A theory for deformation dependent evolution of continuous fibre distribution applicable to collagen remodelling

This work explores the implications of a constitutive framework that introduces a particular remodelling process for materials having a continuous distribution of fibre directions. It is assumed that the matrix constituent is unaffected and that fibres remodel by a process of dissolution and reassembly. Dissolution results from a time dependent chemical kinetic process that is influenced by fibre stretch. Two possibilities for the reassembly of the fibres are considered: (1) fibres reassemble in a stress-free state or (2) fibres assemble in a pre-strained state matching that of the surrounding matrix. The composite is treated as a non-linear hyperelastic material. The constitutive framework accounts for the time dependent redistribution of fibre orientation and density. A directional fibre orientation density function is defined that combines fibre dissolution, reassembly and their dependence on deformation history. Expressions for the time dependence of this function are developed for the two fibre reassembly assumptions and different deformation histories. Numerical results for uniaxial extension are presented in the form of polar plots that illustrate fibre orientation density at different times and fibre density versus time plots that show evolution at different orientations.

Hali tarjima qilinmagan