Tomographic reconstruction of stress from photoelastic measurements using elastic regularization.
Tomographic reconstruction of stress from photoelastic measurements using elastic regularization.
复制标题
使用弹性正则化从光弹性测量中进行断层扫描重建应力。
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
R. Tomlinson
中科院分区：
文献类型：
--
作者：
David Szotten;W. Lionheart;R. Tomlinson
在本文中，我们考虑从三维物体恢复应力张量场的问题
透射光偏振态的测量。与建议的射线变换方法相反
由 Sharafutdinov 提出，它使用平面氡变换的反演来恢复单个分量
垂直于平面的偏应力，我们研究偏应力所有分量的同时重建
使用截断横向射线变换的矩阵近似来计算每个体素中的应力。这种方法允许我们在正则化惩罚项中采用与线性弹性相关的偏微分算子，从而产生适定问题。我们注意到，静水应力是由偏应力决定的（高达
平衡方程中的加性常数），并且我们的数值结果证实可以使用弹性正则化来恢复全应力张量。
In this paper we consider the problem of recovering the stress tensor field of a three dimensional object from
measurements of the polarization state of transmitted light. In contrast to the ray transform approach suggested
by Sharafutdinov, which uses the inversion of planar Radon transforms to recover a single component of the
deviatoric stress normal to a plane, we study the simultaneous reconstruction of all components of the deviatoric
stress in each voxel using a matrix approximation to the truncated transverse ray transform. This approach allows us to employ partial differential operators related to linear elasticity in a regularizing penalty term resulting in a well posed problem. We note that the hydrostatic stress is determined by the deviatoric stress (up to
an additive constant) from the equilibrium equation, and that our numerical results confirm that the full stress tensor can be recovered using elastic regularization.