The identification of nonhomogeneous elastic property distributions has been traditionally achieved with well acknowledged optimization based inverse approaches, but when full-field displacement measurements are available, the virtual fields method (VFM) can be computationally more efficient by converting the large-scale optimization problem into multiple small-scale optimization problems. A possible downside of the VFM so far was not to take into account prior knowledge, which is often available and needed when there is a very large number of unknowns and the inverse problem is ill-posed. In this work, different approaches are proposed for introducing regularization into the VFM, aiming to penalize the local variations of identified stiffness properties in order to reduce the effects of uncertainty in the inverse problem resolution. The feasibility and accuracy of the regularized VFM are tested through several numerical and experimental datasets. It is shown that the main advantage of the novel VFM approaches is the low computational cost, as large-scale inverse problems with 10,000 unknown parameters can be solved within several seconds using a standard personal computer. Although the regularized VFM can successfully detect a stiff inclusion in a soft solid with high accuracy, regularization also introduces unexpected spurious effects in the results, blurring the interface between soft and stiff regions. We also observed that the regularization did not improve the smoothness significantly due to local effects of the small-scale optimization problem introduced in the proposed VFM method. Therefore, traditional regularization, which penalizes local variations of identified stiffness properties, can be combined with the VFM to solve inverse problems with a high computational efficiency, but supplemental regularization conditions will need to be adapted in the future to better delineate soft-stiff interfaces with this methodology.

传统上已经使用公认的基于优化的逆方法来实现非均匀弹性特性分布的识别，但是当可以使用全场位移测量时，通过将大规模优化问题转换为虚拟场方法（VFM），可以提高计算效率。多个小规模优化问题。迄今为止，VFM的一个可能缺点是没有考虑先验知识，而当存在大量未知数且逆问题不适当时，常识是经常需要和需要的。在这项工作中，提出了将正则化引入VFM的不同方法，旨在惩罚已识别刚度属性的局部变化，以减少反问题解决方案中不确定性的影响。通过几个数值和实验数据集测试了正则化VFM的可行性和准确性。结果表明，新颖的VFM方法的主要优点是计算成本低，因为可以使用标准的个人计算机在几秒钟内解决具有10,000个未知参数的大规模逆问题。尽管正则化VFM可以高精度准确地检测到软固体中的刚性夹杂物，但正则化还会在结果中引入意外的杂散效应，从而模糊了软性区域和硬性区域之间的界面。我们还观察到，由于提出的VFM方法中引入的小规模优化问题的局部影响，正则化并没有显着提高平滑度。因此，传统的正则化