Nonlinear Material Properties

Figure 10.6 gives a schemahc view of the test setup of the strain measurement. The boundary conditions in this stretched him method are modeled by hnite element analysis with nonlinear material properties. 

Selection of the material model is another important factor to be considered. Some programs allow the user to specify plastic moment-rotation curves for beam elements. However, the more rigorous and most widely available method of defining nonlinear material properties is to specify the stress versus strain data, Plastic behavior is approximated at the section level in the former method whereas, the latter method tracks plastic behavior at the individual integration points (fibers) through the thickness of the member. Each method has its advantages and disadvantages. 

The most efficient method is to have the supplier use finite element analysis (FEA) to do a simulation. One can use trial and error approaches, but since the process involves cutting metal on a mold, it is faster and less expensive to use a computer simulation. The FEA program chosen must be capable of nonlinear calculations in order to properly model the nonlinear material properties. 

D Octant. In order to avoid the boundary condition approximations of the 3D slice model, a full 3D octant model may be constructed. This model, as depicted in Fig. 3, should produce the most accurate results and is appropriate for situations where certain asymmetries, such as a rectangular die with large aspect ratios, preclude the use of a slice model. For larger packages or in the case of fine meshes, the 3D octant can have a very large number of elements and run slowly. Since the solder balls will have nonlinear material properties, computation with a 3D oc-... 

These parameters can be used to infer the inherent nonlinear material properties of a sample as the trivial scaling for the relative intensities of the higher harmonics, 4/1 oc. yQ, is eliminated. As an example of this, the intrinsic nonlinearity parameter Q, that is derived from the third harmonic, has been shown to be useful in evaluating the topology of polymer melts [20]. 

The present chapter is devoted to the probabilistic analysis of the random response of nonlinear structural systems exposed to random excitation with special attention to earthquake action. The random system response may be due to random excitation, to random system properties, to random boundary conditions. The nonlinear character of the response is mainly due to the nonlinear materials properties and to the effect of large displacements (the so-caUed P-A effect). 

Bulk tensile testing has shown that adhesives generally exhibit plasticity and, hence, nonlinear material properties are required to model their behavior over the fiill load range. Nonlinear properties may also be required for adherends. Thus, a combination of elasto-plastic material models may be used to predict the behavior of adhesive joints under load. The definition of the yield surface is important when using elasto-plastic material models. Von Mises yield surface is commonly used for the analysis of metals, which assumes that the yield behavior is independent of hydrostatic stress. As a result, the yield surface is identical in tension and compression. However, the yield behavior of polymers has been shown to exhibit hydrostatic stress dependence (Ward and Sweeney 2004) as the yielding starts earlier in tension than in compression. Thus, a yield criterion which includes hydrostatic stress effects should be used to determine the yield surface. Various yield criteria with hydrostatic stress dependence such as Drucker-Prager, Mohr-Columb, and modified Drucker-Prager/cap plasticity model have been implemented in commercially available finite element software. 

---