论文标题
关于弹性张量的应力依赖性
On the stress dependence of the elastic tensor
论文作者
论文摘要
理论上研究了弹性张量对平衡应力的依赖性。使用有限弹性的想法，首先表明平衡应力和弹性张量都是根据平衡变形梯度相对于固定的参考主体而独特地给出的。因此，期望变形梯度和应力之间关系之间的关系的反转可能会整齐地导致弹性张量的所需表达。不幸的是，变形梯度只能从应力中回收到旋转矩阵的选择。因此，通常不可能将弹性张量表示为平衡应力的独特功能。但是，通过考虑材料对称性，可以表明有时可以降低非唯一性的程度，在某些情况下甚至完全消除了。这些结果通过范围的数值计算说明，我们还获得了适用于平衡应力下小扰动的线性关系。最后，在考虑对地球物理前进和反向模型的影响之前，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 linearised 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.
