Computational models for multi-scale coupled dynamic problems

摘要

In this paper we describe a systematic methodology for the construction of computational models for coupled multi-scale dynamic problems with a major focus given to a case study example related to the design of shape memory alloy actuators controlled by thermoelectric effect. From a mathematical point of view, the problem in hand is a coupled dynamic system of partial differential equations which is not amenable to analytical treatments and requires an efficient computational tool for its solution. The developed methodology is based on a combination of the analysis of such invariant sets that keep the essentials of the system dynamics and on the reduction procedures of the original model on such sets. A presented numerical example demonstrates the efficiency of the developed tool in describing phase transformations in actuators based on materials with shape memory effects.