基于增量变分理论的多孔岩石多尺度弹塑性本构模型

doi:10.13722/j.cnki.jrme.2021.0660

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摘要为考虑多孔岩石在荷载作用下细观(局部)非均匀的应力场和应变场对其宏观力学特性的影响，提出一种基于增量变分理论的多尺度弹塑性本构模型。首先将多孔岩石看作由压敏性固体基质和球形孔隙组成的复合材料，给出多孔岩石的增量变分理论；其次假设固体基质的局部力学行为服从具有阈值和各向同性硬化的抛物型Mises- Schleicher塑性模型，推导固体基质的局部增量势和多孔岩石的有效增量势，通过对有效增量势进行优化求解并结合Mori-Tanaka均匀化方法获得多孔岩石的宏观应力–应变关系；最后在传统回映算法基础上发展多尺度模型的数值算法，并编制UMAT子程序将多尺度模型嵌入Abaqus软件。将多尺度模型模拟结果和有限元单胞模拟结果(参考解)以及Vosges砂岩试验结果进行对比，验证多尺度模型的准确性和有效性。研究表明，基于增量变分理论的多尺度模型数值解与有限元参考解有很好的一致性，能够准确地再现Vosges砂岩的宏观力学行为。

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	赵伦洋1
	2
	赖远明1
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	牛富俊1
	2
	朱其志4
	邵建富4

关键词 ：岩石力学, 增量变分, 多孔岩石, 均匀化, 弹塑性, 多尺度本构

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.

Key words： rock mechanics incremental variation porous rock homogenization elastoplastic multi scale constitutive

引用本文:

赵伦洋1，2，赖远明1，3，牛富俊1，2，朱其志4，邵建富4. 基于增量变分理论的多孔岩石多尺度弹塑性本构模型[J]. 岩石力学与工程学报, 2022, 41(S2): 3163-3173.
ZHAO Lunyang1，2，LAI Yuanming1，3，NIU Fujun1，2，ZHU Qizhi4，SHAO Jianfu4. A multi-scale elastoplastic constitutive model of porous rock based on incremental variational theory. , 2022, 41(S2): 3163-3173.

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http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2021.0660 或 http://rockmech.whrsm.ac.cn/CN/Y2022/V41/IS2/3163

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