AI 中文总结
该研究提出改进型单调性方法，可独立于第一拉梅参数非均匀性重构剪切模量夹杂，优于此前仅能在特定假设下重构体积模量夹杂的方法。
AI 中文摘要
我们针对线性弹性静力学逆问题中的形状重构问题，提出了一种改进型单调性方法。该方法可重构第二拉梅参数（即剪切模量）中的夹杂，且与第一拉梅参数中的非均匀性无关，优于此前仅能在拉梅参数局部相互作用特定假设下重构体积模量夹杂的方法。证明基于线性化及利用调和向量场的能量无散定位。
英文摘要
We formulate an improved version of the monotonicity method for shape reconstruction in the inverse problem of linear elastostatics. We show that this method can reconstruct inclusions in the second Lamé parameter, i.e., the shear modulus, independently of inhomogeneities in the first Lamé parameter. This improves on earlier methods that only recover inclusions in the bulk modulus under certain assumptions on the local interplay between the Lamé parameters. Our proofs are based on linearization and divergence-free localization of energy using harmonic vector fields.
Comments16 pages, 1 figure
