First strain-gradient elasticity is a generalized continuum theory capable of modelling size effects in materials. This extended capability comes from the inclusion in the mechanical energy density of terms related to the strain-gradient. In its linear formulation, the constitutive law is defined by three elasticity tensors whose orders range from four to six. In the present contribution, the symmetry properties of the sixth-order elasticity tensors involved in this model are investigated. If their classification with respect to the orthogonal symmetry group is known, their classification with respect to symmetry planes is still missing. This last classification is important since it is deeply connected with some identification procedures. The classification of sixth-order elasticity tensors in terms of invariance properties with respect to symmetry planes is given in the present contribution. Precisely, it is demonstrated that there exist 11 reflection symmetry classes. This classification is distinct from the one obtained with respect to the orthogonal group, according to which there exist 17 different symmetry classes. These results for the sixth-order elasticity tensor are very different from those obtained for the classical fourth-order elasticity tensor, since in the latter case the two classifications coincide. A few numerical examples are provided to illustrate how some different orthogonal classes merge into one reflection class.

第一应变梯度弹性是一种广义连续统理论，能够模拟材料中的尺寸效应。这种扩展能力来自机械能密度中包含与应变梯度相关的项。在其线性公式中，本构律由三个弹性张量定义，其阶数从四到六不等。在目前的贡献中，研究了该模型中涉及的六阶弹性张量的对称性。如果它们关于正交对称群的分类是已知的，它们关于对称平面的分类仍然缺失。最后一个分类很重要，因为它与某些识别程序密切相关。六阶弹性张量在关于对称平面的不变性方面的分类在本贡献中给出。确切地说，证明存在 11 个反射对称类。这种分类不同于根据正交群获得的分类，根据正交群存在 17 个不同的对称类。六阶弹性张量的这些结果与经典四阶弹性张量的结果非常不同，因为在后一种情况下，这两种分类是一致的。提供了一些数值示例来说明一些不同的正交类如何合并为一个反射类。这种分类不同于根据正交群获得的分类，根据正交群存在 17 个不同的对称类。六阶弹性张量的这些结果与经典四阶弹性张量的结果非常不同，因为在后一种情况下，这两种分类是一致的。提供了一些数值示例来说明一些不同的正交类如何合并为一个反射类。这种分类不同于根据正交群获得的分类，根据正交群存在 17 个不同的对称类。六阶弹性张量的这些结果与经典四阶弹性张量的结果非常不同，因为在后一种情况下，这两种分类是一致的。提供了一些数值示例来说明一些不同的正交类如何合并为一个反射类。