Visco-elastic element

Here s is the stress and is the strain, respectively. If s = 0,e = 0, we have an elastic element or a spring, if s = 0,e = 0, we have a viscous element or a dashpot. If e = 0, we have an elastic element and a viscous element in series, which is called visco-elastic element. 

Magnitudes of binary and ternary force interactions required in Eq. (62) are calculated by simple elastic or visco-elastic constitutive equations and then projected into force vectors. Elastic model is the direct implementation of the Hook s law with the stress between micro-elements A and B dependent linearly on the strain eAB ... 

The visco-elastic interactions of connected micro-elements of semicrystalline polyolefins are approximated by the Maxwell model, which formally consists of the spring with modulus E and the viscous dashpot characterized by the viscosity rf connected in series,... 

Fig. 21. Morphogenesis model of porous polyolefin particle based on the elastic and visco-elastic interactions among micro-elements (from Grof et al., 2005a).

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... 

Abstract Accidents of some arch dams show that dam failures are mainly caused by crack or failure of their foundation rocks, which are directly related to water seepage in the rock. This kind of fluid-rock interaction has an important influence on deformation and stress characters of the dam-rock system. In this paper, the stress and flow fields of dams and their foundation rocks are studied as a coupled system, using visco-elastic constitutive models and finite element solution method. The developed models and FEM technique were applied for analysing the continuous displacement of the 13 dam section of the Longyangxia Dam, and the calculated results agree well with the measured ones. 

Recognizing the importance of the coupled hydro-mechanical effects on the performance of civil engineering structures involving fractured rocks, the stress-flow coupling mechanism of the dam-foundation system at Longyangxia site was simulated using a three-dimensional Finite Element code, supported by two visco-elastic constitutive models to represent the time-dependent material behaviour of the dam concrete and the foundation rock. The calculated results were concord with the measured ones and helped to interpret the causes of this continuous displacement at the 13" dam section of the Longyangxia hydropower project, towards the left bank. 

For flow over a bluff body, the fluid elements are subjected to a rapid change in deformations near the frontal face hence elastic effects are likely to be important in this region and the simple boundary layer approximations shoifld not be apphed to visco-elastic materials in this region. However, if elastic effects are negligibly small, the previous approach is reasonably satisfactory for viscoelastic fluids. For instance, the normal stresses developed in visco-elastic fluids will give rise to additional terms in the vr-component of the momentum balance. 

Two forms of specimen are commonly nsed to determine the material parameters in the models outlined below (1) bulk tensile tests and (2) thick adheiend shear tests (TAST). There are two common forms of modelling creep at the macroscopic level. The first is through visco-elastic models, which can be visnalized as a combination of spring and dashpot elements. The simplest of these is the Voigt model shown in Fig. 2. The constitutive equation for this model and its solution for the conditions of creep (constant stress) are given" respectively as... 

More complex models can be formed by connecting a number of such elements in series. However, even these are only linear visco-elastic models in which the rate of straining is directly proportional to the stress. For polymers at typical structural levels of load, the stress-strain rate is often highly non-linear. A molecular interpretation of this can be found in a thermally activated rate process model involving motion of chain segments... 

Sometime ago, the author became aware of a research proposal aiming at generalisation of a conventional, linear-elastic finite-element computer code (see Figure 1) to visco-elastic materials the costs amounted to... 

For the soil with density p, an elastic stress-strain consitutive matrix D (Samuelsson and Wiberg, 1998) and an analogous stress-strain rate visco-elastic matrix standard FE procedures based on form functions N and their spatial derivatives B = V N and a volume integration over the element domain lead to the local matrices as defined in equation (4) ... 

The study of polymer viscoelasticity treats the interrelationships among elasticity, flow, and molecular motion. In reality, no liquid exhibits pure Newtonian viscosity, and no solid exhibits pure elastic behavior, although it is convenient to assume so for some simple problems. Rather, all deformation of real bodies includes some elements of both flow and elasticity. Because of the long-chain nature of polymeric materials, their visco-elastic characteristics come to the forefront. This is especially true when the times for molecular relaxation are of the same order of magnitude as an imposed mechanical stress. 

The methods discussed earlier are applied to the seat-occupant-restraint system of an aircraft. A description of a computer-aided analysis environment, including a multibody model of the occupant and a nonlinear finite element model of the seat, is provided, which can be used to re-construct variety of crash scenarios. These detailed models are useful in studies of the potential human injuries in a crash environment, injuries to the head, the upper spinal column, and the lumbar area, and also structural behavior of the seat. The problem of reducing head injuries to an occupant in case of a head contact with the surroundings (bulkhead, interior walls, or instrument panels), is then considered. The head impact scenario is re-constructed using a nonlinear visco-elastic type contact force model. A measure of the optimal values for the bulkhead compliance and displacement requirements is obtained in order to keep the possibility of a head injury as little as possible. This information could in turn be used in the selection of suitable materials for the bulkhead, instrument panels, or interior walls of an aircraft. The developed analysis tool also allows aircraft designers/engineers to simulate a variety of crash events in order to obtain information on mechanisms of crash protection, designs of seats and safety features, and biodynamic responses of the occupants as related to possible injuries. 

To optimize the performances of a lens, it is necessary to extract its intrinsic characteristics allowing one to study the mechanics of the eye. All the elements present have to be considered and their properties, namely, the lachrymal fluid, which is a nearby particular fluid with water behavior, the eyelid, visco-elastic and the porous lens or cornea. The lachrymal film is constituted of three layers ... 

This concept is demonstrated by numerical analysis using ABAQUS [2]. The sheet is discretized into finite elements for the dimensions shown in Fig. 1. The width of the sheet is taken as 10mm with thickness of 1.27 mm. The sheet melt (poly carbonate) temperature is assumed to be 300 C. The dent was created by giving small deformation at bottom and simultaneously cooling for 1 sec. Coupled thermal - visco-elastic analysis is carried out. Stresses are created during this cooling process, and further cooled to ambient temperature in 15 sec. The dent and the associated of stresses are shown in Fig. 2. 

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