Efficient Computational Models for Coupled Nonlinear Dynamics of Materials with Memory

Melnik, R.V.N.

Proceedings of Neural, Parallel and Scientific Computations, Dynamic Publishers, Atlanta, USA, 2(2002), 241--244, 2002

Abstract:

Many models of science and engineering are essentially coupled dynamically in a sense that the response of system components should be obtained concurrently. This dynamic coupling is an intrinsic feature of many systems, processes, and phenomena with numerous examples in mechatronics, geophysics, biomechanics, and many other fields. In some cases the interacting components of the system could be structures, fluid, or solid media, as, e.g., in geophysical applications, while in other cases the interacting components could be given in the form of fields such as mechanical and thermal, or electrical and mechanical, invoking a unification of two or more physical theories that have been considered separately before, e.g. thermoelasticity, electroelasticity, hydroelasticity, etc.

A common feature of all these problems is that in most practically interesting cases the resulting mathematical models are not amenable to the analytical treatment, and the development of efficient numerical procedures for their solutions is required. In this paper I am interested in efficient scientific computing tools allowing us to adequately describe the complex nonlinear behaviour of materials with memory, in particular shape memory alloys. My main tool will be the centre manifold technique linked together with effective computational procedures for the model construction.

Key words: dynamical coupling; phase transformations; nonlinear phenomena; materials with memory; complex systems and their interacting components; shape memory alloys; centre manifold technique; residual minimization.