By Dipl. Ing. Bernd Schwarz (auth.), Dr. G. Q. Zhang, Dr. L. J. Ernst, Mr. O. de Saint Leger (eds.)
Benefiting from Thermal and Mechanical Simulation in Micro-Electronics provides papers from the 1st overseas convention in this subject, EuroSimE2000. For the 1st time, humans from the electronics undefined, examine institutes, software program businesses and universities joined jointly to debate current and attainable destiny thermal and mechanical comparable difficulties and demanding situations in micro-electronics; the cutting-edge methodologies for thermal & mechanical simulation and optimization of micro-electronics; and the views of destiny simulation and optimization method development.
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For this evaluation the whole history of stress and strain is involved and should be kept available. This would result into a huge storage and data handling problem, making the model quite unattractive. The problem, however, can be circumvented or reduced by approximating the kernel function with Prony series. In particular the following Prony series approximation of the cure-dependent relaxation moduli is adopted: CjJal(~),O"(~),(t-~)] ~ ± C;[a l (~),O"(~)]- e-(t-~)Ir" (7) ,,=1 Here the individual terms can be looked upon as responses of Maxwell elements with relaxation times 'to (generalized for 3D).
36) (37) ;=1 These formulations appear to be less adequate for unloading situations (Hadley and Ward, 1975, Ward and Onat, 1963, Rendell et al. 1987). The parameter function investigation requires a large number of creep-recovery experiments at different load levels. , 1997 and later). It originally is based on Shapery's model, but it has 2 non-linearizing functions only (grl, au~I). The kernel function is exponential: (38) Struik also used such an exponential expression in his studies on aging implementation (Struik, 1977 and later).
L:B :<; ) t I 00. 0 . - ..... ooo :-:=::--~o. :-::.... ,.. ec) Fig. _=---;:-;! _ Cyclic loading: Comparison between experiment and model The model gives an excellent description of cyclic loading situations. The investigation of the elastic and creep-Poisson's ratio's requires unit-step creep recovery experiments where both the longitudinal and the lateral strains are measured (see Fig. 24 and 25). Zhang's model was combined with Struik's aging theory to include the effects of ongoing aging. Details can be found in (Zhang, 1997).