Finite element modeling creep properties

The analytical determination of the gravity load distribution between the frame and the infill wall requires several considerations. First, a part of the gravity loads may be applied onto the RC columns before the construction of the infill walls because these walls could be constructed after the frame has been completed. Second, long-term effects such as concrete and masonry creep, concrete shrinkage, and brick masonry expansion with time due to water absorption can significantly affect the gravity load distribution. While refined finite element models with viscoelastic material properties can be employed for the determination of the gravity load distribution, the increased computational burden of such analyses may not necessarily produce results of increased accuracy due to lack of experimental data to allow the cahbration of multiaxial viscoelastic constitutive models. 

The test methodologies, whether tension/ compression tests on bulk solders or shear tests on solder joints, have their merits for specific study objectives. Tension and compression tests on bulk solder provide critical input data for constitutive models. The finite element analysis within those models can account for geometric effects on creep deformation in an actual joint configuration (included spatially varying stress state). However, length-scale effects of small joints, or elemental contamination that alters the intrinsic mechanical and physical properties of the solder, require an entirely new set of constitutive equations because finite element analysis cannot account for these effects. Thus, in the latter circumstance, the most accurate creep data would be results obtained from tests on actual joints. 

This chapter has focused on the numerical tools used in the design for reliability of lead-free solder joints. These tools include the finite element method, in general, and, in particular, the use of 3D strip models, specific material properties, and the use of a creep strain energy... 

Experimental load-displacement history and creep data were used to estimate the partitioned viscoplastic constitutive properties. Load isplacement loops from double lap-shear tests were used in conjunction with finite element (FE) models to refine the estimates of the effective viscoplastic constitutive properties of the three Pb-free solders and eutectic Sn Pb. The constitutive equations for the four solders were used as initial estimates when iterating to match experimental and predicted hysteresis loops. That is, experimentally determined double lap-shear specimen load-displacement hysteresis loops were compared with the FE simulations. The constitutive properties were then adjusted iteratively to improve agreement the equations and properties are presented in Table 16. 

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