Hasan Demirkoparan

On dissolution and reassembly of filamentary reinforcing networks in hyperelastic materials

We generalize a theory for modelling the scission and reforming of cross links in isotropic polymeric materials in order to treat anisotropic mechanical behaviour. Our focus is on materials in which elastic fibres are embedded in an elastic matrix. The fibres may have a different natural stress-free configuration than that of the matrix, e.g. the fibres may be initially crimped in the absence of load. The modelling process allows the fibres to dissolve as deformation proceeds and then to immediately reassemble in the current direction of maximum principal stretch. This results in softening, altered mechanical properties and the possibility of permanent set. We illustrate a rich variety of such mechanical behaviours in the context of uniaxial stretch. The phenomena illustrated have important implications for the influence of mechanical factors in the remodelling of fibrous soft matter including biological tissue.

Bulging bifurcation of inflated circular cylinders of doubly fiber-reinforced hyperelastic material under axial loading and swelling

In this paper, we examine the influence of swelling on the bulging bifurcation of inflated thin-walled cylinders under axial loading. We provide the bifurcation criteria for a membrane cylinder subjected to combined axial loading, internal pressure and swelling. We focus here on orthotropic materials with two preferred directions which are mechanically equivalent and are symmetrically disposed. Arterial wall tissue is modeled with this class of constitutive equation and the onset of bulging is considered to give aneurysm formation. It is shown that swelling may lead to compressive hoop stresses near the inner radius of the tube, which could have a potential benefit for preventing aneurysm formation. The effects of the axial stretch, the strength of the fiber reinforcement and the fiber winding angle on the onset of bifurcation are investigated. Finally, a boundary value problem is studied to show the robustness of the results.

A constitutive model for an internally balanced compressible elastic material

Many large deformation constitutive models for the mechanical behavior of solid materials make use of the multiplicative decomposition F = F ^ F * as, for example, used by Kröner in the context of finite-strain plasticity. Then F ^ describes the elastic effect by letting the potential energy of the deformation depend upon F ^ . In this paper we allow the potential energy to depend upon both portions of the multiplicative decomposition. As in hyperelasticity, energy minimization with respect to displacement gives equilibrium field equations and traction boundary conditions. The new feature, minimization with respect to the decomposition itself, generates an additional mathematical requirement that is interpreted here in terms of a principle of internal mechanical balance. We specifically consider a Blatz–Ko-type solid suitably generalized to incorporate the notion of internal balance. Conventional results of hyperelasticity are retrieved for certain limiting forms of the energy density, whereas the general form of the energy density gives rise to an overall softening response, as is demonstrated in the context of pure pressure and uniaxial loading.

Hyperelastic modeling of the combined effects of tissue swelling and deformation-related collagen renewal in fibrous soft tissue

A continuum mechanics constitutive model is presented for the interaction between swelling and collagen remodeling in biological soft tissue. The model is inherently two-way: swelling stretches the collagen fibers which affects their rate of degradation—the remodeled fibrous microarchitecture provides selective directional stiffening that causes the swollen tissue to expand more in the unreinforced directions. The constitutive model specifically treats stretch-stabilization wherein the rate of enzymatic-induced degradation of collagen is a decreasing function of fiber stretch. New collagen replacement takes place in a generally swollen environment, and this synthesis is tracked as a function of time by means of a time integration scheme that accounts for the historical sequence of collagen recreation. The model allows for the specification of the collagen pre-stretch at the time of first synthesis, thus allowing for the consideration of either initially limp replacement fiber or initially pre-tensioned replacement fiber. Loading and swelling that occurs on time scales that are commensurate with the natural time scales for fiber degradation and replacement lead to the consideration of time-integral constitutive equations. Loading and swelling that take place on time scales that are very different from that of the remodeling time scales provide a simplified treatment in which there are definite notions of a short-time instantaneous response and also a large-time approach to a steady-state condition of homeostasis.