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

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