FEniCS implementation of the Virtual Fields Method (VFM) for nonhomogeneous hyperelastic identification. (January 2023)

• Record Type: Journal Article
• Authors: Deng, Jianwei; Guo, Xu; Mei, Yue; Avril, Stephane
• Is Part Of: Advances in engineering software. Volume 175(2023)
• Publication Date: 2023-01
• Subjects: Virtual Fields Method -- Nonhomogeneous elastic property identification -- Hyperelasticity -- FEniCS; Computer-aided engineering -- Periodicals; Engineering -- Computer programs -- Periodicals; Engineering -- Software -- Periodicals; Periodicals; 620.0028553
• DOI: 10.1016/j.advengsoft.2022.103343
• Languages: English
• ISSNs: 0965-9978

Abstract

Highlights: Novel implementation in FEniCS of the Virtual Fields Method(VFM) for nonhomogeneous hyperelastic identification has been performed. Artificial virtual fields are circumvented in the proposed VFM methods. A novel proposed VFM is capable of identifying the spatially variation of the nonhomogeneous hyperelastic distributions of soft solids. Several examples with solid clinical significance have been presented to show the feasibility of the proposed VFM method. Abstract: It is of great significance to identify the nonhomogeneous distribution of material properties in human tissues for different clinical and medical applications. This leads to the requirement of solving an inverse problem in elasticity. The Virtual Fields Method (VFM) is a rather recent inverse method with remarkable computational efficiency compared with the optimization-based methods. In this study, we aim to identify nonhomogeneous hyperelastic material properties using the VFM. We propose two novel algorithms, RE-VFM and NO-VFM. In RE-VFM, the solid is partitioned in different regions and the elastic properties of each region are determined. In NO-VFM, the distribution of elastic properties is completely reconstructed through the inverse problem without partitioning the solid. As the VFM requires to use virtual fields, we proposed an efficient way to construct them and implemented the approach in the FEniCS package. We validated the proposed methods on several examples, including a bilayer structure, a lamina cribosa (LC) model and a cube model embedded with a spherical inclusion. The numerical examples illustrate the feasibility of both RE-VFM and NO-VFM. Notably, the spatial variations of the Young's modulus distribution can be recovered accurately within only 5 iterations. The obtained results reveal the potential of the proposed methods for future clinical applications such as estimating the risk of vision loss related to glaucoma and detecting tumors.