The present contribution provides a classification of generalized continua constructed by a micromechanical approach, relying on an extension of the Hill macrohomogeneity condition. The virtual power of equilibrium for a micromorphic effective medium is derived from the microscopic Cauchy balance equations, highlighting the classical and higher-order macroscopic stress tensors. The so-called homogeneous displacement associated with the micromorphic effective medium is derived from variational formulations. It allows establishing the extended Hill macrohomogeneity condition that prevails for the micromorphic continuum, wherein the higher-order stress tensors arise as the static variables conjugated to the selected macroscopic degrees of freedom. Suitable projections of the introduced kinematic micromorphic variables into degenerated kinematic variables lead to various subclasses of generalized continua: microstretch, micropolar, couple stress, microdilatation, microstrain, microshear, and strain gradient. An asymptotic ranking of the formulated generalized continua versus a small-scale parameter is formulated in the last part of the paper to quantify their relative importance. The micromorphic homogenization scheme is validated by comparing the predictions of the homogenized response at the macroscale for a double shear test to a reference exact solution. The proposed micromorphic homogenization method remedy most of the limitations of the existing schemes of the literature.

目前的贡献提供了一种由微机械方法构建的广义连续体的分类，依赖于希尔宏观均匀性条件的扩展。微形态有效介质的虚拟平衡力源自微观柯西平衡方程，突出了经典和高阶宏观应力张量。与微形态有效介质相关的所谓均匀位移源自变分公式。它允许建立微形态连续体普遍存在的扩展希尔宏观均匀性条件，其中高阶应力张量作为与所选宏观自由度共轭的静态变量出现。将引入的运动学微形态变量适当投影到简并运动学变量中会产生广义连续体的各种子类：微拉伸、微极性、耦合应力、微膨胀、微应变、微剪切和应变梯度。本文的最后部分制定了广义连续体与小尺度参数的渐近排名，以量化它们的相对重要性。通过将双剪切测试宏观尺度均质响应的预测与参考精确解进行比较来验证微形态均质化方案。所提出的微形态均质化方法弥补了现有文献方案的大部分局限性。微应变、微剪切和应变梯度。本文的最后部分制定了广义连续体与小尺度参数的渐近排名，以量化它们的相对重要性。通过将双剪切测试宏观尺度均质响应的预测与参考精确解进行比较来验证微形态均质化方案。所提出的微形态均质化方法弥补了现有文献方案的大部分局限性。微应变、微剪切和应变梯度。本文的最后部分制定了广义连续体与小尺度参数的渐近排名，以量化它们的相对重要性。通过将双剪切测试宏观尺度均质响应的预测与参考精确解进行比较来验证微形态均质化方案。所提出的微形态均质化方法弥补了现有文献方案的大部分局限性。通过将双剪切测试宏观尺度均质响应的预测与参考精确解进行比较来验证微形态均质化方案。所提出的微形态均质化方法弥补了现有文献方案的大部分局限性。通过将双剪切测试宏观尺度均质响应的预测与参考精确解进行比较来验证微形态均质化方案。所提出的微形态均质化方法弥补了现有文献方案的大部分局限性。