Classical elasticity mechanics fails to explain size-dependent phenomenon, the strain gradient elasticity theories including the couple stress theory, the simplified strain gradient elasticity theory and the general strain gradient elasticity theory are used to describe size effects. In this paper, the relations among the couple stress theory, the simplified strain gradient elasticity theory and the general strain gradient elasticity theory are derived. The general strain gradient elasticity theory contains the effects of all strain gradients while the couple stress theory and the simplified strain gradient elasticity theory include effects of only part of the strain gradients, thus, the general strain gradient elasticity theory can reduce to the couple stress theory, the simplified strain gradient elasticity theory when some strain gradients are neglected. Subsequently, a reasoning comparison with examples is performed to discuss the differences between the general strain gradient elasticity theory and the reduced theories in describing the size effects: one is the static and dynamic responses of a microbeam and the other is the tensile of a microbar. In the beam bending and vibration example, the material length-scale parameters and the deflections predicted by the reduced theories are larger while the natural frequency is smaller than that of the general strain gradient elasticity theory. The reduced theories underestimate the size-dependent response of a bending beam. In the bar tensile example, the couple stress theory fails to predict the size-dependent tensile behaviour. This illustrates clearly that compared with the reduced theories, the general strain gradient elasticity theory is capable to describe the size effects more appropriately.

古典弹性力学无法解释尺寸依赖性现象，包括耦合应力理论，简化应变梯度弹性理论和一般应变梯度弹性理论在内的应变梯度弹性理论被用来描述尺寸效应。本文推导了耦合应力理论，简化应变梯度弹性理论和一般应变梯度弹性理论之间的关系。一般应变梯度弹性理论包含所有应变梯度的影响，而耦合应力理论和简化应变梯度弹性理论仅包含部分应变梯度的影响，因此，一般应变梯度弹性理论可以简化为偶应力理论，忽略某些应变梯度时的简化应变梯度弹性理论。随后，与实例进行推理比较，以讨论一般应变梯度弹性理论与简化理论在描述尺寸效应时的区别：一个是微梁的静态和动态响应，另一个是微棒的拉伸。在梁的弯曲和振动示例中，材料长度尺度参数和由简化理论预测的挠度较大，而固有频率小于一般应变梯度弹性理论的固有频率。简化的理论低估了弯曲梁的尺寸相关响应。在钢筋拉伸示例中，耦合应力理论无法预测尺寸相关的拉伸行为。