On the stress dependence of the elastic tensor
On the stress dependence of the elastic tensor
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DOI：
10.1093/gji/ggaa591
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发表时间：
2020-07
影响因子：
2.8
通讯作者：
Matthew Maitra;D. Al-Attar
中科院分区：
文献类型：
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作者：
Matthew Maitra;D. Al-Attar
从理论上研究了弹性张量对平衡应力的依赖关系。利用有限弹性力学的思想，首先证明了平衡应力和弹性张量都是相对于固定选择的参考体的平衡变形梯度唯一给出的。因此，变形梯度和应力之间的关系的反演，可以预期会整齐地导致所需的弹性张量的表达式。不幸的是，变形梯度只能从应力恢复到旋转矩阵的选择。因此，一般不可能将弹性张量表示为平衡应力的唯一函数。通过考虑材料的对称性，虽然，它表明，非唯一性的程度有时可以减少，在某些情况下，甚至完全删除。这些结果通过一系列的数值计算来说明，我们也得到了适用于平衡应力小扰动的线性关系。最后，在考虑地球物理正演和反演建模的影响之前，我们与以前的研究进行了比较。
The dependence of the elastic tensor on the equilibrium stress is investigated theoretically. Using ideas from finite elasticity, it is first shown that both the equilibrium stress and elastic tensor are given uniquely in terms of the equilibrium deformation gradient relative to a fixed choice of reference body. Inversion of the relation between the deformation gradient and stress might, therefore, be expected to lead neatly to the desired expression for the elastic tensor. Unfortunately, the deformation gradient can only be recovered from the stress up to a choice of rotation matrix. Hence it is not possible in general to express the elastic tensor as a unique function of the equilibrium stress. By considering material symmetries, though, it is shown that the degree of non-uniqueness can sometimes be reduced, and in some cases even removed entirely. These results are illustrated through a range numerical calculations, and we also obtain linearized relations applicable to small perturbations in equilibrium stress. Finally, we make a comparison with previous studies before considering implications for geophysical forward- and inverse-modelling.