Faculty Advisor

Burt S. Tilley

Faculty Advisor

Homer F. Walker

Faculty Advisor

Vadim V. Yakovlev

Faculty Advisor

Suzanne L. Weekes

Faculty Advisor

Didier Bouvard


In recent years, sintering of powdered materials in microwaves has emerged as a manufacturing technique with many potential advantages over conventional sintering methods, including the possibility of faster processing and finer microstructure, along with the potential for vast energy savings. However, the technique remains on the level of laboratory studies and is underutilized in industry, mostly due to the difficulty of controlling the process: the intrinsically nonuniform temperature pattern that results from microwave heating routinely induces nonuniform mechanical deformation. Mathematical models and computer simulations can help to clarify the factors that influence this process and aid experimentalists in the design of efficient processing equipment. Although a number of modelling techniques have been reported to this end, they appear to inadequately represent the entire chain of related physical phenomena, which involves interaction of the electromagnetic field with the material, heat transfer, and mechanical deformation, each of which is coupled with both of the others, and all of which occur on different time scales. In this work, we present an original comprehensive mathematical formulation that accounts for the chain of physical processes comprising microwave sintering in one- and two-dimensional scenarios. We develop models for simulating the coupled electromagnetic, thermal, and mechanical phenomena at their appropriate time and spatial scales, and in addition, we account for the temperature and density dependence of the full set of thermal and dielectric properties of the material undergoing sintering. The electromagnetic and temperature fields are approximated using finite difference methods, and the mechanical problem is solved using the Master Sintering Curve representation of the density kinetics, which gives a way of accounting for the effect of microscale transport on the macroscopic property of relative density. For constant-rate sintering trials, we use the exponential integral to compute the work of sintering, which reduces computation time. The presented algorithms are all implemented and shown in MATLAB and Python. Simulation of density and temperature evolution of the sintered sample shows processing times and shrinkage rates comparable to experimental results. This work lays a theoretical and computational foundation for modelling the general three-dimensional problem and computer-aided design of efficient sintering processes.


Worcester Polytechnic Institute

Degree Name



Mathematical Sciences

Project Type


Date Accepted





modeling, simulation, materials, ceramics, dielectrics, modelling, microwave, sintering