Stress-strain relationship including

Figure 10.2. Stress-strain behavior. With elastic (reversible) deformation, stress and strain are linearly proportional in most materials (exceptions include polymers and concrete). With plastic (permanent) deformation, the stress-strain relationship is nonlinear.

The continuum mechanics modeled by JAS3D are based on two fundamental governing equations. The kinematics is based on the conservation of momentum equation, which can be solved either for quasi-static or dynamic conditions (a quasistatic procedure was used for these analyses). The stress-strain relationships are posed in terms of the conventional Cauchy stress. JAS3D includes at least 30 different material models. 

Blood and lymphatic vessels are soft tissues with densities which exhibit nonlinear stress-strain relationships [1]. The walls of blood and lymphatic vessels show not only elastic [2, 3] or pseudoelastic [4] behavior, but also possess distinctive inelastic character [5, 6] as well, including viscosity, creep, stress relaxation and pressure-diameter hysteresis. The mechanical properties of these vessels depend largely on the constituents of their walls, especially the collagen, elastin, and vascular smooth muscle content. In general, the walls of blood and lymphatic vessels are anisotropic. Moreover, their properties are affected by age and disease state. This section presents the data concerning the characteristic dimensions of arterial tree and venous system the constituents and mechanical properties of the vessel walls. Water permeability or hydraulic conductivity of blood vessel walls have been also included, because this transport property of blood vessel wall is believed to be important both in nourishing the vessel walls and in affecting development of atherosclerosis [7-9]. 

The containment shell is analyzed for individual and various combinations of loading cases of dead load, live load, prestress, temperature, and pressure. The design output includes direct stresses, shear stresses, principal stresses, and displacements of each nodal point. Stress plots which show total stresses resulting from appropriate combinations of loading cases are made and areas of high stress identified. If necessary, the modulus of elasticity is corrected to account for the nonlinear stress-strain relationship at high stresses. Stresses are then recomputed if a sufficient number of areas requiring attention exist. 

Gomes, A. Sc Appleton, J. 1997. Nonlinear cyclic stress-strain relationship of reinforcing bars including buckling. Engineering Structures 19(10) 822-826. 

Useful physical properties of textile fiberglass include a hnear stress-strain relationship up to the yield stress (3400 MPa for E glass and 4500 MPa for S glass approximately 5 percent deformation), heat resistance and lack of flammability. 

A subtraction of the total amount of stress decay, Aazz(t oo), from the respective initial stresses measmed along the stretching curve gives the stress-true strain relationship associated with the limit of zero strain rates, i.e., under quasi-state conditions. The quasi-static stress-strain relationship obtained in this manner for PEVA12 is included in Fig. 10.5. 

Stress-strain relationships for the steel material including strain hardening and softening... 

Stress-strain relationships for the crmcrete material including cycUng loading regimes and the effect of the confinement on the peak stress and corresponding strain... 

As a starting point it is useful to plot the relationship between shear stress and shear rate as shown in Fig. 5.1 since this is similar to the stress-strain characteristics for a solid. However, in practice it is often more convenient to rearrange the variables and plot viscosity against strain rate as shown in Fig. 5.2. Logarithmic scales are common so that several decades of stress and viscosity can be included. Fig. 5.2 also illustrates the effect of temperature on the viscosity of polymer melts. 

A linear relationship exists between the toughness (integrated stress-strain curve) and the dynamic mechanical dissipation factor. The types of materials that fit this relationship include glassy polymers, elastomers, and an impregnated fabric. The existence of this relationship indicates that toughness arises from the molecular motions which give rise to the dynamic mechanical properties. 

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