Analytical investigations of temperature effects on creep strain relaxation of biomaterials using homotopy perturbation and differential transform methods

Adeleye, Olurotimi and Abdulkareem, Olakanla and Yinusa, Ahmed and Sobamowo, Gbeminiyi (2019) Analytical investigations of temperature effects on creep strain relaxation of biomaterials using homotopy perturbation and differential transform methods. JOURNAL OF COMPUTATIONAL AND APPLIED MECHANICS, 14 (1-2). pp. 5-23. ISSN 1586-2070

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Abstract

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 effcient 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.

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