On the computation of the coupled thermo‐electromagnetic response of continua with particulate microstructure

Recently, several applications, primarily driven by micro‐technology, have emerged where the use of materials with tailored electromagnetic properties is necessary for a successful design. The ‘tailored’ properties are achieved by doping an easily moldable base matrix with particles having dielectric constants that are chosen to give overall desired properties. In many cases, the analysis of such materials requires the simulation of the macroscopic and microscopic electromagnetic response, as well as its resulting coupled thermal response, which can be important to determine possible failure in ‘hot spots’. In this study, a model and a solution strategy are developed to compute the response of a class of fully coupled electro‐magneto‐thermal systems composed of heterogeneous materials, involving the absorption of electromagnetic energy, its conversion to heat and changes in the electromagnetic material properties. The algorithm involves recursive staggering, whose convergence is dependent on the discretized time‐step size. The multifield system coupling can change, becoming weaker, stronger or alternating back and forth. Therefore, it is quite difficult to determine a priori the time‐step size needed to meet a prespecified tolerance on the staggering error, i.e. the incomplete resolution of the coupling between the fields. The presented solution process involves time‐step size adaptivity to control the contraction mapping constant of the multifield system operator in order to induce desired staggering rates of convergence within each time step and to control the staggering error. Three‐dimensional numerical experiments are performed to illustrate the behavior of the model and the solution strategy. Copyright © 2008 John Wiley & Sons, Ltd.