu4 |
| (1. School of Civil Engineering and Transportation，South China University of Technology，Guangzhou，Guangdong 510641，China；
2. State Key Laboratory of Subtropical Building Science，South China University of Technology，Guangzhou，Guangdong 510641，China；3. State Key Laboratory of Frozen Soil Engineering，Northwest Institute of Eco-environment and Resources，
Chinese Academy of Sciences，Lanzhou，Gansu 730000，China；4. Key Laboratory of Ministry of Education
for Geomechanics and Embankment Engineering，Hohai University，Nanjing，Jiangsu 210098，China) |
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Abstract In order to consider the effects of nonuniform mesoscopic(local) stress field and strain field on the macroscopic mechanical response of porous rock under loading, a multi-scale elastoplastic constitutive model based on incremental variational theory was established. Firstly，the porous rock was assumed to be a composite material composed of a pressure-sensitive solid matrix and spherical pores. In this context，the incremental variational principle for porous rock was proposed. Secondly，the local mechanical behaviors of solid matrix were assumed to obey a threshold and isotropic hardening parabolic Mises-Schleicher plastic model, the local increment potential of solid matrix as well as the effective incremental potential of porous rock were deduced. The macroscopic stress-strain relationship of porous rock was obtained by optimizing the effective incremental potential and combining with the Mori-Tanaka homogenization method. Finally，a numerical algorithm for the multi-scale elastoplastic constitutive model was developed based on the traditional return mapping algorithm，and a UMAT subroutine was compiled to embed the multi-scale model into Abaqus software. The accuracy and effectiveness of the multi-scale model were verified by comparing the simulation results of the multi-scale model with the finite element unit cell model(reference solutions) as well as the test data of typical Vosges sandstone. The results show that the numerical solution of the multi-scale model based on the incremental variational theory was in a good agreement with the finite element reference solution，and can accurately reproduce the macroscopic mechanical behavior of the Vosges sandstone.
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2022, Vol. 41 
