We derive the Green tensor of Mindlin’s anisotropic first strain gradient elasticity. The Green tensor is valid for arbitrary anisotropic materials, with up to 21 elastic constants and 171 gradient elastic constants in the general case of triclinic media. In contrast to its classical counterpart, the Green tensor is non-singular at the origin, and it converges to the classical tensor a few characteristic lengths away from the origin. Therefore, the Green tensor of Mindlin’s first strain gradient elasticity can be regarded as a physical regularization of the classical anisotropic Green tensor. The isotropic Green tensor and other special cases are recovered as particular instances of the general anisotropic result. The Green tensor is implemented numerically and applied to the Kelvin problem with elastic constants determined from interatomic potentials. Results are compared to molecular statics calculations carried out with the same potentials.

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Mindlin各向异性第一应变梯度弹性的Green张量

我们推导了Mindlin各向异性第一应变梯度弹性的Green张量。Green张量适用于任意各向异性的材料，在三斜介质的一般情况下，其弹性常数最多为21，梯度弹性常数最大为171。相对于经典张量，格林张量在原点处不是奇异的，并且收敛到经典张量时离原点有几个特征长度。因此，可以将Mindlin的第一张应变梯度弹性的格林张量视为经典各向异性格林张量的物理正则化。各向同性格林张量和其他特殊情况作为一般各向异性结果的特定实例得以恢复。Green张量通过数值实现，并通过由原子间电势确定的弹性常数应用于开尔文问题。将结果与在相同电势下进行的分子静力学计算进行比较。