By Ivo Babuška, Philippe G. Ciarlet, Tetsuhiko Miyoshi (eds.)
This e-book indicates the most recent frontiers of the study through the main energetic researchers within the box of numerical arithmetic. The papers within the publication have been provided in a symposium at Yamaguchi, Japan. the topic of the symposium used to be mathematical modeling and numerical simulation in continuum mechanics. the themes of the lectures ranged from solids to fluids and incorporated either mathematical and computational research of phenomena and algorithms. The readers can research the most recent effects on shells, plates, flows in numerous events, fracture of solids, new methods of tangible blunders estimates and plenty of different topics.
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Additional info for Mathematical Modeling and Numerical Simulation in Continuum Mechanics: Proceedings of the International Symposium on Mathematical Modeling and Numerical Simulation in Continuum Mechanics, September 29 – October 3, 2000 Yamaguchi, Japan
Mathematical Modeling and Numerical Simulation in Continuum Mechanics © Springer-Verlag Berlin Heidelberg 2002 24 Ken Kaminishi considerable attention has been paid to the fatigue strength of Pb-free solder -. 7Cu) in order to examine the crack initiation and growth behavior. Torsion fatigue tests are performed in parallel on bulk specimen of solder used in this work to obtain basic fatigue data of the solder materials, such as mechanical properties, cyclic stress-strain curves and prediction formulae used in numerical simulation.
37. •. 560E-03 1. 000[+00 Fig. 9. Distribution of the equivalent inelastic strain range initiation life of solder joints can be predicted somewhat conservatively using the proposed formulae. Table 3. Results of experiments and numerical analyses for crack initiation life Material Disp. frequency Temp. 1 Prediction of the crack growth path and life Crack growth path Because the inner part of solder fillet in Gullwing type joints can be regarded as in an approximate plane strain condition, two-dimensional FEM program for crack growth analyses was developed in order to predict the fatigue crack growth life in solder joints.
6. Fatigue lives divided int o four ph ases 30000 28 Ken Kaminishi Table 1. 2 Stress-strain analysis of solder joints The st ress-strain analyses of t he solde r joints were performed by three dimensional elasto-inelastic FEM in order to predict the crack initiation locus and life in the solder joint. In our st rain analyses, an expe rime nt ally determined cyclic stress range versus inelastic st rai n range relat ion was incorp orated into the const it utive equation t o consider the creep effect .
Mathematical Modeling and Numerical Simulation in Continuum Mechanics: Proceedings of the International Symposium on Mathematical Modeling and Numerical Simulation in Continuum Mechanics, September 29 – October 3, 2000 Yamaguchi, Japan by Ivo Babuška, Philippe G. Ciarlet, Tetsuhiko Miyoshi (eds.)