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We highlight the basic errors found in a related set of couple-stress hyperelasticity articles and evince some statements are incorrect, which suggest that the results obtained in these set of articles are questionable. [ABSTRACT FROM AUTHOR]

In this investigation, the mechanical modeling of nonlinear visco-hyperelastic residually stressed materials obtained from an invariant-based constitutive energy framework is coupled with the phase field approach to fracture. The main target regards the extension of the phase field method to simulate pre-stressed cylindrical structures subjected to monotonic axial pulling load upon failure. This formulation is incorporated into a numerical procedure using the Finite Element Method (FEM), in particular, it is implemented in the commercial FE package ABAQUS as a user subroutine UMAT. Results suggest the dependence of the mechanical behavior and the crack pattern of these structures on not only viscous parameters like the relaxation time and the displacement rate, but also on the strength of the residual stress field, which in turn depends on geometrical characteristics of the cylindrical structure such as the radius or the length. A range of solutions related to crack propagation is shown for different cylindrical structures, from azimuthal crack propagation to axial one. The proposed framework aims to provide an extended application for the already-defined visco-hyperelastic formulation by the inclusion of residual stresses. [ABSTRACT FROM AUTHOR]

In this paper, we propose a spectral approach to model finite deformations of fibre-reinforced elastic solids with fibre bending stiffness. The constructed constitutive equations depend on spectral invariants, where each one has a clear physical meaning and hence are attractive for use in experiment and analysis. With the use of spectral invariants, we easily obtain the number of independent invariants and the number of invariants in the corresponding minimal integrity or irreducible basis. The proposed finite strain energy prototypes are consistent with their infinitesimal strain energy function counterparts. Some results for pure bending of a slab, and the extension and torsion of solid cylinder, that could be useful for experiments and numerical validations, are given. The proposed model could be used to obtain numerical results via modification of some computational methods found in the literature. [ABSTRACT FROM AUTHOR]

Abstract: Many biological, geological and synthetic bodies are anisotropic. In particular, some of these bodies reflect the anisotropy due to fiber reinforcement along a direction or more than one direction. [...]