3D full-time anisotropic TEM modelling using a mixed BDF2/SAI method

Transient electromagnetic (TEM) data are affected by resistivity anisotropy, which should be considered in 3D modelling. The influence of anisotropy on full-time response is the main focus of this research. For spatial discretisation of an anisotropic model, the mimetic finite volume approach was applied. The accuracy of the shift-and-invert (SAI) Krylov subspace approach and the two-step backward differentiation formula (BDF2) for modelling 3D full-time electromagnetic data has been demonstrated. However, both algorithms require time-consuming calculations. The SAI technique requires a number of projection subspace constructions, whereas the BDF2 algorithm necessitates numerous coefficient matrix decompositions. We proposed a novel mixed BDF2/SAI algorithm in this paper, which combines the advantages of the two algorithms. The on-time response is computed using BDF2, while the off-time response is computed using the SAI-Krylov subspace method. The forward results of a 1D model with a half-sine waveform demonstrated that the new algorithm is accurate and faster than both the BDF2 algorithm and the SAI algorithm. During the full-time period, the forward results of a 3D anisotropic model with half-sine waveform show that abnormal responses can be induced. It was shown that the relative abnormal of ${{{\bf b}}_{\boldsymbol{z}}}$ is higher during the on-time period, while the relative abnormal of $\partial {{{\bf b}}_{\boldsymbol{z}}}/\partial t$ is higher during the off-time period. Furthermore, the change in relative anomaly is more obvious as the anisotropic block rotates around the x-axis. And the larger the rotation angle, the larger the relative anomaly.

Biaxial estimation of biomechanical constitutive parameters of passive porcine sclera soft tissue

This study assesses the modelling capabilities of four constitutive hyperplastic material models to fit the experimental data of the porcine sclera soft tissue. It further estimates the material parameters and discusses their applicability to a finite element model by examining the statistical dispersion measured through the standard deviation. Fifteen sclera tissues were harvested from porcine’ slaughtered at an abattoir and were subjected to equi-biaxial testing. The results show that all the four material models yielded very good correlations at correlations above 96 %. The polynomial (anisotropic) model gave the best correlation of 98 %. However, the estimated material parameters varied widely from one test to another such that there would be needed to normalise the test data to avoid long optimisation processes after applying the average material parameters to finite element models. However, for application of the estimated material parameters to finite element models, there would be needed to consider normalising the test data to reduce the search region for the optimisation algorithms. Although the polynomial (anisotropic) model yielded the best correlation, it was found that the Choi-Vito had the least variation in the estimated material parameters thereby making it an easier option for application of its material parameters to a finite element model and also requiring minimum effort in the optimisation procedure. For the porcine sclera tissue, it was found that the anisotropy more influenced by the fiber-related properties than the background material matrix related properties.

The nonlinear patterns of the cosmic anisotropy: the spatially flat perfect fluid universes.

In this manuscript, we investigate the patterns of the cosmological anisotropy in the spatially flat Bianchi models filled with a perfect fluid. We analyse the factor 1 + ∆R, the ratio of the Hubble parameter in the anisotropic model over its isotropic counterpart. In general, ∆R starts to deviate significantly from zero at a specific redshift zA, which depends on the type of the fluid and the value of the anisotropy magnitude. We also show that the deceleration and the jerk along the principal directions of the expansion tensor are constrained by simple algebraic equations that do not depend on the type of matter present. These characteristic patterns form a valuable framework to probe the cosmological anisotropy in the late-time universe.

FITTING OF HYPERELASTIC CONSTITUTIVE MODELS IN DIFFERENT SHEEP HEART REGIONS BASED ON BIAXIAL MECHANICAL PROPERTIES

Heart failure remains one of the leading causes of death especially among people over the age of 60 years worldwide. To develop effective therapy and suitable replacement materials for the heart muscle it is necessary to understand its biomechanical behaviour under load. This paper investigates the passive mechanical response of the sheep myocardia excised from three different regions of the heart. Due to the relatively higher cost and huge ethical demands in acquisition and testing of real animal heart models, this paper evaluates the fitting performances of five different constitutive models on the myocardial tissue responses. Ten sheep were sacrificed, and their hearts excised and transported within 3h to the testing biomechanical laboratory. The upper sections of the hearts above the short axes were carefully dissected out. Tissues were dissected from the mid-sections of the left ventricle, mid-wall and right ventricle for each heart. The epicardia and endocardia were then carefully sliced off each tissue to leave the myocardia. Stress-strain curves were calculated, filtered and resampled. The results show that Choi-Vito model was found to provide the best fit to the LV, the polynomial (Anisotropic) model to RV, the Four-Fiber Family model to RV, Holzapfel (2000) to RV, Holzapfel (2005) to RV and the Fung model to LV.

Biomechanical behaviour and hyperelastic model parameters identification of sheep omasum

The function of the omasum is incompletely understood; however, the omasum plays an important role in the transport of appropriately sized feed particles from the reticulorumen to the abomasum, oesophageal groove closure, fermentation of ingesta, and absorption of water, volatile fatty acids, and minerals. The aim of this study is to evaluate the suitable hyperelastic anisotropic model based on biomechanical properties of sheep omasum. The results show that all five (5) hyperelastic models may be suitable for the evaluation of sheep omasum. The average coefficient of determination (R2) of Fung, Polynomial (Anisotropic), Holzapfel (2000), Holzapfel (2005) and Four-Fiber-Family hyperelastic models were found to be 0.79 ± 0.19, 0.95 ± 0.05, 0.92 ± 0.07, 0.93 ± 0.05 and 0.94 ± 0.03, respectively. Also, it was found that the best hyperelastic model for fitting uniaxial data of the sheep omasum was Polynomial (Anisotropic) with EI of 100.0 followed by the Four-Fiber-Family model with EI of 96.18.

Understanding regional mechanics of rat myocardia by fitting hyperelatsic models

Availability of biaxial mechanical data for heart myocardia remains high in demand for the development of accurate and detailed computational models. The aim of this study is to study the regional difference of wall mechanics using rat heart in the left ventricle (LV), septal wall (STW) and right ventricle (RV). This was achieved by conducting a biaxial test on three rat heart myocardia (i.e LV, RV and STW). Fung, Choi-Vito, Polynomial (Anistropic), Four-Fiber family, Holzapfel (2000) and Holzapfel (2005) hyperelastic models were selected and fitted on the bixial data of the LV, RV and STW. The best hyperelastic model was the selected based on evaluation index (EI) determined from the coefficient of determination (R2). All the six models were then compared in all three rat heart myocardia. The results show that the Polynomial (Anisotropic) model outperforms the other five models in all myocardial tissues with EI’s above 90 % goodness of fit. The Four-fiber-family and the two Holzapfel models perform equally in the LV and STW myocardial tissue between 50 and 70 % goodness of fit. The Fung and Choi-Vito models yielded poor goodness of fit in the LV and STW myocardial tissues. Parameter fitting is useful method in advancing reliable data to be used in the development of accurate computational models.

Mass correction and deformation of slowly rotating anisotropic neutron stars based on Hartle–Thorne formalism

Due to their compactness, neutron stars are the best study matter in high density and strong-field gravity. Hartle and Thorne have proposed a good approximation or perturbation procedure within general relativity for slowly rotating relativistic stars by assuming the matter inside the stars is an ideal isotropic fluid. This study extends the analytical Hartle–Thorne formalism for slowly rotating neutron stars, including the possibility that the neutron star pressure can be anisotropic. We study the impact of neutron stars’ anisotropy pressure on mass correction and deformation numerically. For the anisotropic model, we use the Bowers-Liang model. For the equation of state of neutron stars, we use a relativistic mean-field BSP parameter set with the hyperons, and for the crust equation of state, we use the one of Miyatsu et al. We have found that the mass of neutron stars increases but the radius decreases by increasing $$\lambda _{BL}$$ λ BL value. Therefore, the NS compactness increases when $$\lambda _{BL}$$ λ BL becomes larger. This fact leads to a condition in which NS is getting harder to deformed when the $$\lambda _{BL}$$ λ BL increased.