Abstract A large class of rock-like materials are composed of a plastic solid matrix in which various inclusions and pores are embedded. This paper is devoted to determine macroscopic inelastic responses of such materials by a nonlinear homogenization procedure. The plastic behavior of solid matrix is described by a plastic model based on the pressure-dependent Drucker-Prager criterion. The plastic strain field of solid matrix is divided into a volumetric part and a shear part. Unlike most mean-field methods previously developed, the strain field in the solid matrix is non-uniform and this non-uniform field is taken into account by using an incremental variational model. The whole loading history is divided into a limit number of increment. For the sake of simplicity, the behavior of solid matrix is first assumed to be elastic-perfectly plastic at each loading increment. With the help of a time derivative approximation, the local incremental potential of the solid matrix is deduced. By considering the effect of inclusions and pores, the effective incremental potential of the heterogeneous composite is determined and estimated with the help of a linear comparison material. The macroscopic stress of the composite is finally estimated from the effective incremental potential. The accuracy of the proposed model is assessed by a series of comparisons with reference results obtained from direct finite element simulations respectively for inclusion-reinforced and porous materials. Finally, by assuming that the general form of incremental variational model remains valid when the solid matrix exhibits an isotropic plastic hardening, the proposed model is extended by updating the value of frictional coefficient of solid matrix and keeping it as a constant at each loading increment. The proposed model in this case is also well validated by comparisons with finite element reference results. Moreover, as examples of application, the model is used to simulate laboratory tests performed on a cement mortar and a typical porous sandstone.

中文翻译：

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基于增量变分原理的塑性基体类岩石材料均质化

摘要 一大类类岩石材料是由内嵌有各种包裹体和孔隙的塑性固体基质组成。本文致力于通过非线性均质化程序确定此类材料的宏观非弹性响应。固体基体的塑性行为由基于压力相关的 Drucker-Prager 准则的塑性模型描述。固体基体的塑性应变场分为体积部分和剪切部分。与以前开发的大多数平均场方法不同，固体基质中的应变场是非均匀的，并且通过使用增量变分模型来考虑这种非均匀场。整个加载历史被划分为一个限制数量的增量。为了简单起见，固体基体的行为首先被假定为在每个加载增量下都是完全弹塑性的。借助时间导数近似，推导出固体基质的局部增量势。通过考虑夹杂物和孔隙的影响，在线性比较材料的帮助下确定和估计非均质复合材料的有效增量潜力。复合材料的宏观应力最终由有效增量电位估计。所提出的模型的准确性是通过与分别针对夹杂物增强材料和多孔材料的直接有限元模拟获得的参考结果进行一系列比较来评估的。最后，通过假设当固体基体呈现各向同性塑性硬化时增量变分模型的一般形式仍然有效，通过更新固体基体的摩擦系数值并在每个加载增量下保持它为常数来扩展所提出的模型。通过与有限元参考结果的比较，在这种情况下提出的模型也得到了很好的验证。此外，作为应用示例，该模型用于模拟对水泥砂浆和典型多孔砂岩进行的实验室测试。