Dynamic deformation model

In particular it can be shown that the dynamic flocculation model of stress softening and hysteresis fulfils a plausibility criterion, important, e.g., for finite element (FE) apphcations. Accordingly, any deformation mode can be predicted based solely on uniaxial stress-strain measurements, which can be carried out relatively easily. From the simulations of stress-strain cycles at medium and large strain it can be concluded that the model of cluster breakdown and reaggregation for prestrained samples represents a fundamental micromechanical basis for the description of nonlinear viscoelasticity of filler-reinforced rubbers. Thereby, the mechanisms of energy storage and dissipation are traced back to the elastic response of tender but fragile filler clusters [24]. 

Figure 2. L-alanine. Dynamic deformation density in the COO plane, (a) Model dynamic deformation density A Modei. (b) MaxEnt dynamic deformation density (Agj, (x)) map obtained with a non-uniform prior of spherical-valence shells. Map size 6.0A x 6.0A Contour levels from -1.0 to 1.0 eA 3, step 0.075 e A-f...

Figure 6. l-Alanine. Fit to noisy data. Calculation A. MaxEnt deformation density and error map in the COO- plane Map size, orientation and contouring levels as in Figure 2. (a) MaxEnt dynamic deformation density A uP. (b) Error map qME - Model. 

When observed structure factors are used, the thermally averaged deformation density, often labeled the dynamic deformation density, is obtained. An attractive alternative is to replace the observed structure factors in Eq. (5.8) by those calculated with the multipole model. The resulting dynamic model deformation map is model dependent, but any noise not fitted by the muitipole functions will be eliminated. It is also possible to plot the model density directly using the model functions and the experimental charge density parameters. In that case, thermal motion can be eliminated (subject to the approximations of the thermal motion formalism ), and an image of the static model deformation density is obtained, as discussed further in section 5.2.4. 

Petrie and Ito (84) used numerical methods to analyze the dynamic deformation of axisymmetric cylindrical HDPE parisons and estimate final thickness. One of the early and important contributions to parison inflation simulation came from DeLorenzi et al. (85-89), who studied thermoforming and isothermal and nonisothermal parison inflation with both two- and three-dimensional formulation, using FEM with a hyperelastic, solidlike constitutive model. Hyperelastic constitutive models (i.e., models that account for the strains that go beyond the linear elastic into the nonlinear elastic region) were also used, among others, by Charrier (90) and by Marckmann et al. (91), who developed a three-dimensional dynamic FEM procedure using a nonlinear hyperelastic Mooney-Rivlin membrane, and who also used a viscoelastic model (92). However, as was pointed out by Laroche et al. (93), hyperelastic constitutive equations do not allow for time dependence and strain-rate dependence. Thus, their assumption of quasi-static equilibrium during parison inflation, and overpredicts stresses because they cannot account for stress relaxation furthermore, the solutions are prone to numerical instabilities. Hyperelastic models like viscoplastic models do allow for strain hardening, however, which is a very important element of the actual inflation process. 

Fig. 4. The phosphazene ring (a) island delocalization model predicting nodes in TT-density at the phosphorus atoms (b) dynamic deformation density (at 0.1 eA 3) in the plane of the ring (c) theoretical deformation density (at 0.05 eA-3) of cyclic phosphazene was used as a model (reproduced with permission from Cameron et al. [43]).

Once the multipole analysis of the X-ray data is done, it provides an analytical description of the electron density that can be used to calculate electrostatic properties (static model density, topology of the density, dipole moments, electrostatic potential, net charges, d orbital populations, etc.). It also allows the calculation of accurate structure factors phases which enables the calculation of experimental dynamic deformation density maps [16] ... 

The theory of relaxation spectra in polarized luminescence for various dynamic models of a flexible polymer chain has been developed by several groups of workers. Wahl has proposed a theory for the model of Gaussian subchains. The authors and coworkers used dynamic chain models consisting of rigid or deformable elements with continuous visco-elastic mechanism of mobility and rotational-isomeric lattice chain... 

These new concepts for membrane constitutive behavior have yet to be thoroughly explored. The temperature dependence of these moduli is unknown, and the implications that such a model will have on interpretation of dynamic deformations of the membrane remain to be resolved. 

Schmidt et alT used a pair of high speed cameras to record the dynamic deformation, showing shape and strain details of a fabric upon ballistic impact The information obtained is used to validate the FE model in LS-DYNA and to quantily the transverse deflection. Nurick used light rays emitted from a silicon photovoltaic... 

For the hybrid model (ANSYS FLUENT POLYFLOW), the moving parts were taken into consideration using a sliding and dynamic mesh model in FLUENT. As shown in Fig. 4, smoothing and dynamic layering methods were adopted to adjust the mesh of a zone with moving and/or deforming boundaries. The total cell count for the hybrid model is 126,000. 

The dynamic flocculation model of stress softening and filler induced hysteresis assumes that the breakdown of filler clusters during the first deformation of the virgin samples is totally reversible, though the initial virgin state of filler-... 

The constitutive equations (2.7) and (2.12) of derived adsorption-induced deformation model and deformable lattice model are regarded as dynamical systems. Its definition[178] is as ... 

At first, discrete model, deformable lattice model, were proposed from adsorption-induced deformation model, utihzing cell dynamic scheme. Both adsorption model and cellular model are ubiquitously used in the field of physics. 

A simple one-dimensional model of electrically-induced dynamic deformation or vibration of a cantilever beam made with such IPMC artificial muscle strips is given by the following equations ... 

Linear deformation model was used in (5) to account for the effect of dynamic deformation on dynamic properties, but its effect on stability threshold is still to be investigated, and more elaborate deformation model might also be applied. These are attempted in this paper. 

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