The research is carried out by the Institute for Industrial Mathematics in cooperation with Microswiss Co. and is financially supported by the Israeli Ministry of Science through grant 9641--1--96.

Ultrasonic welding is a comprehensive technological process for producing bonds between metals and polymers by high-frequency vibration (from 20 to 120 kHz). It is widely used in microelectronics (wire bonding for joining microstructures into circuit packages), and in manufacturing advanced thermoplastic composites, because

1. ultrasonic welding is fast and easily automated;
2. it produces repeatedly high-quality joints;
3. it ensures the highest strength of bonds compared to other welding techniques.

The aim of the study is to design advanced mathematical models for ultrasonic welding, which include as components the following submodels:

1. elastic deformations of a capillary of the vibrator;
2. thermoplastic deformations of welded parts;
3. heating of contacting bodies by ultrasonic oscillations;
4. wear of contacting surfaces;
5. plastic flow and melting in the vicinity of the bond, etc.

The objectives are (i) to derive complex models, which could correctly predict the bond strength for given technological parameters and geometry of sonotrons; and (ii) to apply these models for optimal design of capillaries which ensure the required strength of bonds produced by ultrasonic welding.