In this paper, the effect of temperature on relaxation of creep strain in biomaterials is modeled and analyzed with homotopy perturbation and differential transform methods. Polymeric biomaterials used as implants undergo both geometric and material nonlinear deformation when subjected to different loading conditions. The present study is concerned with the effects of temperature on the geometric nonlinear deformation of the relaxation of creep strain in these materials. Polymeric biomaterials exhibit time dependent response as observed in viscoelastic materials and this is represented by a one-dimensional rheological material model with constant material parameters. This model is then extended to capture the effects of temperature and the resulting final governing model is a nonlinear differential equation which cannot be easily solved by the standard analytic techniques. Here, two efficient special nonlinear analytic techniques, the homotopy perturbation and differential transform methods, are applied to obtain the solution of the developed nonlinear differential equation. The obtained analytical solutions are validated with the fourth-order Runge-Kutta numerical method. An error analysis shows that good agreement exists between the solutions obtained with these methods. The effects of some parameters on the model were investigated. As observed from the study, it can be shown that an increase in thermal conductivity and viscosity resulted in an increase in resistance to deformation of the material, while an increase in the material stiffness resulted in an increase in the rate of deformation and relaxation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.