In this work, we shall propose a new micro-mechanical constitutive model for the estimation of effective elastic-plastic behaviors of heterogeneous rocks. A bi-potential based incremental variational (BIV) approach is developed in order to take into account non-uniform local strain fields of constituents. The studied materials are composed of a non-associated and pressure sensitive plastic matrix, elastic inclusions and/or voids. For clarity, the local behavior of matrix is first described by an elastic perfectly-plastic model. Based on the bi-potential theory to dealing with non-associated plastic flow, the solid matrix is considered as pertaining to implicit standard materials (ISMs). The effective incremental bi-potential and macroscopic stress tensor are then estimated through an extension of the incremental variational method initially established for generalized standard materials(GSMs). The accuracy of the BIV model is verified by comparing the model’s predictions with the reference results obtained from direct finite element simulations. Furthermore, by assuming that the general formulation obtained for the perfectly plastic matrix remains valid for each loading increment, the BIV model is extended to considering that the solid matrix exhibits an isotropic hardening by using an explicit algorithm. The accuracy of the extended BIV model is also validated by a series of comparisons with the reference solutions obtained by direct finite element simulations for both inclusion-reinforced composites and porous materials. Both local and macroscopic responses are compared. As an example of application, the extended BIV model is finally applied to estimating the mechanical responses of typical claystone and sandstone under different loading paths.

在这项工作中，我们将提出一个新的微机械本构模型，用于估算非均质岩石的有效弹塑性行为。为了考虑成分的不均匀局部应变场，开发了一种基于双电位的增量变分（BIV）方法。所研究的材料由非缔合且压敏的塑料基质，弹性夹杂物和/或空隙组成。为了清楚起见，首先通过弹性完全塑性模型描述矩阵的局部行为。基于处理非关联塑性流的双势理论，将固体基质视为与隐式标准材料（ISM）有关。然后，通过最初为通用标准材料（GSM）建立的增量变分方法的扩展，估算有效的增量双电势和宏观应力张量。通过将模型的预测与直接有限元模拟获得的参考结果进行比较，可以验证BIV模型的准确性。此外，通过假设为完美塑性基体获得的一般配方对于每个加载增量保持有效，BIV模型可以扩展到考虑使用显式算法使固体基体表现出各向同性的硬化。扩展的BIV模型的准确性还通过与包含固溶增强复合材料和多孔材料的直接有限元模拟获得的参考解决方案进行了一系列比较来验证。比较了局部响应和宏观响应。作为一个应用实例，扩展的BIV模型最终被用于估计不同荷载路径下典型粘土和砂岩的力学响应。