Chain Stretch Research Articles

Constitutive Modeling of the Stress-Stretch Behavior of Biological Membranes Containing Folded Domains

AbstractThe mechanical behavior of the red blood cell membrane is governed by the lipid bilayer which resists changes in surface area and the underlying spectrin network which resists changes in shape. The spectrin network can be modeled as an idealized triangulated network. Each spectrin chain consists of folded domains along the length of the chain which can unfold during stretching of the chain. A domain will completely unfold under the application of a chain force of20to35 pNdepending on the rate of imposed chain stretch. During macroscopic stretch of a network, individual chains within the network will experience different levels of chain stretch since the network chains will collectively stretch and rotate to accommodate the imposed stretch. Hence, the stretch on any individual chain will depend on the magnitude and state of macroscopic strain. A microstructurally informed continuum level constitutive model is developed which tracks individual chain deformation behavior as a function of macroscopic strain and also determines the overall macroscopic network stress-strain behavior. Using the introduced continuum approach and statistical mechanics based models of individual chain force-extension behavior, the stress-stretch behavior of the membrane under uniaxial tension is simulated at large stretches and the behavior of the constituent chains is monitored. Domain unfolding occurs within constituent chains during network deformation and the effects of this domain unfolding on the overall macroscopic stress-strain behavior of the network subject to deformation at different strain rates is revealed.

Parameter-Free Prediction of DNA Conformations in Elongational Flow by Successive Fine Graining

Brownian dynamics simulations are used to predict the evolution of DNA conformations in elongational flow. The DNA molecule is represented by a bead−spring chain model, and excluded-volume and hydrodynamic interactions between the beads are taken into account. Two distinct types of behavior are examined, corresponding to infinite and finite chains. In the former case, Hookean springs are used, and simulations data accumulated for chains with increasing numbers of beads, N, are extrapolated to the limit N → ∞. In this nondraining limit, universal DNA stretch vs strain curves are obtained as a function of the solvent quality parameter z. In the case of finite chains with Nk Kuhn steps, finitely extensible springs are used, and the extrapolation of finite chain data is restricted to the limit (N − 1) → Nk. It is shown that in the presence of finitely extensible springs both the excluded-volume and hydrodynamic interaction parameters need to be redefined appropriately. The role of finite size effects and sensitivity to the choice of parameter values is examined by comparing the finite chain stretch vs strain curves with the universal curves. Theoretical predictions are also shown to compare favorably with experimental observations of DNA stretch.

A constitutive model with moderate chain stretch for linear polymer melts

In our previous publication, we presented a molecular model to describe the dynamics of the interfacial layer between a flowing polymer melt and a die wall. We showed that the ensemble-averaged behavior of polymer molecules adsorbed on the wall could be successfully described in terms of the so-called bond vector probability distribution function (BVPDF). The BVPDF couples the chain orientation and chain stretch on the level of single segment, and thus is an extension of the orientation distribution function of Doi and Edwards introduced for inextensible chains. In this paper, the developed formalism is extended to molecules in the polymer bulk. We show how the well-known Doi and Edwards theory (DE) for inextensible chains based on the orientation distribution function can be naturally extended to include chain stretch and (convective) constraint release (CCR). The final constitutive equation accounts for such mechanisms on polymer chains as reptation, retraction, convection, contour length fluctuations, and (convective) constraint release. It is valid for both linear and non-linear flow regimes. The proposed theory is quantitative, and contains the same input parameters as the original DE model. As an application of the full theory, a simple equation of motion for the stress tensor is derived. Despite the simplicity, its predictions are found to be in good agreement with available experimental data over a wide range of flow regimes and histories.

Nonlinear shear rheology of polystyrene melt with narrow molecular weight distribution—Experiment and theory

Measurements of the shear viscosity and the first and second normal stress coefficients are shown at 175 °C for a nearly monodisperse polystyrene melt with Mw=200 kg/mol (PS 200 k). Tests are performed on a cone-partitioned plate shear rheometer and cover a range of Weissenberg numbers (τdγ̇) from 0.13 to 40. Experimental problems encountered are the axial compliance of the rheometer and the normal force capacity of the transducer. The later limits the maximum shear rate to τdγ̇=40. Experimental data are compared with the models of Öttinger [termed thermodynamically consistent reptation model (TCR), Öttinger, H. C., J. Rheol. 43, 1461–1493 (1999)] for the convective constraint release parameter δ2=0, 1, and 2 and Mead, Larson, and Doi [termed Mead, Larson, and Doi (MLD), Mead, D. W., R. G. Larson, and M. Doi, Macromolecules 31, 7895–7914 (1998)] for δ2=1. The steady state and transient values of p21, N2, and N1 agree qualitatively well between both models and the experiment. The predicted normal stress ratio −N2/N1 is sensitive to the magnitude of δ2 in the TCR model, similar to the extinction angle. The MLD model yields |N2| and Ψ values lower than both experiments and the TCR model with δ2=1. From a comparison with the chain stretch time τs (0.065 s) it can be shown that the overshoot O of |N2| and p21 are linked to chain orientation, whereas O(N1) is associated with chain stretching. The magnitude of the overshoot for all shear rates increases as O(N1)<O(N2)<O(η) for PS 200 k. In comparison, a polydisperse polystyrene melt shows stronger shear thinning of −N2/N1 and an increase of the magnitude of the overshoot as O(N1)<O(η)<O(N2).

Validity of the linear stress optical rule in mono-, bi- and polydisperse systems of entangled linear chains

The influence of the molecular weight distribution (MWD) of bidisperse entangled linear polymer systems on the critical stress at which the stress-optical rule (SOR) fails for uniaxial extensional flows is investigated numerically. The model predictions show that the critical extensional stress where the SOR fails, Δ τ FSOR , depends on the molecular weight distribution and the extension rate. The variation in Δ τ FSOR results primarily from the change in the mass fraction of stretched chains. In addition, the interplay between the contribution from the non-stretched and stretched chains to the stress and birefringence is significant for the magnitude of Δ τ FSOR . The latter is the reason why Δ τ FSOR is larger compared to that expected from the mass fraction of stretched chains alone. A comparison of the model predictions with experimental data for a nearly monodisperse concentrated polystyrene (PS) solution, reported in the literature, shows that the SOR fails for a chain stretch of about one-third of the maximum stretch ratio. For bidisperse PS melts, the critical stretch ratio varies with the MWD. For monodiperse PS melts, the critical stretch ratio is about two-fifth of the maximum value. A simplified procedure is proposed to analyze polydisperse melts. Compared to experimental data reported in the literature, the trend is qualitatively correct, but the predicted magnitude of Δ τ FSOR is too low.

Molecular chain stretch is a multiaxial failure criterion for conventional and highly crosslinked UHMWPE

The development of accurate theoretical failure, fatigue, and wear models for ultra-high molecular weight polyethylene (UHMWPE) is an important step towards better understanding the micromechanisms of the surface damage that occur in load bearing orthopaedic components and improving the lifetime of joint arthoplasties. Previous attempts to analytically predict the clinically observed damage, wear, and fatigue failure modes have met with limited success due to the complicated interaction between microstructural deformations and continuum level stresses. In this work, we examined monotonic uniaxial and multiaxial loading to failure of UHMWPE using eight failure criteria (maximum principal stress, Mises stress, Tresca stress, hydrostatic stress, Coulomb stress, maximum principal strain, Mises strain, and chain stretch). The quality of the predictions of the different models was assessed by comparing uniaxial tension and small punch test data at different rates with the failure model predictions. The experimental data were obtained for two conventional (unirradiated and gamma radiation sterilized in nitrogen) and two highly crosslinked (150 kGy, remelted and annealed) UHMWPE materials. Of the different failures models examined, the chain stretch failure model was found to capture uniaxial and multiaxial failure data most accurately for all of the UHMWPE materials. In addition, the chain stretch failure criterion can readily be calculated for contemporary UHMWPE materials based on available uniaxial tension data. These results lay the foundation for future developments of damage and wear models capable of predicting multiaxial failure under cyclic loading conditions.

Towards more realistic kinetic models for concentrated solutions and melts

In this paper we consider modifications of two kinetic models for concentrated polymer solutions and melts: the simplified uniform (SU) version of a thermodynamically admissible single segment reptation model by Öttinger [A thermodynamically admissible reptation model for fast flows of entangled polymers. J. Rheol. 43 (1999) 1461–1493] and Fang et al. [A thermodynamically admissible reptation model for fast flows of entangled polymers. II. Model predictions for shear and extensional flows, J. Rheol. 44 (2000) 1293–1317] and the encapsulated FENE dumbbell (EFD) model [R.B. Bird, J.R. Deaguiar, An encapsulated dumbbell model for concentrated polymer solutions and melts. I. Theoretical developments and constitutive equation, J. Non-Newtonian Fluid Mech. 13 (1983) 149–160]. The two modified models incorporate double reptation, convective constraint release (CCR), and chain stretching. In the modified SU model, orientation and stretching are still modelled in a decoupled way, while in the case of the modified EFD model they are modelled in a coupled way. Quantitative comparisons are made for a number of shear and extensional flows between the predictions of the modified EFD model with those of the SU model, the modified SU model, the original EFD model and a recent simple constitutive model by Marrucci and Ianniruberto [Flow-induced orientation and stretching of entangled polymers, Phil. Trans. R. Soc. Lond. A 361 (2003) 677–687]. The models’ predictions are also tested against experimental data for entangled polystyrene solutions. For steady simple shear flow it is shown that good quantitative agreement with experimental data using physically realistic parameters requires that orientation and stretching be modelled in a coupled way. In particular, predictions with the modified SU model of the steady shear viscometric functions are only accurate with a maximum chain stretch ratio parameter an order of magnitude smaller than is required by the polymer chemistry. The use of the modified EFD model with realistic model parameters leads to better overall fits in all cases with the experimental data than either variant of the SU model or the Marrucci–Ianniruberto model.

Impact of decoupling approximation between stretch and orientation in rheometrical and complex flow of entangled linear polymers

We study the rheometrical and complex flow response of the coupled version of the double-convection-reptation model with chain stretch. This model for monodisperse entangled linear polymers has recently been proposed by Marrucci and Ianniruberto [G. Marrucci, G. Ianniruberto, Flow-induced orientation and stretching of entangled polymers, Philos. Trans. R. Soc. A 361 (2003) 677–688] to overcome the anomalous shear thickening that was present in an earlier version of the theory. It avoids the decoupling approximation between orientation and stretch. Except for the shear thickening, both coupled and decoupled models show very similar results that are in qualitative agreement with available rheometrical data for two nearly monodisperse polymer solutions. In contraction/expansion flow simulations, however, higher Weissenberg numbers can be attained with the coupled model. Simulations in the stretch-dominated regime predict a dramatic growth of the upstream vortex activity and an increase of the pressure correction.

Towards a rheological classification of flow induced crystallization experiments of polymer melts

Departing from molecular based rheology and rubber theory, four different flow regimes are identified associated to (1) the equilibrium configuration of the chains, (2) orientation of the contour path, (3) stretching of the contour path, and (4) rotational isomerization and a deviation from the Gaussian configuration of the polymer chain under strong stretching conditions. The influence of the ordering of the polymer chains on the enhanced point nucleation, from which spherulites grow, and on fibrous nucleation, from which the shish-kebab structure develops, is discussed in terms of kinetic and thermodynamic processes. The transitions between the different flow regimes, and the associated physical processes governing the flow induced crystallization process, are defined by Deborah numbers based on the reptation and stretching time of the chain, respectively, as well as a critical chain stretch. An evaluation of flow induced crystallization experiments reported in the literature performed in shear, uniaxial and planar elongational flows quantitatively illustrates that the transition from an enhanced nucleation rate of spherulites towards the development of the shish-kebab structure correlates with the transition from the orientation of the chain segments to the rotational isomerization of the high molecular weight chains in the melt. For one particular case this correlation is quantified by coupling the wide angle X-ray diffraction and birefringence measurements of the crystallization process to numerical simulations of the chain stretch of the high molecular weight chains using the extended Pom-Pom model in a cross-slot flow.

Evaluation of a transient network model for telechelic associative polymers

A number of models are available to describe the rheological behaviour of associative polymers. Model evaluation has most often been limited to the linear properties and to a qualitative prediction of the characteristic shear thickening at intermediate shear rates. Several other nonlinear features of associative behaviour have, however, been identified. These include failure of the Cox–Merz analogy and an unusual response in nonlinear stress relaxation, large amplitude oscillatory flow and in superposition flows. Here, experimental results for such experiments are compared with the predictions of a transient network model, i.e. the Vaccaro–Marrucci model [J. Non-Newtonian Fluid Mech. 92 (2000) 261], which has only a single adjustable parameter to describe nonlinear behaviour. It is shown that the various nonlinearities are well predicted qualitatively. The only deviation is a substantial overprediction of the critical strain or strain rate for the onset of these nonlinearities. The effect of changing the value of the model parameters and of relaxing the model assumptions on the predictions is investigated. The results suggest that the presence of a small number of highly stretched chains could be responsible for the observed deviation from the experimental data.

The Chain Stretching Effect on the Morphology and Rheological Properties of Phase‐Separating Polymer Blends Subjected to Simple Shear Flow

AbstractSummary: The spinodal decomposition of a binary mixture subjected to simple shear flow is investigated in the framework of the modified time‐dependent Ginzburg‐Landau (TDGL) equation with an external velocity term. The domain growth and related rheological properties of a binary mixture under shear flow are simulated in three dimensions by means of the cell dynamics scheme (CDS). The simulation results show that the domain growth is anistropic and depends on the terminal relaxation time of the polymer chain. It is found that lamellae‐like domains with the normal parallel to the velocity gradient direction are observed when the terminal relaxation time is long enough. This result has also been confirmed by carefully checking the scattering functions in different incident light directions and the evolution of the domain size in different directions. In addition, when the chain stretching effect is strong, the transients of the excess shear viscosity are much higher than the case without the chain stretching effect. The terminal relaxation time of the chain also has an important effect on the first and second normal stress differences.The time evolution of the morphology for the case with strong chain stretching effect.imageThe time evolution of the morphology for the case with strong chain stretching effect.

Convective constraint release with chain stretch: Solution of the Rouse-tube model in the limit of infinite tubes

This article derives a constitutive equation for entangled polymer melts and solutions, including the effects of convective constraint release (CCR) and chain stretch. It uses a model for CCR based upon the conjecture that constraint release events produce local hops of the tube, giving rise to a dynamical equation similar to the Rouse model. This equation is solved in the limit of infinite tubes. Although the solution in this limit ignores chain-end effects, the method presented has the following advantages; (i) it is less computationally expensive to implement than a full “finite chain” solution, (ii) it retains separate variables for chain stretch and tube orientation, allowing for straightforward modification of the equations to include different stretch dynamics, and (iii) it allows the possibility of smoothly changing the characteristics of the tube (such as tube diameter) upon deformation. In the latter context, this article explores the consequences of possible changes to the tube characteristics (tube diameter, persistence length, and CCR hop length) in response to chain stretch. It is found that the CCR-stretch equations are highly sensitive to the nature of the tube upon deformation, and in particular to the lower lengthscale cutoff used to describe the CCR process. The effect of CCR on chain stretch is explicitly derived from the microscopic model. The behavior of the constitutive equations is described for steady states under shear and startup under steady shear (where the results are compared against experiment).

Shear-induced migration in flowing polymer solutions: simulation of long-chain DNA in microchannels [corrected

We simulate dilute solution dynamics of long flexible polymer molecules in pressure driven flow in channels with widths of roughly 0.1-10 times the polymer bulk radius of gyration. This is done using a self-consistent coarse-grained Langevin description of the polymer dynamics and a numerical simulation of the flow in the confined geometry that is generated by the motions of polymer segments. Results are presented for a model of DNA molecules of approximately 10-100 microm contour length in micron-scale channels. During flow, the chains migrate toward the channel centerline, in agreement with well-known experimental observations. The thickness of the resulting hydrodynamic depletion layer increases with molecular weight at constant flow strength; higher molecular weight chains therefore move with a higher average axial velocity than lower molecular weight chains. In contrast, if the hydrodynamic effects of the confining geometry are neglected, depletion of concentration is observed in the center of the channel rather than at the walls, contradicting experimental observations. The mechanisms for migration are illustrated using a simple kinetic theory dumbbell model of a confined flexible polymer. The simple theory correctly predicts the trends observed in the detailed simulations. We also examine the steady-state stretch of DNA chains as a function of channel width and flow strength. The flow strength needed to stretch a highly confined chain away from its equilibrium length is shown to increase with decreasing channel width, independent of molecular weight; this is fairly well explained using a simple blob picture.

Conformational behavior of a single polymer chain confined by a two-dimensional harmonic potential in good solvents

Monte Carlo simulations have been conducted to investigate the conformational behavior of a flexible chain polymer confined to a two-dimensional harmonic potential. The polymer molecule is modeled as a tangent hard sphere chain, and the two-dimensional harmonic potential is chosen to mimic nonrigid cylindrical pores. The simulations show that as field strength is increased, the mean chain dimension decreases first and then increases again after passing a minimum due to anisotropic deformation. A modified Flory-type theory is utilized to derive the power laws for the chain deformation against the strength of the applied field in different directions. These power laws agree with the simulations at strong fields when the confined polymer molecule exhibits a rodlike conformation. Meanwhile, a simple model, consisting of a dimer in a two-dimensional harmonic potential, is solved to elucidate the alignment of chain segments in very strong applied potentials. From this model, the crossover regime of a tangent hard sphere chain from the rodlike chain to a totally stretched chain at limiting strong fields is identified. Furthermore, a first-order perturbation theory is employed to interpolate the mean chain size for different field strengths. The field strength corresponding to the minimum mean chain size decreases as chain length is increased, consistent with the prediction of the modified Flory-type theory. These studies provide physical insights into the conformational behavior of a flexible polymer chain in nonspherical two-dimensional harmonic potentials.

Microscopic theory of linear, entangled polymer chains under rapid deformation including chain stretch and convective constraint release

A refined version of the Doi and Edwards tube model for entangled polymer liquids is presented. The model is intended to cover linear chains in the full range of deformation rates from linear to strongly nonlinear flows. The effects of reptation, chain stretch, and convective constraint release are derived from a microscopic stochastic partial differential equation that describes the dynamics of the chain contour down to the length scale of the tube diameter. Contour length fluctuations are also included in an approximate manner. Predictions of mechanical stresses as well as the single chain structure factor under flow are shown. A comparison with experimental data is made in which all model parameters are fixed at universal values or are obtained from linear oscillatory shear measurements. With no parameter modification the model produces good agreement over a wide range of rheological data for entangled polymer solutions, including both nonlinear shear and extension.

Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie–Poly equation

Recently we developed a theory for fast flows of entangled polymer melts which includes the processes of reptation, convective and reptation-driven constraint release, chain stretch and contour length fluctuations. The theory is derived from a stochastic microscopic equation of motion of the chain inside the tube and of the tube itself. As a result we obtain a partial differential equation for the tube tangent correlation function, the solution of which requires quite intensive calculations. At the same time the application of this theory to realistic flows (which is anything other than the laboratory rheometer) requires a simple and less computationally intensive set of equations for the stress tensor similar to the Giesekus, PTT, Larson or Pom–Pom equations. In particular, the last was derived from molecular theory for a generic type of branched polymer. In this paper we demonstrate that molecular tube theory can also provide a route to constructing a family of very simple differential constitutive equations for linear polymers. They capture the full model quite well and therefore can be used in flow solving software to model spatially inhomogeneous flows. We present a comparison of the proposed equations with our full model and with experimental data.

Molecular Dynamics Simulations of Polyelectrolyte Solutions: Nonuniform Stretching of Chains and Scaling Behavior

We present the results of molecular dynamics simulations of polyelectrolyte solutions in near-ϑ-solvent conditions for polymer backbone. Polyelectrolyte solutions are modeled as an ensemble of bead-spring chains of charged Lennard-Jones particles with explicit counterions. Simulations were performed for both fully and partially charged polyelectrolyte chains with the number of monomers N varying from 25 to 300 in the range of polymer concentrations covering both dilute and semidilute regime. Polyelectrolyte chains in dilute solutions are nonuniformly stretched with the projection of the linear monomer density onto the end-to-end vector increasing logarithmically from the middle of the chain. The simulation results for chain size dependence on the degree of polymerization at different polymer concentrations are in good qualitative agreement with predictions of the modified scaling model that takes into account nonuniform stretching of polyelectrolyte chains. In semidilute solutions we confirm that the correlation length is inversely proportional to the square root of polymer concentration. By measuring the bond angle correlation function, we have determined that polyelectrolyte chains can be viewed as flexible chains with the persistence length proportional to the correlation length. Our results for the concentration dependence of chain size Re on polymer concentration for the longest chains (N = 187 and N = 300) are approaching the power law c-1/4, predicted by the scaling model of salt-free polyelectrolyte solutions.

Prediction of rheometrical and complex flows of entangled linear polymers using the double-convection-reptation model with chain stretch

We study the rheometrical and complex flow response of the double-convection-reptation (DCR) model with chain stretch proposed recently by Ianniruberto and Marrucci (2002) for entangled linear polymers. The single- and two-mode differential versions of the model are used, with the parameter values identified by Ianniruberto and Marrucci (2002) for a nearly monodisperse polybutadiene solution. These authors found that the DCR model with stretch predicts the rheometrical shear behavior of the fluid well in the modest experimental range of deformation rates. Our calculations for the higher shear rates reached in simulations of complex flow reveal anomalous or questionable behavior, namely, shear thickening over an intermediate range of shear rates and large chain stretch in fast shear flows. This behavior is shown to be shared by the original integro-differential DCR theory, of which the differential DCR model is actually a mathematical approximation. We also show that the original DCR theory with stretch predicts excessive shear thinning at high shear rates, while its differential approximation remains stable for all shear rates. Using the backward-tracking Lagrangian particle method [Wapperom et al. (2000)], we investigate the response of the differential DCR model in start-up flow through an axisymmetric contraction/expansion geometry. We compare the single- and two-mode model predictions (in terms of the steady-state vortex structure, chain stretch, and overall pressure drop), and correlate these with the steady and start-up rheometrical responses in shear and extension. Significant chain stretch is predicted in the vicinity of the axis of symmetry and in thin boundary layers located at the constriction wall. As a result, the DCR predictions significantly depart from the stress-optical rule in these flow regions. Chain stretch also affects the flow kinematics, with the appearance of a large upstream steady-state vortex. Surprisingly, however, the predicted pressure drop is not affected much by these kinematical changes, and is qualitatively described by a simple inelastic, shear-thinning model.

Extensional stress growth and stress relaxation in entangled polymer solutions

We report an evaluation of the double constraint release model with chain stretch (DCR-CS) suggested by Ianniruberto and Marrucci [J. Rheol. 45, 1305–1318 (2001)], in predicting the transient stress growth and stress relaxation behavior of two well-characterized entangled polymer solutions undergoing homogeneous uniaxial extensional flow. The experiments are conducted using a filament stretching rheometer. The DCR-CS model belongs to a family of simplified single-segment models that incorporate constraint release, double reptation, and segmental stretching into the basic reptation mechanism proposed in the original Doi–Edwards theory and seeks to extend the predictive capacity of the theory to more complex flow fields. We show that the single-mode DCR-CS differential model performs well in predicting the transient extensional stress growth and steady-state extensional viscosity over a range of stretch rates. The model also predicts the observed stress relaxation following cessation of stretching satisfactorily. We further show that the model predicts shear thickening even in steady shear flow.

Prediction of multiaxial mechanical behavior for conventional and highly crosslinked UHMWPE using a hybrid constitutive model

The development of theoretical failure, fatigue, and wear models for ultra-high molecular weight polyethylene (UHMWPE) used in joint replacements has been hindered by the lack of a validated constitutive model that can accurately predict large deformation mechanical behavior under clinically relevant, multiaxial loading conditions. Recently, a new Hybrid constitutive model for unirradiated UHMWPE was developed Bergström et al., (Biomaterials 23 (2002) 2329) based on a physics-motivated framework which incorporates the governing micro-mechanisms of polymers into an effective and accurate continuum representation. The goal of the present study was to compare the predictive capability of the new Hybrid model with the J 2-plasticity model for four conventional and highly crosslinked UHMWPE materials during multiaxial loading. After calibration under uniaxial loading, the predictive capabilities of the J 2-plasticity and Hybrid model were tested by comparing the load-displacement curves from experimental multiaxial (small punch) tests with simulated load-displacement curves calculated using a finite element model of the experimental apparatus. The quality of the model predictions was quantified using the coefficient of determination ( r 2). The results of the study demonstrate that the Hybrid model outperforms the J 2-plasticity model both for combined uniaxial tension and compression predictions and for simulating multiaxial large deformation mechanical behavior produced by the small punch test. The results further suggest that the parameters of the HM may be generalizable for a wide range of conventional, highly crosslinked, and thermally treated UHMWPE materials, based on the characterization of four material properties related to the elastic modulus, yield stress, rate of strain hardening, and locking stretch of the polymer chains. Most importantly, from a practical perspective, these four key material properties for the Hybrid constitutive model can be measured by relatively simple uniaxial tension or compression tests.