On Different Approaches to Simulate the Mechanical Behavior of Scaffolds during Degradation

Abstract Only using biodegradable polymers is possible to develop new regenerative concepts for implantable biomedical devices, to be used in tissue engineering, where the biomaterials will temporarily replace the biomechanical functions, and these will be gradually transferred to the neo-tissue formed over the scaffolds, while the materials will degrade and ultimately erode and be assimilated by the host tissue. These types of scaffold concepts find many applications, in the market or under study, for the regeneration of non vascular tissues, such as cartilage, vascular stents, ligaments, etc. However, there still is a lack of design and dimensioning tools for these devices and methods to predict and simulate the mechanical behavior during hydrolytic degradation. Many times, the convergence to an optimal solution is obtained by iterative “trial and error”, becoming a costly project. It is common to use Finite Element Methods (FEM) in problems with complex geometries and boundary conditions, enabling the simulation of the 3D mechanical behavior of the device in the initial step of degradation. In the ambit of this context, the main scope of this work is to review the current methodologies able to simulate the mechanical behavior in biodegradable polymers, during several steps of degradation. Hence, the convergence to an optimal solution can be obtained computationally, through material models implemented in a FEM software package, such as ABAQUS. Ideally, the device should degrade its mechanical properties compatibly with the required life cycle and according to the regeneration time of the biologic tissue. Therefore, in this work the equations commonly used to describe the diffusion of water and hydrolysis kinetics will be reviewed. Furthermore, constitutive models commonly used to predict the mechanical behavior of polymers are also reviewed. Due to the nonlinear nature of the stress vs. strain relation, the classical linear elastic model is not valid for simulation under large strains. Current designs of biodegradable devices are carried out by considering hyperelastic or elastoplastic behavior and neglect any changing on the mechanical behavior with degradation. Concomitantly to its nonlinear nature, the mechanical behavior of polymeric materials is also time dependent. The mechanical behavior of polymers, under large deformations and dynamic loading at varying strain rates, is a combination of elastoplastic behavior, typical of metals, and a viscous behavior typical of fluids. Different combinations of hyperelastic, plastic and viscous models can be used to describe their mechanical behavior. Since this mechanical behavior will evolve during degradation, recent approaches that will be reviewed in this work, enable to associate the evolution of material model parameters with the hydrolysis kinetics and therefore simulate the mechanical behavior of biodegradable structures during its hydrolytic degradation.