A three-dimensional nonlinear visco-elastic constitutive model for ultra high molecular weight polyethylene

Ultra high molecular weight polyethylene (UHMWPE) is used extensively in biomedical implant applications. The design of the UHMWPE components is critical to the longevity of the implant. Although the material has been used for decades as a biological material, its three-dimensional behavior is still not fully understood, and a better understanding of the material will allow UHMWPE implant components to be more rigorously designed to the benefit of both the manufacturing company and the person receiving the implant. At body temperature, 37C, UHMWPE is a nonlinear visco-elastic material. This purpose of this study is to measure the time-dependent mechanical behavior of UHMWPE, and set forth a representative three-dimensional constitutive model. Eight earlier viscous, molecular, and phenomenological constitutive models are reviewed in this study. Two time-dependent phenomenological models, Visco Plasticity based on Overstress (VBO), and Bernstein-Kearsley-Zappas visco-elasticity (BKZ), three elastic molecular models, Phantom Network, Constrained Chain, Eight-Chain, and Mooney-Rivlin, and three general elastic models, four parameter uniaxial visco-elasticity, Ogden, and Valanis-Landel models are included in the review. Tension-torsion single step stress relaxation tests are performed on cylindrical UHMWPE specimens at temperatures ranging from 25C to 55C, with the focus of the tests being at 37C. A piecewise linear function in addition to the reviewed models are then used to attempt to describe the experimental material behavior determined from these tests. A piecewise linear function is chosen for the isochronal strain energy function derivative, and is incorporated into the three-dimensional BKZ visco-elasticity model. The Fortran programming language is used to implement the model and numerically solve for the stress based on an arbitrary strain history. The model developed in this thesis is verified against the tests performed in this study, and then compared to constant strain rate uniaxial tension test data, and is able to predict stress-strain behavior observed experimentally in UHMWPE. This is the first application of the BKZ viso-elastic material theory to a semi-crystalline material, and demonstrates that within the strain ranges studied the BKZ material model is a valid choice.