Model representation of deformation

Fig. 2 gives our model representation of the entangled solid polymer network prior to deformation (Termonia and Smith, 1987, 1988). The dots denote the entanglement loci. The dashed lines represent the weak attractive (Van der Waals) intermolecular bonds connecting sections of either the same chain or, of different chains. Since the... 

FIGURE 4.1 Schematic representation of deformation oftwo sequences of atoms according to the Frenkel model. Positions before (a) and after (b) deformation [3],... 

One model for the deformation of polymer solids has been described at length in References 8 and 9. It is briefly reviewed here. Figure 1 gives this model representation of the entangled solid polymer network prior to deformation. The entanglements, ie, knots formed between chains, are denoted by the... 

Thus far model representations of polymer deformation have been discussed. Each of those could be converted into a model representing the fracture behavior if it were possible to formulate an adequate fracture criterion within the range of validity of these models. Having dealt with deformation the fracture criteria to be formulated would have to involve finite extensibility, critical load, or limited volume concentration of stored or dissipated energy. Dealing with fracture one will find that strain, stress, and energy are not sufficient as variables and that one will have to add at least two new dimensions time and structural discontinuity. This will be explained in the following Chapter. 

Both models, the Maxwell element and the Kelvin-Voigt element, are limited in their representation of the actual viscoelastic behaviour the former is able to describe stress relaxation, but only irreversible flow the latter can represent creep, but without instantaneous deformation, and it cannot account for stress relaxation. A combination of both elements, the Burgers model, offers more possibilities. It is well suited for a qualitative description of creep. We can think it as composed of a spring Ei, in series with a Kelvin-Voigt element with 2 and 772. and with a dashpot, 771... 

Figure 9 (a) Schematic representation of fountain flow, showing the velocity and shear rate profiles and the deformation of a cubic element of melt as it approaches the flow front, (b) Model for growth of the frozen layer in a mould cavity... 

The constraining potential represented by virtual chains must be set up so that the fluctuations of junction points are restricted, but the virtual chains must not store any stress. If the number of monomers in each virtual chain is independent of network deformation, these virtual chains would act as real chains and would store elastic energy when the network is deformed. A principal assumption of the constrained-junction model is that the constraining potential acting on junction points changes with network deformation. In the virtual chain representation of this con-... 

C. Davatzikos and R. N. Bryan. 1996. Using a deformable surface model to obtain a shape representation of the cortex. IEEE Transactions on Medical Imaging 15(6) 785-795. 

The free body diagram is considered for the entire structure and each node is examined. The FEA model breaks a structure into smaller elements, each representing the material s stiffness. Load transfer is calculated through smaller elements and by considering equilibrium, compatibility of deformation, and Hooke s law. In Figure 4.11, a load is placed on a fixed beam as shown. In the three-element representation, each element is affected by the initial downward and axial loads. 

Fracture Stress and Strain. Yielding and plastic deformation in the schematic representation of tensile deformation were associated with microfibrillation at the interface and stretching of the microfibrils. Because this representation was assumed to apply to both the core-shell and interconnected-interface models of compatibilization, the constrained-yielding approach was used without specific reference to the microstructure of the interface. In extending the discussion to fracture, however, it is useful to consider the interfacial-deformation mechanisms. Tensile deformation culminated in catastrophic fracture when the microfibrillated interface failed. This was inferred from the quasi-brittle fracture behavior of the uncompatibilized blend with VPS of 0.5, which indicated that the reduced load-bearing cross section after interfacial debonding could not support plastic deformation. Accordingly, the ultimate properties of the compatibilized blend depended on interfacial char-... 

The DNF model incorporates the experimentally observed characteristics by using a micromechanism-inspired approach in which the material behavior is decomposed into a viscoplastic response, corresponding to irreversible molecular chain sliding due to the lack of chemical crosslinks in the material, and atime-dependent viscoelastic response. The viscoelastic response is further decomposed into the response of two molecular networks acting in parallel the first network (A) captures the equilibrium response and the second network (B) the time-dependent deviation from the viscoelastic equilibrium state. A onedimensional rheological representation of the model framework and a schematic illustrating the kinematics of deformation are shown in Fig. 11.6. 

Figure 11.6 (a) Rheological representation of the constitutive model (b) kinematios of deformation. 

Abstract Modeling of the drift-scale heater test at the Exploratory Studies Facility at Yucca Mountain, Nevada, U.S.A. was performed. The objectives of the analysis were to investigate the (i) temperature effects on mechanical deformation surrounding the heated drift and (ii) thermal-mechanical effects on rock-mass permeability. The continuum representation of a deformation-permeability relationship based on fracture normal stress was developed to assess rock-mass permeability variations because of temperature changes. The estimated rock-mass displacements and permeability variations as a function of heating time were compared with field measurements. The estimated trend of permeability responses using a normal stress-based deformation-permeability relationship compared reasonably to that measured. 

Modeling the heat generation therefore requires some representation of the interface contact behavior together with the viscous dissipation behavior of the material. Simple analytical approaches are discussed in this section numerical methods, in which heat generation is calculated directly from coupled models of the temperature field and metal deformation, are discussed in section 10.3, Metal Flow. ... 

The four-parameter model provides a crude quahtative representation of the phenomena generally observed with viscoelastie materials instantaneous elastie strain, retarded elastic strain, viscous flow, instantaneous elastie reeovery, retarded elastie reeovery, and plastic deformation (permanent set). Also, the model parameters ean be assoeiated with various molecular mechanisms responsible for the viscoelastic behavior of linear amorphous polymers under creep conditions. The analogies to the moleeular mechanism can be made as follows. 

---