Uniaxial tension simulations

Mention has already been made that one of the advantages of the controlled pressure molecular dynamics discussed in Section 5.2 is that the form of the apphed pressure tensor P can be used to impart strain to a sample as a function of time in much the same way as in laboratory experiments. Control of appropriate components of the pressure tensor can be used to produce, to take just three examples, uniaxial tension, compression or shear as illustrated in Fig. 5.7 

Current limitations on simulation times have meant that very high rates of strain must be used in order to observe the system response. Nevertheless the general form of the results show striking similarities to those obtained in laboratory experiments performed on time scales many orders of magnitude slower. 

To give an example of what can be achieved in such simulations we discuss below the stress-strain behavior as observed in simulations of the model PE I of polyethylene at a range of temperatures in the glass and melt. The sample size was 1000 monomers formed into a single linear chain as described in Section 5.4. The coohng curve for these samples is shown in 

The prepared samples were subjected to a gradually increasing uniaxial tension by changing the component of the applied pressure tensor, constant rate 

The strain induced in the sample is of primary interest so the applied tension is best considered as a control variable which produces a change in the strain. The response is given by the measured tension, i.e. —pyy, within the sample. In these experiments then, both the strain and the measured tension are dependent variables. The method is preferable to direct control 

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It is interesting to note the strain dependence of the fraction of trans conformers. This data is shown in Fig. 5.14 and they reveal a common feature of all uniaxial tension simulations to date, namely that there is a... 

Fond et al. [84] developed a numerical procedure to simulate a random distribution of voids in a definite volume. These simulations are limited with respect to a minimum distance between the pores equal to their radius. The detailed mathematical procedure to realize this simulation and to calculate the stress distribution by superposition of mechanical fields is described in [173] for rubber toughened systems and in [84] for macroporous epoxies. A typical result for the simulation of a three-dimensional void distribution is shown in Fig. 40, where a cube is subjected to uniaxial tension. The presence of voids induces stress concentrations which interact and it becomes possible to calculate the appearance of plasticity based on a von Mises stress criterion. 

To further illustrate how extended ensembles can be designed to conduct MD simulations under various macroscopic constraints, we discuss here the NTLxPyycr ensemble. NTL yyOzz is an appropriate statistical ensemble for the simulation of uniaxial tension experiments on solid polymers [12] or relaxation experiments in uniaxially oriented polymer melts [13]. This ensemble is illustrated in Fig. 2. The quantities that are kept constant during a molecular simulation in this ensemble are the following ... 

Here, Wo is a characteristic level of back stress that primarily affects the initial slope of the uniaxial stress versus remanent strain curve, and m is another hardening parameter that controls how abruptly the strain saturation conditions are reached. Figure 2a illustrates the predictions of the effective stress versus the effective remanent strain from the constitutive law for uniaxial compression, pure shear strain, pure shear stress and uniaxial tension. It is interesting to note that the shear strain and shear stress curves do not coincide. This feature is due to the fact that the material can strain more in tension than in compression, and has been confirmed in micromechanical simulations. Figure 2b illustrates the uniaxial stress versus remanent strain hysteresis curves for two sets of the material parameters Wq and m. 

Furthermore, anticipated in-service conditions may call for conducting simulated laboratory fatigue tests that use either uniaxial tension-compression or torsional stress cycling instead of rotating-bending. 

When a geotextile subjected to concentrated forces normal to the plane is kept under pre-tensioned conditions, the distribution and magnitude of these forces result in the puncture failure. In general, a biaxial tensile failure simulates puncture failure more appropriately than uniaxial tensile tests. The puncture properties of geotextiles are significantly affected by the fabric and soil parameters. ... 

After the optimal set of maferial paramefers was found, the same parameters were then used to simulate the small pimch test. This validation simulation was performed to check the capability of the HM to predict a multiaxial deformation history. It is well known that many constitutive models can predict uniaxial deformation histories relatively well, but that it is significantly more difficult to accurately predict multiaxial deformation states. It has been shown, for example, that the /2-plasticity model can accurately predict monotonic imiaxial tension or compression data for UTTMWPE, buf is very poor at predicting cyclic or multiaxial deformation states (Bergstrom, Rimnac, and Kurtz 2003). 

Many other important impact design parameters such as yield stress, energy to yield, initial modulus, and deformation at break can be measured with high-speed tension tests (38). In spite of the capability of high-rate tension tests to provide stress at strain rates that simulate actual service, the tests have not been popular because the delivered stress is uniaxial. Normally, the real-life impact stress is multiaxial. 

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