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Recently, hyperelastic mechanical models were proposed to well capture the aneurismal arterial wall anisotropic and nonlinear features experimentally observed. These models were formulated assuming the material incompressibility. However in numerical analysis, a nearly incompressible approach, i.e., a mixed formulation pressure-displacement, is usually adopted to perform finite element stress analysis of abdominal aortic aneurysm (AAA). Therefore, volume variations of the material are controlled through the volumetric energy which depends on the initial bulk modulus κ. In this paper, an analytical analysis of the influence of κ on the mechanical response of two invariant-based anisotropic models is first performed in the case of an equibiaxial tensile test. This analysis shows that for the strongly nonlinear anisotropic model, even in a restricted range of deformations, large values of κ are necessary to ensure the incompressibility condition, in order to estimate the wall stress with a reasonable precision. Finite element simulations on idealized AAA geometries are then performed. Results from these simulations show that the maximum stress in the AAA wall is underestimated in previous works, committed errors vary from 26% to 58% depending on the geometrical model complexity. In addition to affect the magnitude of the maximum stress in the aneurysm, we found that too small value of κ may also affect the location of this stress.

In the present paper, we have been investigated a new dark energy model in anisotropic Bianchi-type-I (B-I) space-time with redshift-dependent equation of state (EoS) parameter. The Einstein’s field equations have been solved by applying a variation-law for hyperbolic scale factor $a(t)={[\mathrm{\text{sin}}h(\alpha t)]}^{\frac{1}{n}}$ which provides a time-dependent deceleration parameter and time-dependent EoS parameter. We also have been found the redshift-dependent EoS parameter. The existing range of the dark energy EoS parameter $\omega$ for derived model is found to be in good agreement with the recent observations. The cosmological constant $\mathrm{\Lambda }$ is found to be a decreasing function of time and it approaches a small positive value at the present epoch which is collaborated by results from recent supernovae Ia observations. It has also been suggested that the dark energy that explains the observed accelerating universe may arise due to the contribution to the vacuum energy of the EoS in a time-dependent background. Geometric and Kinematic properties of the model and the behavior of the anisotropy of the dark energy have been discussed.

In this work, we develop some interesting models of cosmos exhibiting anisotropic properties in the extended scalar-tensor theory. In the first place, we consider the LRS Bianchi type I (BI) geometry filled with matter contents as magnetized bulk viscous cloud of strings. We developed analytic solutions and explore the cosmological significance of some interesting physical measures like cosmic volume, directional Hubble parameter, deceleration parameter, viscosity factor, particle energy density, shear and expansion scalars, and string tension density. Moreover, modified holographic Ricci dark energy is introduced in anisotropic scenario to discuss the dynamics of anisotropic comic models. In order to construct the exact cosmic solutions, we take hybrid law of scale factor as well as some viable ansatz for scalar field and its scalar potential. The physical viability of model parameters is discussed through graphical analysis. Physical analysis of both models show that our results are in agreement with the current observations and hence are cosmologically viable and promising.