A hyperelastic-damage model to study the anisotropic mechanical behavior of coral-hydrogel bio-composite

In this research, a hyperelastic strain energy function was developed to investigate the anisotropic mechanical behavior of a soft bio-composite containing the coral collagen fibers and alginate hydrogel matrix. This hyperelastic function considers the matrix isotropic response, anisotropic behavior of soft crimpled fibers, and matrix-fiber interaction. The material parameters of the model were assumed as a function of the volume fraction of fibers to consider the fiber content. The published experimental data of matrix and bio-composites with different volume fractions of fibers in different directions were used to find the material parameters. A damage model was developed to take into account the damage of matrix, fibers, and fiber-matrix interaction. Results showed that the interaction contribution increases by increasing the volume fraction of fibers due to the crosslinks between the matrix and fibers. Moreover, by exceeding the fibers volume fraction from 20%, the anisotropic stiffening dominates the interaction stiffening in the longitudinal test owing to the load-bearing of soft fibers. Simulation results exhibited that cross-plied bio-composites show more uniform deformations than angle-plied bio-composites. Moreover, the damage results showed that the matrix plays a significant role in the failure of bio-composites.

The effect of fiber-matrix interaction on the kinking instability arising in the torsion of stretched fibrous biofilaments

The response of fibrous soft tissues undergoing torsional deformations is a topic of current interest. Such deformations are common in ligaments and tendons and are also of particular interest in cardiac mechanics. The problem of torsion superimposed on extension of incompressible hyperelastic solid circular cylinders is a classic problem of nonlinear elasticity that has been considered by many authors in the context of rubber elasticity particularly for isotropic materials. A striking feature of such problems is the instability that arises with sufficiently large twist where a kink and then a knot suddenly appears. An energy approach to examining this instability when the extension and twist are prescribed was described by Gent and Hua (2004) and illustrated there for a neo-Hookean isotropic elastic material. The theoretical results were compared with experimental observations on natural rubber rods. Murphy (2015) has shown that the approach of Gent and Hua (2004) for isotropic materials can be simplified when the rods are assumed to be thin and this theory was applied to transversely isotropic materials by Horgan and Murphy (2016). In contrast with the case for isotropic materials, it was shown there that the kinking instability occurs even in the absence of stretch, i.e., for the case of pure torsion. Here we are concerned with the implications of this simplified thin rod instability theory for fiber-reinforced transversely isotropic materials that reflect fiber-matrix interaction. It is again shown that the kinking instability occurs even in the absence of stretch, i.e., for the case of pure torsion. The results are illustrated for a specific strain-energy density function that models fiber-matrix interaction. It is shown that the critical twist at which kinking occurs decreases as a measure of fiber-matrix interaction is increased so that the fiber-matrix interaction has a destabilizing effect. The results are illustrated using experimental data of other authors for skeletal muscles and for porcine brain white matter tissue.

The effect of fiber-matrix interaction on the Poynting effect for torsion of fibrous soft biomaterials

The response of fibrous soft tissues undergoing torsional deformations is a topic of considerable current interest. Such deformations are common in ligaments and tendons and are also of particular interest in cardiac mechanics. A well-known context where such issues arise is in understanding the mechanical response of papillary muscles of the heart. Thus the classical torsion problem for solid or hollow cylinders composed of rubber-like materials has received renewed recent attention in the context of anisotropic materials. Here we consider the torsion of a solid circular cylinder composed of a transversely isotropic incompressible fiber-reinforced hyperelastic material. The focus of the work is on examining the effect of fiber-matrix interaction on the axial stress response with emphasis on the Poynting effect. The classic Poynting effect for isotropic rubber-like materials where torsion induces elongation of the cylinder is shown to be significantly different for the transversely isotropic models considered here. For sufficiently small total angles of twist, well within the range of physiological response, a reverse-Poynting effect is shown to hold where the cylinder tends to shorten on twisting while for larger angles of twist, the usual positive Poynting effect occurs. It is shown that the influence of the fiber-matrix interaction is to enhance the reverse Poynting effect. The results are illustrated using experimental data of other authors for skeletal muscles and for brain white matter.