As part of his groundbreaking work on generalized continuum mechanics, Eringen proposed what he called 3M theories, namely the concept of micromorphic, microstretch, and micropolar materials modeling. The micromorphic approach provides the most general framework for a continuum with translational and (internal) rotational degrees of freedom (DOF), whilst the rotational DOFs of micromorphic and micropolar continua are subjected to more and more constraints. More recently, an “extended” micropolar theory has been presented by one of the authors: Eringen’s 3M theories were children of solid mechanics based on the concept of the indestructible material particle. Extended micropolar theory was formulated both ways for material systems as well as in spatial description, which is useful when describing fluid matter. The latter opens the possibility to model situations and materials with a continuum point that on the microscale consists no longer of the same elementary units during a physical process. The difference culminates in an equation for the microinertia tensor, which is no longer a kinematic identity. Rather it contains a new continuum field, namely an independent production term and, consequently, establishes a new constitutive quantity. This makes it possible to describe processes of structural change, which are difficult if not impossible to be captured within the material particle model. This paper compares the various theories and points out their communalities as well as their differences.

作为广义连续介质力学开创性工作的一部分，Eringen 提出了他所谓的 3M 理论，即微形态、微拉伸和微极材料建模的概念。微形态方法为具有平移和（内部）旋转自由度 (DOF) 的连续体提供了最通用的框架，而微形态和微极连续体的旋转自由度受到越来越多的约束。最近，其中一位作者提出了“扩展的”微极理论：Eringen 的 3M 理论是基于坚不可摧的材料粒子概念的固体力学的子代。扩展的微极理论既适用于材料系统，也适用于空间描述，这在描述流体物质时很有用。后者开启了用连续点对情况和材料进行建模的可能性，该点在微观尺度上不再由物理过程中的相同基本单元组成。差异在微惯性张量的方程中达到顶峰，它不再是运动学恒等式。相反，它包含一个新的连续域，即一个独立的生产项，因此，它建立了一个新的构成量。这使得描述结构变化过程成为可能，即使不是不可能，也很难在材料粒子模型中捕获。本文比较了各种理论，指出了它们的共同点和不同点。差异在微惯性张量的方程中达到顶峰，它不再是运动学恒等式。相反，它包含一个新的连续域，即一个独立的生产项，因此，它建立了一个新的构成量。这使得描述结构变化过程成为可能，即使不是不可能，也很难在材料粒子模型中捕获。本文比较了各种理论，指出了它们的共同点和不同点。差异在微惯性张量的方程中达到顶峰，它不再是运动学恒等式。相反，它包含一个新的连续域，即一个独立的生产项，因此，它建立了一个新的构成量。这使得描述结构变化过程成为可能，即使不是不可能，也很难在材料粒子模型中捕获。本文比较了各种理论，指出了它们的共同点和不同点。在材料粒子模型中即使不是不可能也很难捕获。本文比较了各种理论，指出了它们的共同点和不同点。在材料粒子模型中即使不是不可能也很难捕获。本文比较了各种理论，指出了它们的共同点和不同点。