Hardening model kinematic

The stress-strain relationship for FGMs is assumed to be a bilinear form and can be described by the isotropic hardening model and kinematic hardening model as ... 

Figure 13 Wall under Dynamic Loading Conditions, first and third stage (a) experimental, (b) bilinear kinematic hardening model, (c) M-P model and (d) M-N model.

We illustrate the isotropic and kinematic hardening models for the onedimensional problem in Fig. 2.18a, b, and for the two dimensional problem in Fig. 2.19. Note that the behavior shown in Fig. 2.18b is known as the Bauschinger effect. In geotechnical engineering practice the isotropic hardening model is widely used because, except in earthquake situations, it is rare that the loading direction is completely reversed. 

The more rigorous stress/strain nonlinear material model, oflen referred to as the plastic zone method, is theoretically capable of handling any general cross section Both isotropic and kinematic hardening rules are usually available. This method is... 

Usually, the material starts with a kinematic behavior. With increasing strain level, the kinematic behavior saturates and isotropic hardening is taken place. The problem now is to describe the behavior of a as a function of the strain and strain-rate level. Several models are available but only the models from Armstrong and Frederick (Armstrong and Frederick 1966) and the Yoshida model (Yoshida and Uemori 2002) are described in the following because of their popularity in the last decades. 

In practice, is often the variable which determines the size (isotropic hardening) or the amount of translation (kinematic hardening) of the yield surface and represents in a simplified manner all the effects of the loading history. One particular example is the preconsolidation pressure which determines the current yield envelope of clays (as in Camclay model). 

The response obtained using three different reinforcing steel models is shown in Figure 10. The widely used bilinear model with kinematic hardening and the model... 

The cyclic stress-strain curve can be used, for example, to perform finite element simulations of cyclic loadings. To simulate the complete experiment in the computer, it would be necessary to obtain information on the hardening of the material (isotropic and kinematic hardening) and to determine a material model that correctly describes it. This would be an extremely comphcated procedure. Furthermore, the entire number of cycles would have to be calculated, which would require an immense amount of computing time. Instead, the flow curve, taken by the finite element software to be monotonous, can be replaced by the cyclic stress-strain curve. A single, monotonous loading of the component is then simulated. Stresses and strains calculated in this way correspond well with those in the cyclically loaded component. 

Fig. 7.18. Variation of normalized equi-biaxial film stress as a function of normalized temperature, using conditions specified in the example in Section 7.5.2. The film material is now modeled as a kinematically hardening solid. The solid lines...

Equation 5 shows that the Bouc-Wen model accounts for kinematic hardening (i.e., post-yield force increases with increasing deformation) due to the post-yield stiffness ratio p. However, the model does not account for the isotropic hardening (i.e., yield force Fy increases due to cyclic inelastic deformation) in the hysteresis of steel energy dissipation devices. 

The constitutive law describing the behavior of the steel material is the uniaxial Menegotto-Pinto model (1973). This computationally efficient nonlinear law is capable to model both kinematic and isotropic hardening as well as the Bauschinger effect, allowing for accurate simulation and reproduction of experimental results. The response of the steel material is defined by the following nonlinear equation ... 

The matrix material was chosen to be a polyester resin for both the inner and outer layer. The FEA model consisted of four parts namely the helmet shell, the foam liner, the head-form and the hemispherical test anvil. The foam liner was modeled using a set of 8500 solid elements, the woven ply was modeled as an orthotropic material with damage and the glass mat polyester layer was modeled as an isotropic elastic-plastic material with kinematic hardening. 

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