This paper presents a method to derive the virtual fields for identifying constitutive model parameters using the Virtual Fields Method (VFM). The VFM is an approach to identify unknown constitutive parameters using deformation fields measured across a given volume of interest. The general principle for solving identification problems with the VFM is first to derive parametric stress field, where the stress components at any point depend on the unknown constitutive parameters, across the volume of interest from the measured deformation fields. Applying the principle of virtual work to the parametric stress fields, one can write scalar equations of the unknown parameters and solve the obtained system of equations to deduce the values of unknown parameters. However, no rules have been proposed to select the virtual fields in identification problems related to nonlinear elasticity and there are multiple strategies possible that can yield different results. In this work, we propose a systematic, robust and automatic approach to reconstruct the systems of scalar equations with the VFM. This approach is well suited to finite-element implementation and can be applied to any problem provided that full-field deformation data are available across a volume of interest. We also successfully demonstrate the feasibility of the novel approach by multiple numerical examples. Potential applications of the proposed approach are numerous in biomedical engineering where imaging techniques are commonly used to observe soft tissues and where alterations of material properties are markers of diseased states.

Purpose: This study aimed to employ the incremental digital image correlation (DIC) method to obtain displacement and strain field data of the cornea from Corvis ST (CVS) sequences and access the performance of embedding these biomechanical data with machine learning models to distinguish forme fruste keratoconus (FFKC) from normal corneas. Methods: 100 subjects were categorized into normal (N = 50) and FFKC (N = 50) groups. Image sequences depicting the horizontal cross-section of the human cornea under air puff were captured using the Corvis ST tonometer. The high-speed evolution of full-field corneal displacement, strain, velocity, and strain rate was reconstructed utilizing the incremental DIC approach. Maximum (max-) and average (ave-) values of full-field displacement V, shear strain γxy, velocity VR, and shear strain rate γxyR were determined over time, generating eight evolution curves denoting max-V, max-γxy, max-VR, max-γxyR, ave-V, ave-γxy, ave-VR, and ave-γxyR, respectively. These evolution data were inputted into two machine learning (ML) models, specifically Naïve Bayes (NB) and Random Forest (RF) models, which were subsequently employed to construct a voting classifier. The performance of the models in diagnosing FFKC from normal corneas was compared to existing CVS parameters. Results: The Normal group and the FFKC group each included 50 eyes. The FFKC group did not differ from healthy controls for age (p = 0.26) and gender (p = 0.36) at baseline, but they had significantly lower bIOP (p < 0.001) and thinner central cornea thickness (CCT) (p < 0.001). The results demonstrated that the proposed voting ensemble model yielded the highest performance with an AUC of 1.00, followed by the RF model with an AUC of 0.99. Radius and A2 Time emerged as the best-performing CVS parameters with AUC values of 0.948 and 0.938, respectively. Nonetheless, no existing Corvis ST parameters outperformed the ML models. A progressive enhancement in performance of the ML models was observed with incremental time points during the corneal deformation. Conclusion: This study represents the first instance where displacement and strain data following incremental DIC analysis of Corvis ST images were integrated with machine learning models to effectively differentiate FFKC corneas from normal ones, achieving superior accuracy compared to existing CVS parameters. Considering biomechanical responses of the inner cornea and their temporal pattern changes may significantly improve the early detection of keratoconus.

In this article, the finite element model considering the casing eccentricity of high-pressure, high-temperature wellbore integrity is established, where the cohesive zone element is introduced to evaluate the mechanical behavior of the casing–cement sheath interface. In this analysis, the bilinear traction–separation law is used to estimate the interfacial failure, and a damage factor is simultaneously defined to describe the damage evolution of the cohesive element. In addition, to achieve the interfacial separation, the pressure fluctuation inside the casing is applied. Using the finite element approach, we investigate the effect of mechanical parameters including Young’s modulus, Poisson’s ratio, thermal conductivity of the cement sheath, and pressure fluctuation inside the casing on the interfacial failure of the casing–cement sheath. The simulation results show that the damage factor increases with the increase in the mechanical parameters including Young’s modulus and Poisson’s ratio of the cement sheath and the casing pressure fluctuation. We also observe that the maximum damage factor under higher thermal conductivity is higher than that under lower thermal conductivity for the casing concentricity, while it is lower than that under lower thermal conductivity for the casing eccentricity. This indicates that the casing eccentricity has an important impact on the damage factor. What’s more, the casing eccentricity can change the location where the maximum damage factor occurs.