On dissolution and reassembly of filamentary reinforcing networks in hyperelastic materials

Abstract

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.

Modeling Bioactive Materials

“…The decomposition of the deformation tensor is similar to the approach taken by Rajagopal and Wineman (1992) and Demirkoparan et al (2009) for the formation and breaking of cross-links in polymeric materials and has been used for muscle tissue by Cherubini et al (2008), and Nardinocchi and Teresi (2007). The introduction ofF leads to the definition of the related right and left Cauchy-Green tensors, respectivelŷ…”

Emergence of fibrous fan morphologies in deformation directed reformation of hyperelastic filamentary networks

“…Such a development is given in [7] where the notation b(t) becomes b (1) (t). Here we restrict attention to processes for which the secondary fiber network does not itself undergo additional dissolution and reassembly, so that it is not necessary to introduce the function b (2) (t,t ).…”

“…This framework was extended by Demirkoparan et al [7] so as to treat similar issues in the fibrous component of composite materials. The extended framework resulted in a model for dissolution and reassembly of filamentary reinforcing networks in hyperelastic materials.…”

“…In this model, fibers undergo dissolution as a result of increasing elongation and then reassemble in a direction defined as part of the model. In [7] the fibers reassembled in the direction of maximum principal stretch of the matrix. The model was illustrated in detail for uniaxial stretching along the direction of the fibers.…”

Network evolution model of anisotropic stress softening in filled rubber-like materials: Parameter identification and finite element implementation

“…Using a similar technique, Demirkoparan et al [2009] generalized the two-reference configuration theory proposed in [Wineman and Rajagopal 1990] to fibrous soft matter by considering the material as a composition of two components, in which the microstructure change only occurs in the fibrous component. The resulting model was able to capture stress softening and permanent set in fibrous materials.…”