Introducing regularization into the virtual fields method (VFM) to identify nonhomogeneous elastic property distributions

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

“…Compared to [15], the NO-VFM method can be used to identify the material properties for a hyperelastic solid with a complex geometry. The feasibility of the proposed method has been successfully tested by several numerical examples were shown in the…”

“…However, if the boundary of each homogeneous region is unknown, the inverse problem becomes highly challenging to solve due to the large number of unknown elastic parameters. To address this issue, a novel scheme considering virtual work balance between neighborhood elements was recently proposed [15]. However, this previous study focused on a simple geometry.…”

Adaptation of the virtual fields method for the identification of biphasic hyperelastic model parameters in soft biological tissues with osmotic swelling

“…However, two other heterogeneous virtual fields are required to be introduced to ensure independence among the three VFM equations. Based on Equation (26), two other virtual fields can be determined as illustrated in Figure 8b,c where parameters setting details can also be found.…”

“…The identification of constitutive model parameters for soft biological tissues is still flourishing. [18,19] Among the available identification approaches, the virtual fields method (VFM) has been widely used in solid mechanics, [20][21][22][23][24][25][26] given its advantages, such as its insensitivity to the uncertainty of boundary conditions, [27] robustness, [28] and fast convergence. [29] Avril et al [30] first applied VFM to arterial tissues to identify anisotropic hyperelastic material parameters.…”

Combining physics-based modeling and deep learning for ultrasound elastography

“…Conventional FEM-based elastography methods which employ governing partial differential equations (PDEs) use Gaussian-Newton methods which assume an initial elasticity modulus and solve the constrained global stiffness equation iteratively until converging to a stationary point leading to a poor and unstable performance in noisy condition [1]. Furthermore, these methods employ fixed hand-crafted regularizers [2] for all tissue patterns although adaptive priors should be exploited for each specific tissue type. Deep neural network (DNN) capabilities propose to integrate the forward imaging model with learned data-driven priors as a constrained optimization problem rather than using end-to-end learning approaches [3,4,5,6].…”