A persistent feature of complex systems in engineering and science is the emergence of macroscopic, coarse
grained, coherent behaviour from microscale interactions. In current modeling, ranging from ecology to materials
science, the underlying microscopic mechanisms are known, but the closures to translate microscale knowledge to
a large scale macroscopic description are rarely available in closed form. Kevrekidis proposes new 'equation free'
computational methodologies to circumvent this stumbling block in multiscale modelling. Nonlinear coordinate
transforms underpin analytic techniques that support these computational methodologies. But to do so we must
cross multiple space and time scales, in both deterministic and stochastic systems, and where the microstructure
is either smooth or detailed. Using examples, I describe progress in using nonlinear coordinate transforms to
illuminate such multiscale modelling issues.
Since the phase change in SMA-based devices such as actuators is accompanied by a significant heat exchange with the surroundings, different concepts to heat/cool SMAs have been proposed in the literature. Most of these concepts require the analysis of a multilayered (e.g., "sandwich"-type) structure where the SMA layer is placed between layers with another material. In this paper we propose a mathematical model and an efficient numerical method for this analysis. Although our approach can be applied to a wide range of different designs of multilayered actuators, the basic idea of the model construction is explained in this paper for a specific design based on the introduction of semiconductor "heat pump" modules into the device and the Peltier effect for the heat exchange. The dynamics of thermomechanical fields is studied with a coupled system of PDEs based on conservation laws. The system, supplemented by constitutive relationships in the Falk form, is reduced to a differential-algebraic (DA) model and solved with an effective DA solver developed in our previous works. Numerical results on thermomechanical behaviour of SMA components in multilayered actuators are presented.
In this paper we present results on numerical studies of the martensitic-austenitic phase transition mechanism in a large shape-memory-alloy rod. Three groups of experiments are reported. They include results on stress- and temperature- induced phase transformations as well as the analysis of the hysteresis phenomenon. All computational experiments are presented for Cu-based structures.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.