On the response of viscoelastic biodegradable polymeric solids

摘要

We study the time-dependent response of a biodegradable polymeric solid which has relevance to applications in biomedicine, for example biodegradable polymeric stents. The degradation mechanism of these polymers is primarily due to hydrolysis and high strains/stresses can accelerate the degradation. In order to mimic the environment and the external stimuli which the stent is subject to, the polymers are subject to three different types of external stimuli, that are due to prescribed mechanical loading, the diffusion of water, and the degradation that occurs over a period of time, ensuring that we have a strong coupling between the deformation, degradation, and diffusion response. We assume that the polymer is described by a linearized viscoelastic constitutive model, with material parameters varying due to the degradation, in the case of biodegradable polymers. We study the effect of time-dependent response on the degradation of biodegradable polymers. We also analyze an initial-boundary value problem corresponding to a cylindrical annulus of a biodegradable viscoelastic polymeric solid of finite length, the geometry that is relevant to a biodegradable stent, in contact with another cylindrical annulus (the arterial wall) of viscoelastic solid. The stent is subject to internal radial pressure, and the diffusion of a fluid, while the arterial wall is subjected to external radial pressure. We examine the coupling between the response of the biodegradable stent and the arterial wall. This is done in order to support the design of biodegradable polymeric stents by considering reasonably realistic geometrical and material models.