Models for UHMWPE

UHMWPE, as well as other thermoplastics, exhibit a complicated nonlinear response when subjected to external loads. Their behavior, as demonstrated previously, is characterized by initial linear viscoelasticity at small deformations, followed by distributed yielding, viscoplastic flow, and material stiffening at large deformations until ultimate failure occurs. The response is further complicated by a dependence on strain rate and temperature. It is clear that higher deformation rates and lower temperatures increase the stiffness of the material. 

It is also clear that thermoplastics are very different and typically exhibit a broader range of behavior in comparison with other structural materials, such as metals. The observed behavior is a manifestation of the different microstructures of the two types of materials and the different micromechanisms controlling the deformation resistance. It is therefore not surprising that different material models should be used when simulating UHMWPE compared with metals. 

Several candidate material models are available to predict e behavior of UHMWPE. Because the models have varying degrees of complexity, computational expense, and difficulty in extracting the material parameters from experimental data, it is a good idea to use the simplest material model that captures the necessary material characteristics for the application and situation at hand. Unfortunately, it is often difficult to determine the required conditions on the material model. Hence, it is recommended that a more advanced model be used in order to ensure accuracy and reliability of the predicted data. At a later stage, a less advanced model can be attempted if the computational expense is too great. At that time the accuracy of the different model predictions can also be tested and validated. 

The next few sections present tirese traditional models and how they apply to UHMWPE. Then, as an example of a more advanced material model, the Hybrid model (Bergstrom, Rimnac, and Kurtz 2003, Bergstrom et al. 2002a, Bergstrom et al. 2002b) is presented. 

Linear elasticity is the most basic of all material models. Only two material parameters need to be determined experimentally Young s modulus (E) and Poisson s ratio (v). Young s modulus can be obtained directly from uniaxial tension or compression experiments typical values (Kurtz et al. 2002) for a few select UHMWPEs at room temperature are presented in Table 14.3. 

---

Safaa A, Tarun G (2008) Wear rate model for UHMWPE in total joint applications. Wear 265 8-13... 

The theory behind linear viscoelasticity is simple and appealing. It is important to realize, however, that the applicability of the model for UHMWPE is restricted to strains below the yield strain. One example comparing predictions based on linear viscoelasticity for experimental data for UHMWPE past yield is shown in Figures 14.10 and 14.11. Figure 14.10 shows the best predictive... 

What are the main disadvantages of isotropic plasticity as a material model for UHMWPE ... 

Notched monotonic tensile specimens can be a useful approach to begin to understand the effect of structural notches on the behavior of UHMWPE total joint replacement components. Therefore, we developed a testing methodology to characterize the stress strain and fracture behavior of a notched tensile specimen. Additionally, the stress-strain behavior of notched tensile specimens can be used to challenge the Hybrid Constitutive Model for UHMWPE (see Chapter 35) with a multiaxial stress state. Accurate prediction of the behavior of a notched specimen by a simulation utihzing the Hybrid Model would be one vahdation of its accuracy in describing the mechanical behavior of UHMWPEs. 

Bergstrom 1, et al. Development and Implementation of an advanced user material model for UHMWPE. 9th International LS-DYNA Users Conference. Dearborn, Ml 2006. 

Given their obvious advantages, the development of advanced constitutive models for UHMWPE and other thermoplastics is an active area of research that is continuously evolving and improving. In the last few years, models... 

Modeling of damage processes such as fatigue, fracture, and wear have not been explored in this chapter but could be important to consider depending on the particular research objectives. Constitutive models for UHMWPE will continue to evolve as our understanding of the micromechanics and damage behavior of this versatile material are more fuUy understood and as the availability of computational resources continues to increase. 

A direct comparison between these and other failure models has not been performed for fluoropolymers, but a recent study of UHMWPEl showed that, for UHMWPE, these models are very different. For example, it was shown that the chain stretch model is the most promising for predicting multiaxial deformation states, and that the hydrostatic stress, and the volumetric strain are not good predictors of failure. 

Hyperelastic models are often used to represent the behavior of crosslinked elastomers, where the viscoelastic response can sometimes be neglected compared with the nonlinear elastic response. Because UHMWPE behaves differently than do elastomers, there are only a few specific cases when a hyperelastic representation is appropriate for UHMWPE simulations. One such case is when the loading is purely monotonic and at one single loading rate. Under these conditions it is not possible to distinguish between nonlinear elastic and viscoplastic behavior, and a hyperelastic representation might be considered. Note that if a hyperelastic model is used in an attempt to capture the... 

A number of more advanced and general models for predicting the yielding, viscoplastic flow, time-dependence, and large strain behavior of UHMWPE and other thermoplastics have recently been developed (Bergstrom, Rimnac,... 

The most advanced material model presently available for UHMWPE is the HM. This model focuses on creating a mathematical representation of the deformation resistance and flow characteristics for conventional and highly crosslinked UHMWPE at the molecular level. The physics of the deformation mechanisms establish the framework and equations necessary to model the behavior on the macroscale. As already mentioned, to use the constitutive model for a given material requires a calibration step where material-specific parameters are determined. A variety of numerical methods may be used to determine the material-specific parameters for a constitutive theory. In the previous section we employed a numerical optimization technique to identify the material parameters for the constitutive theory. 

Jump-like creep was also studied for UHMWPE films with intentionally varied structural organization of interfaces between fibrils at the expense of their different preparation (gel-casting, crystallization from the melt), various draw ratios X (from 7 to 119), and the special cross-linking of fibrils [315,317]. The fibrils were weakly connected and loosely packed, weakly tied but closely packed, or cross-linked by long molecular segments or connected by short crosslinks, in these samples. As a result, absolutely different jump-like creep rate vs deformation curves and jump sharpness parameter h vs strain dependencies were obtained for these model samples with different interfacial structures. Short interfibrillar crosslinks provided the largest effect on creep behavior. Creep occurred basically through shear of fibrillar structural units relative to one another in an acceleration-deceleration way deceleration was due to slip resistance by some stoppers. ... 

Muratoglu OK, Bragdon CR, O Connor DO, Jasty M, Harris WH, Gul R, et al. Unified wear model for highly crosslinked ultra-high molecular weight polyethylenes (UHMWPE). Biomaterials 1999 20(16) 1463-70. 

The novel video-based method used for the evaluation of axial stress-strain behavior of notched cylindrical specimens is a valuable tool. Experimentally, this method is simple to implement and has the advantage of providing strain behavior up to failure using a noncontacting extensom-etry approach. The notched tensile test is also an attractive experimental method with which to check the validity of the development of constitutive models of UHMWPE (see Chapter 35). The methodology has the advantage of creating a multiaxial stress state without contact, and the specimen can be modeled as axisymmetric in finite element analyses. 

Bergstrom J, Rimnac C, Kurtz S. An augmented hylaid constitutive model for simulation of unloading and cyclic loading behavio-of conventional and highly crossUnked UHMWPE. Biomaterials 2004 25 2171-8. 

FIGURE 35.9 Comiarison between experimental data (obtained from a uniaxial compression test with an engineering strain rate of -0.05/s) for UHMWPE (GUR 1050, 30kGy TN2) > <1 predictions made using the Ogden hyperelasticity model. 

A number of more advanced models capable of predicting the yielding, viscoplastic flow, time-dependence, and large strain behavior of UHMWPE and other thermoplastics have recently been developed [6, 9-13]. One model formulation that was specifically developed for UHMWPE, the augmented Hybrid Model (which has been recently updated), will be thoroughly detailed (based on information largely contained in [ 11 ]) in the remainder of this section. 

UHMWPE exhibits a complicated, nonlinear mechanical response that is dependent upon initial processing (radiation and/or thermal treatment), as well as the strain rate and temperature. Due to UHMWPE s complex mechanical behavior, finding an appropriate constitutive model for simulating the behavior of a UHMWPE component can be challenging. For example, the use of a simple elastic or viscoelastic model may yield accurate results for a particular component geometry and material formulation in a specific loading scenario. Small changes to any of these parameters, however, may render this choice of constitutive model inappropriate. 

FIGURE 35.19 Comparison between experimental small punch data (punch rate=0.5 mm/min) for UHMWPE (GUR 1050, 30kGy 1-N2) and predictions made using the augmented Hybrid Model (adapted from [11]). 

Overall, a number of different approaches can be taken toward modeling UHMWPE components. The analyst must carefully consider what type of constitutive model is most appropriate for a particular situation. Presently, the most versatile and accurate material model for predicting the macroscale behavior of both conventional and highly crosslinked UHMWPE specimens is the augmented HM. 

A full transient elastohydrodynamic lubrication analysis for UHMWPE-on-metal hip implants was undertakoi by Jalali-Vahid and Jin (2002). A simplified elasticity equation, based on the column model, was employed fw calculating die elastic... 

---